Things to Learn (Key words, Notation & Formulae)
|
|
- Elizabeth Baker
- 5 years ago
- Views:
Transcription
1 Things to Learn (Key words, Notation & Formulae) Key words: Percentage This means per 100 or out of 100 Equivalent Equivalent fractions, decimals and percentages have the same value. Example words Rise, inflate, added, growth, more, extra, up, etc. for Increase Example words for Decrease Fall, drop, decline, reduction, discount, cut, deflate, shrink, less, down, decay, etc Key skills: Percentage of amounts E.g. Find 10% of 340 You could spot that 10% is 1 10 so finding 10% is equivalent to finding 1 10 of something. To find 1 we divide by 10 so the answer is E.g. Find 15% of 420 You could find 10% or 1 as seen above 10 then use this to find 5% by halving the amount and add them to make 15%. 10% = 42 so 5% = 21 15% = = 63 You could spot that 15% is 3 and then 20 calculate = 63 1 You could spot that 15% is 3 20 so you could divide by 20 then multiply by = = 63 There are always many ways of getting to a particular percentage. You simply have to be confident finding key values like 1%, 2%, 5%, 10%, 20%, 25%, 50% and 75% and you can build up percentages from those. Strong fraction and FDP skills also help a lot with quicker methods! E.g. Find 17.5% of 225 A useful calculator skill for more complex numbers is to type in either of the following: 17.5% = as normal decimal so or alternatively, newer calculators have a % button = so % = (or to nearest penny)
2 Expressing one number as a percentage of another E.g. A score of 3 marks out of 10 on a test as a % You could use equivalent fractions to find 3 10 = = 30% For nice denominators which convert into 100 easily this is a good method. E.g. A score of 5 out of 9 on a test as a % You could calculate the division 3 10 = 0.3 Then multiply by = 30% You could spot or know that 1 = = 0. 5 (0.555 ) = % As a calculator method you can type in = % or % This method work is equivalent to calculating = 30% 1 10 This example has no easy equivalent fraction which converts to 100 so we must use either fraction knowledge or a calculator method. Increasing or decreasing an amount by a percentage E.g. Tom s savings One method is to find the 2% amount of 500 increase (using the above methods) and then add by 2% in one it on. year, how much 2% of 500 does he have = 10 after one year? = 510 A calculator method to find a 2% increase is to add that 2% onto the whole starting amount, which is 100%. 102% = 1.02 as a decimal so or % will calculate an answer of 510 as well E.g. A shop is having a sale of 20% off. A T-shirt originally costs 22, what is the sale price? One method is to find the 20% amount (using the above methods) and then subtract it off. 20% of = Is the same as = = A calculator method to find a 20% decrease is to subtract 20% from the whole starting amount, which is 100%. 80% = 0.8 as a decimal so or 22 80% will calculate an answer of as well
3 Section 1. Finding a percentage of an amount: 1) Easy questions (non-calculator): a) Find 10% of 20 b) Find 20% of 45 c) Find 15% of 60 d) Find 35% of 80 e) Find 75% of 120 f) Find 150% of 40 g) Find 200% of 27 2) Harder questions (non-calculator): a) Find 7.5% of 40 b) Find 17.5% of 60 c) Find 12.5% of 88 d) Find 87.5% of 56 e) Find 48% of 200 f) Find 89% of 300 3) Calculator questions: a) Find 1.2% of 155
4 b) Find 3.4% of 120,000 c) Find 0.01% of 30,500 Section 2. Expressing one number as a percentage of another: 1) Express the shaded part of each diagram as a percentage of the whole. a) b) c) d) 2) Answer the following percentage questions: a) What is 7 out of 10 as a percentage? b) What is 11 out of 20 as a percentage? c) What is 24 out of 75 as a percentage? d) What is 3 out of 8 as a percentage? e) What is 124 out of 200 as a percentage? f) What is 4 out of 11 as a percentage? (hint: there is a nice pattern to elevenths) 3) Answer the following worded percentage problems: a) A crisp packet weighing 25g contains 7g of fat. What percentage is this?
5 b) Joey scores 37 out of 40 in a French test. What percentage is this? c) On Monday, 3 of my class of 29 students were late for school. What percentage were on time? (Calculator question) Section 3. Increasing or decreasing an amount by a percentage: 1) Increase by a percentage questions (non-calculator): a) Increase 40 by 10% b) Increase 50 by 20% c) Increase 4 by 50% d) Increase 16 by 75% e) Increase 95 by 100% f) Increase 15 by 200% g) Increase 200 by 2% h) Increase 124 by 17.5% (calculator question) 2) Decrease by a percentage questions: a) Decrease 50 by 30% b) Decrease 60 by 15% c) Decrease 200 by 80% d) Decrease 24 by 75% e) Decrease 1,234,567,890 by 100% f) Decrease 405 by 1.3% (calculator question) 3) Worded percentage change questions: a) Sarah s salary is a year. She receives a pay rise of 1%, what is her new salary?
6 b) A car is worth and depreciates in value by 12% in a year. What is the value of the car next year?
7 Section 1. Finding a percentage of an amount: 1) Easy questions (non-calculator): a) Find 10% of 20 You should be able to recognise that 10% means divide the amount by ten, since 10% And multiplying by 1/10 is the same as dividing by 10. So: 10% of 20 = = = 2 b) Find 20% of 45 Like the above, you should be able to see that 20% means divide the amount by five. So: 20% of 45 = = 45 5 = 9 c) Find 15% of 60 A bit trickier than the first two. For cases like this, it s always easier to convert to a fraction. 15% % of 60 = = = = 9 You might be able to see you can cross-cancel, which makes it easier to multiply numbers together, so in the last example: = = = 9 d) Find 35% of 80 We ll use the same method as before, but using cross-cancelling to make the multiplication easier. e) Find 75% of % % of 80 = = = = 28 75% % of 120 = = = = 90
8 f) Find 150% of 40 If the percentage is greater than 100, then our answer will increase. We can still use the same method as before! 150% = = % of 40 = = = = 60 g) Find 200% of 27 You should be able to see that 200% of an amount means twice that amount (follow through the similar steps as before if you re unsure). So: 200% of 27 = 2 27 = 54 2) Harder questions (non-calculator): a) Find 7.5% of 40 These questions are harder, but the method is exactly the same as before: 7.5% % of 40 = = = = 3 Another way is to find easier percentages and add them together, so 10% of 40 = 4 You should be able to see that 5% of 40 is half of that amount, so 5% of 40 = 2, and 2.5% of 40 is half of that, so 2.5% of 40 = 1. Now we can write 7.5% of 40 = (5% of 40) + (2.5% of 40) = = 3 b) Find 17.5% of 60 You can use either method for this calculation, so either: 17.5% = = % of 60 = = = = 21 2 (or 10.5) Or: 10% of 60 = 6, so 5% of 60 = 3, and 2.5% of 60 = % of 60 = (10% of 60) + (5% of 60) + (2.5% of 60) = = 10.5
9 c) Find 12.5% of 88 Again, you can use either method. So: 12.5% (It is useful to remember that 12.5% 1/8) 12.5% of 88 = = = = 11 Or: 10% of 88 = 8.8, so 5% of 88 = 4.4, and 2.5% of 88 = % of 88 = (10% of 88) + (2.5% of 88) = = 11 d) Find 87.5% of 56 Again, you can use either method. So: 87.5% (It is useful to remember that 87.5% 7/8) 87.5% of 56 = = = = 49 Or: 50% of 56 = 28, so 25% of 56 = 14, and 12.5% of 56 = % of 56 = (50% of 56) + (25% of 56) + (12.5% of 56) = = 49 e) Find 48% of 200 Again, you can use either method, so either: 48% % of 200 = = = = 96 Sometimes, it can be helpful to not convert the percentage into a fraction in its simplest form. In that last example, if we write 48% 48/100, then the calculation becomes = = = 96
10 For the other method, it s slightly different. Rather than adding percentages of amounts together, we can also subtract percentages of amounts. So: 50% of 200 = 100, and 1% of 200 = 2, so 2% of 200 = 4 48% of 200 = (50% of 200) (2% of 200) = = 96 f) Find 89% of 300 As before, the first method always works, so: 89% % of 300 = = = = 267 For the second method, we can use something similar to what we did with the previous question, but take it one step further. If you want to calculate a large percentage of something, you can calculate the percentage of the whole that you don t want, and subtract it from the whole. We can write that as: 10% of 300 = 30, and 1% of 300 = 3, so 89% of 300 = 100% of % of % of 300 = (10% of 300) + (1% of 300) = = 33 89% of 300 = (100% of 300) (11% of 300) = = 267 3) Calculator questions: a) Find 1.2% of 155 When using a calculator, you can either convert the percentage into a fraction (as we ve done before): 1.2% % of 155 = = Or you can in your calculator (if it s modern enough!): % = To work out the answer, which is 1.86
11 b) Find 3.4% of 120,000 Using either method: c) Find 0.01% of 30,500 Using either method: 3.4% of 120,000 = ,000 = % of 30,500 = 1 30,500 = Section 2. Expressing one number as a percentage of another: 1) Express the shaded part of each diagram as a percentage of the whole. a) b) c) d) a) There are 5 5 squares in total, which is 25 squares. 6 of the squares are shaded, so as a fraction, the shaded amount is 6/25. To express this as a percentage, you want to make the denominator = 4, so the shaded region as a percentage is: = = 24% b) There are 8 squares in total, and 3 of them are shaded, so the fraction of shaded squares is 3/ = 12.5, so the shaded region as a percentage is: = = 37.5% c) There are 9 squares in total, and 4 of them are shaded, so the fraction of shaded squares is 4/ = 11. 1, so the shaded region as a percentage is: = = % d) There are 25 squares in total, and 1 of them is shaded, so the fraction of shaded squares is 1/ = 4, so the shaded region as a percentage is: = = 4%
12 2) Answer the following percentage questions: a) What is 7 out of 10 as a percentage? We can use the same method as before: convert to a fraction out of 100, and that is the percentage = 10, so: 7 10 = = = 70% b) What is 11 out of 20 as a percentage? = 5, so: = = = 55% c) What is 24 out of 75 as a percentage? Some questions are a lot easier if you put the fraction in its simplest form first! = = 8 25 Now we do as before = 4, so: 8 25 = = = 32% d) What is 3 out of 8 as a percentage? = 12.5, so: 3 8 = = = 37.5% e) What is 124 out of 200 as a percentage? Again, try to simplify the fraction a bit first, and the question becomes easier! = = = 62% f) What is 4 out of 11 as a percentage? (hint: there is a nice pattern to elevenths) If we work out 1/11, we see there is a pattern of 0. 09, i.e. the pattern repeats forever as: = This means we can write 4/11 as: 4 11 = = = So as a percentage, we can write 4/11 as: 4 11 = = 100 = %
13 3) Answer the following worded percentage problems: a) A crisp packet weighing 25g contains 7g of fat. What percentage is this? First, write what the fraction of fat is: 7g fat out of 25g = = 4, so as a percentage: 7 25 = = = 28% b) Joey scores 37 out of 40 in a French test. What percentage is this? Again, we write what the fraction of marks Joey scored: 37 out of 40 = = 2.5 (you can show this by using long division!), so as a percentage: = (37 2) + (37 0.5) = = = = 92.5% c) On Monday, 3 of my class of 29 students were late for school. What percentage were on time? (Calculator question) If we put 3/29 into a calculator, we get We can write this as a percentage by multiplying the amount by 100, which means the percentage of late students is: = % (to 1 decimal place) Section 3. Increasing or decreasing an amount by a percentage: 1) Increase by a percentage questions (non-calculator): a) Increase 40 by 10% Start by finding 10% of 40, which is 4. An increase by 10% means we add this number to the whole, so: Increase 40 by 10% = 40 + (10% of 40) = = 44 Note that increasing something by 10% is the same as saying 110% of something, so in the previous example: 110% of 40 = = 40 = 40 = = = 44
14 b) Increase 50 by 20% 20% of 50 = 10, so an increase of 20% is: Increase 50 by 20% = 50 + (20% of 50) = = 60 c) Increase 4 by 50% 50% of 4 = 2, so an increase of 50% is: Increase 4 by 50% = 4 + (50% of 4) = = 6 d) Increase 16 by 75% So to find the new amount: 75% of = = = 12 Increase 16 by 75% = 16 + (75% of 16) = = 28 e) Increase 95 by 100% 100% of 95 = 95, so an increase of 100% is: Increase 95 by 100% = 95 + (100% of 95) = = 190 f) Increase 15 by 200% 200% of = 30, so: Increase 15 by 200% = 15 + (200% of 15) = = 45 g) Increase 200 by 2% 2% of 200 = = = = 4 Therefore: Increase 200 by 2% = (2% of 200) = = 204 h) Increase 124 by 17.5% (calculator question) The easy way to type this into a calculator is to realise that an increase by 17.5% is the same as 117.5% of the whole. So you would type in a calculator: which gives an answer of % =
15 2) Decrease by a percentage questions: a) Decrease 50 by 30% The method for these questions is the same as the previous ones, but this time a decrease by a percentage means you subtract that amount from the whole. So for this question: 30% of 50 = = = = 15 Therefore: Decrease 50 by 30% = 50 (30% of 50) = = 35 b) Decrease 60 by 15% 15% of 60 (10% of 60) + (5% of 60) = = 9 Therefore: Decrease 60 by 15% = 60 (15% of 60) = 60 9 = 51 c) Decrease 200 by 80% 80% of 200 = = = = 160 Therefore: Decrease 200 by 80% = 200 (80% of 200) = = 40 d) Decrease 24 by 75% 75% of 24 = = = = 18 Therefore: Decrease 24 by 75% = 24 (75% of 24) = = 6 e) Decrease 1,234,567,890 by 100% Decreasing the whole of something by 100% means you are subtracting the whole from the whole, so the answer is 0 f) Decrease 405 by 1.3% (calculator question) A decrease of something by 1.3% is the same as saying 98.7% of something. We can put this in a calculator as: % = which gives an answer of
16 3) Worded percentage change questions: a) Sarah s salary is a year. She receives a pay rise of 1%, what is her new salary? A pay rise of 1% means her salary has increased by 1%. 1% of = = = = Therefore: A pay rise of 1% on = (1% of 24000) = = b) A car is worth and depreciates in value by 12% in a year. What is the value of the car next year? Depreciates by 12% means the value has decreased by % of = = = = = 1680 Therefore: A depreciation of 12% = (12% of 14000) = = 12320
Help with fractions, percentages and decimals! 1 Numerator 2 Denominator
Help with fractions, percentages and decimals! 1 Numerator 2 Denominator Finding a fraction of an amount To find a fraction of an amount we divide the number by the denominator and then multiply our answer
More informationNumeracy Worksheet Name... Percentages
What's a Percentage? The symbol for percent is %. are out of 100. That means the whole thing (or the whole lot) equals 100%, and 20% means 20 parts out of 100. 1 cat is 100% cat.. 50% = 50 parts out of
More informationFoundation tier unit 4a check in test. Non-calculator. Q1. Three of these fractions are equivalent. Which is the odd one out? 6 8
Foundation tier unit a check in test Non-calculator Q1. Three of these fractions are equivalent. Which is the odd one out? 6 8 18 2 2 2 28 6 Q2. Helen scored 6 out of 50 possible points in a quiz. Write
More information5.06 Rationalizing Denominators
.0 Rationalizing Denominators There is a tradition in mathematics of eliminating the radicals from the denominators (or numerators) of fractions. The process is called rationalizing the denominator (or
More informationModule 6 Percent % Section 6.1 Understanding Percent. 1 of MAT001 MODULE 6 PERCENT. Denominators of 100
Module 6 Percent % Section 6.1 Understanding Percent CQ-6-01. Write 0.19% 19% 1900% 0.0019% 19 as a percent. P. 1 of 54 P. 4 of 54 Denominators of The word percent means per hundred. A percent is another
More informationFinance 197. Simple One-time Interest
Finance 197 Finance We have to work with money every day. While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for
More informationEqualities. Equalities
Equalities Working with Equalities There are no special rules to remember when working with equalities, except for two things: When you add, subtract, multiply, or divide, you must perform the same operation
More informationHere are the steps required for Adding and Subtracting Rational Expressions:
Here are the steps required for Adding and Subtracting Rational Expressions: Step 1: Factor the denominator of each fraction to help find the LCD. Step 3: Find the new numerator for each fraction. To find
More information1. FRACTIONAL AND DECIMAL EQUIVALENTS OF PERCENTS
Percent 7. FRACTIONAL AND DECIMAL EQUIVALENTS OF PERCENTS Percent means out of 00. If you understand this concept, it then becomes very easy to change a percent to an equivalent decimal or fraction. %
More informationExamples of Strategies
Examples of Strategies Grade Essential Mathematics (40S) S Begin adding from the left When you do additions using paper and pencil, you usually start from the right and work toward the left. To do additions
More informationPre-Algebra, Unit 7: Percents Notes
Pre-Algebra, Unit 7: Percents Notes Percents are special fractions whose denominators are 100. The number in front of the percent symbol (%) is the numerator. The denominator is not written, but understood
More informationCHAPTER 7: RELATING FRACTIONS, DECIMALS, AND PERCENTS
CHAPTER 7: RELATING FRACTIONS, DECIMALS, AND PERCENTS 7. CONVERTING FRACTIONS TO DECIMALS P. -3 7. CONVERTING DECIMALS TO FRACTIONS P. 4-5 7.3 CONVERTING DECIMALS AND PERCENTS P. 6-7 7.4 CONVERSIONS REVIEW
More informationAdding and Subtracting Fractions
Adding and Subtracting Fractions Adding Fractions with Like Denominators In order to add fractions the denominators must be the same If the denominators of the fractions are the same we follow these two
More information100 3 e.g. to a percentage becomes
PERCENTAGES Percentage (written %) means "out of one hundred" i.e. % means "twelve out of a hundred" or 00 50 50% means "50 out of a hundred" or 00 Fractions and decimals can easily be changed into percentages
More information4 Percentages Chapter notes
4 Percentages Chapter notes GCSE Specification concepts and skills Find a percentage of a quantity (N o): 4. Use percentages to solve problems (N m): 4., 4.2, 4., 4.4 Use percentages in real-life situations:
More information3.4.1 Convert Percents, Decimals, and Fractions
3.4.1 Convert Percents, Decimals, and Fractions Learning Objective(s) 1 Describe the meaning of percent. 2 Represent a number as a decimal, percent, and fraction. Introduction Three common formats for
More informationTOPIC SKILLS R A G. Expand Double Brackets Including brackets with 3 terms. Squaring Brackets (x + 8) 2. Amber/Red Go to. Page 8-10.
TOPIC SKILLS R A G Amber/Red Go to Expand Double Brackets Including brackets with 3 terms (x + 2)(x + 3) = x 2 + 2x + 3x + 6 = x 2 + 5x + 6 Page 8-10 (x + 2)(x 6) = x 2 + 2x 6x 12 = x 2 4x 12 (2x 8)(3x
More information6.1 Simple Interest page 243
page 242 6 Students learn about finance as it applies to their daily lives. Two of the most important types of financial decisions for many people involve either buying a house or saving for retirement.
More informationLearning Plan 3 Chapter 3
Learning Plan 3 Chapter 3 Questions 1 and 2 (page 82) To convert a decimal into a percent, you must move the decimal point two places to the right. 0.72 = 72% 5.46 = 546% 3.0842 = 308.42% Question 3 Write
More informationAdding & Subtracting Percents
Ch. 5 PERCENTS Percents can be defined in terms of a ratio or in terms of a fraction. Percent as a fraction a percent is a special fraction whose denominator is. Percent as a ratio a comparison between
More informationFinding the Sum of Consecutive Terms of a Sequence
Mathematics 451 Finding the Sum of Consecutive Terms of a Sequence In a previous handout we saw that an arithmetic sequence starts with an initial term b, and then each term is obtained by adding a common
More informationCollege Prep Mathematics Mrs. Barnett
College Prep Mathematics Mrs. Barnett 3-1 Percent and Number Equivalents Goals: Write any number as a percent equivalent Write any percent as a numerical equivalent Writing numbers as percents Remember
More informationYear 6 Spring Term Week 3 to 4 Number: Percentages
1 Fractions to percentages Equivalent FDP Order FDP Percentage of an amount (1) Percentage of an amount (2) Percentages missing values Solve problems involving the calculation of percentages [for example,
More informationThe word gives a strong clue to its meaning. Per means out of and Cent means 100 so percentages are numbers out of 100 or 100
Numeracy Introduction to percentages Percentages are commonly used in everyday language to express fractional numbers as whole numbers mostly between zero and one hundred which is the range of numbers
More informationPercents. Writing percents as decimals. How to change a percent to a decimal.
Percents Introduction: Percent (%) means per hundred or hundredths. When you read in the newspaper that 80% of the voters voted, it means that 80 out of 100 eligible citizens voted. A percent can be considered
More informationtroduction to Algebra
Chapter Six Percent Percents, Decimals, and Fractions Understanding Percent The word percent comes from the Latin phrase per centum,, which means per 100. Percent means per one hundred. The % symbol is
More informationNumeracy Booklet A guide for pupils, parents and staff
Numeracy Booklet A guide for pupils, parents and staff The aim of this booklet is to ensure that there is a consistent approach throughout the academy and at home on basic mathematical concepts Place Value
More informationChapter 6 Confidence Intervals
Chapter 6 Confidence Intervals Section 6-1 Confidence Intervals for the Mean (Large Samples) VOCABULARY: Point Estimate A value for a parameter. The most point estimate of the population parameter is the
More informationLeith Academy. Numeracy Booklet Pupil Version. A guide for S1 and S2 pupils, parents and staff
Leith Academy Numeracy Booklet Pupil Version A guide for S1 and S2 pupils, parents and staff Introduction What is the purpose of the booklet? This booklet has been produced to give guidance to pupils and
More informationIntroduction. What exactly is the statement of cash flows? Composing the statement
Introduction The course about the statement of cash flows (also statement hereinafter to keep the text simple) is aiming to help you in preparing one of the apparently most complicated statements. Most
More informationPercent: Slide 1 / 194. Slide 2 / 194. Slide 4 / 194. Slide 3 / 194. Slide 6 / 194. Slide 5 / 194. Table of Contents. Ratios as Percents
Slide 1 / 194 Percents Slide 2 / 194 Table of Contents Ratios as Percents Decimals as Percents Percents as Decimals Fractions as Percents Percents as Fractions Fractional Parts and Equivalent Names Relating
More informationBridging Units: Resource Pocket 8
Bridging Units: Resource Pocket 8 Growth and Decay Students may be familiar with the concepts of growth and decay from science lessons. This is a natural progression from the work in resource pocket 1
More informationMENTAL CALCULATION. 1. RE-ARRANGING When trying to add a row of numbers, we should look for pairs that add up to make a multiple of 10 or 100
MENTAL CALCULATION 1. RE-ARRANGING When trying to add a row of numbers, we should look for pairs that add up to make a multiple of 10 or 100 e.e. 13 + 8 + 7 + 6 + 2 13 + 8 + 7 + 6 + 2 20 10 2. UNITS, 20
More informationANSWERS CALCULATOR TEST Write down all the steps and calculations you make (even if it s on the calculator). Don t round until the end!
ANSWERS CALCULATOR TEST Write down all the steps and calculations you make (even if it s on the calculator). Don t round until the end! 1. After an 8% pay rise, Mr Brown s salary was 15714. What was his
More information1 / * / * / * / * / * The mean winnings are $1.80
DISCRETE vs. CONTINUOUS BASIC DEFINITION Continuous = things you measure Discrete = things you count OFFICIAL DEFINITION Continuous data can take on any value including fractions and decimals You can zoom
More informationConversions Review. 1. Convert the following Percent s to Decimals. a. 50% = f. 65% = b. 25% = g. 150% = h. 86% = c. 5% = i. 60% = d. 9% = j.
Conversions Review Name: Date: 1. Convert the following Percent s to Decimals Move the decimal two places to the LEFT. When there is no decimal in the number, it would be at the end of the number. a. 50%
More informationArithmetic. Mathematics Help Sheet. The University of Sydney Business School
Arithmetic Mathematics Help Sheet The University of Sydney Business School Common Arithmetic Symbols is not equal to is approximately equal to is identically equal to infinity, which is a non-finite number
More informationMath League SCASD. Meet #2. Self-study Packet
Math League SCASD Meet #2 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and complements 3. Number Theory:
More informationAnalysis of Financial Statements
HOSP 2110 (Management Acct) Learning Centre Analysis of Financial Statements PURPOSE: The goal of financial analysis is to predict the future performance of a business based on its past performance. The
More information12.3 Geometric Series
Name Class Date 12.3 Geometric Series Essential Question: How do you find the sum of a finite geometric series? Explore 1 Investigating a Geometric Series A series is the expression formed by adding the
More information3 Ways to Write Ratios
RATIO & PROPORTION Sec 1. Defining Ratio & Proportion A RATIO is a comparison between two quantities. We use ratios everyday; one Pepsi costs 50 cents describes a ratio. On a map, the legend might tell
More informationUnderstanding and Using Percentages
Percentages Understanding and Using Percentages If you haven t done maths for a while, it might be best for you to start with Fractions 4. Fractions, Decimals, and Percentages. WHAT ARE THEY? Percentages
More information5.6 Special Products of Polynomials
5.6 Special Products of Polynomials Learning Objectives Find the square of a binomial Find the product of binomials using sum and difference formula Solve problems using special products of polynomials
More informationNot for sale or distribution
TALK.9 Fractions, Decimals, and Percentages In this section you will convert between fractions, decimals, and percentages, and work with recurring decimals. Exercise.9 Warm Up Moza says, The numbers,.0
More informationLesson 5.5 and 5.6. Changing Fractions to Decimals and Decimals to Fractions
Lesson 5.5 and 5.6 Name: Changing Fractions or Decimals to Percents 1) Key in the fraction or decimal. 2) Hit the 2 nd key, then the % key, then enter. Changing Fractions to Decimals and Decimals to Fractions
More informationREVIEW PROBLEMS FOR NUMERICAL SKILLS ASSESSMENT TEST-Rev 1 (Note: No calculators are allowed at the time of the test.)
- - REVIEW PROBLEMS FOR NUMERICAL SKILLS ASSESSMENT TEST-Rev (Note: No calculators are allowed at the time of the test.). 9 + 67 =. 97 7 =. 7 X 6 =. 6 7 =. = 6. 6 7 7. Anne saves $7 every month out of
More informationFractions, Decimals, and Percents
Fractions, Decimals, and Percents Focus on After this lesson, you will be able to... convert between fractions, decimals, and percents Sports commentators often use statistics to report on the performance
More informationFACTORISING EQUATIONS
STRIVE FOR EXCELLENCE TUTORING www.striveforexcellence.com.au Factorising expressions with 2 terms FACTORISING EQUATIONS There are only 2 ways of factorising a quadratic with two terms: 1. Look for something
More informationBuild your skills for managing your money
Choosing your mortgage Part 1 This task has three parts to it. Part 1 This is where you will find information and activities to help you understand your mortgage payments and feel more confident to make
More informationReteaching. Ratios. For every 6 boys in the class, there are 5 girls in the class. Write each ratio in two other ways.
- Ratios on a Tape Diagram: The tape diagram shows the ratio of boys to girls in a swimming class. How can you describe the ratio of boys to girls? Boys Girls For every 6 boys in the class, there are girls
More informationSimple and Compound Interest
Chp 11/24/08 5:00 PM Page 171 Simple and Compound Interest Interest is the fee paid for borrowed money. We receive interest when we let others use our money (for example, by depositing money in a savings
More information6, 6 to 8 8. , 3 : 1, or 3 to 1 1
- Ratios on a Tape Diagram: The tape diagram shows the ratio of boys to girls in a swimming class. How can you describe the ratio of boys to girls? Boys Girls For every 6 boys in the class, there are girls
More informationEstimating and Calculating Percents in Money
Estimating and Calculating Percents in Money Examples Canada has a 7% General Sales/Service Tax (GST) on most items. Many provinces have an additional Provincial Sales Tax (PST) that is added to the cost
More informationText transcription of Chapter 5 Measuring a Nation s Income
Text transcription of Chapter 5 Measuring a Nation s Income Welcome to the Chapter 5 Lecture on the Measuring a Nation s Income. We are going to start working with statistics to measure the size of economies
More information(x + 2)(x + 3) + (x + 2)(x + 3) 5(x + 3) (x + 2)(x + 3) + x(x + 2) 5x + 15 (x + 2)(x + 3) + x 2 + 2x. 5x x 2 + 2x. x 2 + 7x + 15 x 2 + 5x + 6
Which is correct? Alex s add the numerators and the denominators way 5 x + 2 + x Morgan s find a common denominator way 5 x + 2 + x 5 x + 2 + x I added the numerator plus the numerator and the denominator
More informationSince his score is positive, he s above average. Since his score is not close to zero, his score is unusual.
Chapter 06: The Standard Deviation as a Ruler and the Normal Model This is the worst chapter title ever! This chapter is about the most important random variable distribution of them all the normal distribution.
More informationChapter 5 Financial Maths
Chapter 5 Financial Maths (Usually Q1/Q2 Paper 1) This revision guide covers Ordinary level notes Miss McDonnell 1 o Ratio and proportions o Currency transactions o Converting between decimal, percent
More informationMA 1125 Lecture 05 - Measures of Spread. Wednesday, September 6, Objectives: Introduce variance, standard deviation, range.
MA 115 Lecture 05 - Measures of Spread Wednesday, September 6, 017 Objectives: Introduce variance, standard deviation, range. 1. Measures of Spread In Lecture 04, we looked at several measures of central
More informationPERCENT. Ex. 2: If you used 50 out of 200 postcard stamps, then you used 25% of your stamps.
Percent PERCENT Percent is an important mathematical topic. It is used frequently in real life situations, particularly in business when working with discounts, interest, commission and changes in price.
More informationPersonal tax interactive worksheet. Calculating car and fuel benefits in kind
Rachel Powell AAT Student Personal tax interactive worksheet Calculating car and fuel benefits in kind The calculation of car and fuel benefits is an important skill for a tax professional and as such
More informationCOPYRIGHTED MATERIAL. Time Value of Money Toolbox CHAPTER 1 INTRODUCTION CASH FLOWS
E1C01 12/08/2009 Page 1 CHAPTER 1 Time Value of Money Toolbox INTRODUCTION One of the most important tools used in corporate finance is present value mathematics. These techniques are used to evaluate
More informationWe can use fractions to describe things that have been broken into equal parts, for example:
Fractions Fractions describe parts of a whole. Part Whole The top of the fraction is called the numerator, and the bottom of the fraction is called the denominator. The numerator refers to a section of
More information3 Ways to Write Ratios
RATIO & PROPORTION Sec 1. Defining Ratio & Proportion A RATIO is a comparison between two quantities. We use ratios every day; one Pepsi costs 50 cents describes a ratio. On a map, the legend might tell
More informationACCUPLACER Elementary Algebra Assessment Preparation Guide
ACCUPLACER Elementary Algebra Assessment Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre
More informationEdexcel past paper questions
Edexcel past paper questions Statistics 1 Chapters 2-4 (Discrete) Statistics 1 Chapters 2-4 (Discrete) Page 1 Stem and leaf diagram Stem-and-leaf diagrams are used to represent data in its original form.
More informationInterest Rates. Countrywide Building Society. Saving Data Sheet. Gross (% per annum)
Interest Rates Gross (% per annum) Countrywide Building Society This is the rate of simple interest earned in a year (before deducting tax). Dividing by 12 gives a good estimate of the monthly rate of
More informationARITHMETIC CLAST MATHEMATICS COMPETENCIES. Solve real-world problems which do not require the use of variables and do
ARITHMETIC CLAST MATHEMATICS COMPETENCIES IAa IAb: IA2a: IA2b: IA3: IA4: IIA: IIA2: IIA3: IIA4: IIA5: IIIA: IVA: IVA2: IVA3: Add and subtract rational numbers Multiply and divide rational numbers Add and
More informationYear 8 Term 1 Math Homework
Yimin Math Centre Year 8 Term Math Homework Student Name: Grade: Date: Score: Table of contents Year 8 Term Week Homework. Topic Percentages.................................... The Meaning of Percentages.............................2
More informationDATA HANDLING Five-Number Summary
DATA HANDLING Five-Number Summary The five-number summary consists of the minimum and maximum values, the median, and the upper and lower quartiles. The minimum and the maximum are the smallest and greatest
More informationUnit 8 - Math Review. Section 8: Real Estate Math Review. Reading Assignments (please note which version of the text you are using)
Unit 8 - Math Review Unit Outline Using a Simple Calculator Math Refresher Fractions, Decimals, and Percentages Percentage Problems Commission Problems Loan Problems Straight-Line Appreciation/Depreciation
More information4: Single Cash Flows and Equivalence
4.1 Single Cash Flows and Equivalence Basic Concepts 28 4: Single Cash Flows and Equivalence This chapter explains basic concepts of project economics by examining single cash flows. This means that each
More informationProbability Notes: Binomial Probabilities
Probability Notes: Binomial Probabilities A Binomial Probability is a type of discrete probability with only two outcomes (tea or coffee, win or lose, have disease or don t have disease). The category
More information6.1 Introduction to Percents and Conversions to Fractions and Decimals
CHAPTER 6: PERCENTS CHAPTER 6 CONTENTS 6.1 Introduction to Percents 6.2 Solve Percent Problems 6.3 Application Problems 6.4 Financial Literacy 6.5 Circle Graphs 6.1 Introduction to Percents and Conversions
More informationUnit 3: Rational Numbers
Math 9 Unit 3: Rational Numbers Oct 9 9:04 AM 3.1 What is a Rational Number? Any number that can be written in the form m n, where m and n are integers and n = 0. In other words, any number that can be
More informationChapter 2 Algebra Part 1
Chapter 2 Algebra Part 1 Section 2.1 Expansion (Revision) In Mathematics EXPANSION really means MULTIPLY. For example 3(2x + 4) can be expanded by multiplying them out. Remember: There is an invisible
More informationAdjusting Nominal Values to
Adjusting Nominal Values to Real Values By: OpenStaxCollege When examining economic statistics, there is a crucial distinction worth emphasizing. The distinction is between nominal and real measurements,
More informationWeek 19 Algebra 2 Assignment:
Week 9 Algebra Assignment: Day : pp. 66-67 #- odd, omit #, 7 Day : pp. 66-67 #- even, omit #8 Day : pp. 7-7 #- odd Day 4: pp. 7-7 #-4 even Day : pp. 77-79 #- odd, 7 Notes on Assignment: Pages 66-67: General
More informationPark Forest Math Team. Meet #2. Self-study Packet
Park Forest Math Team Meet #2 Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and complements 3. Number
More informationSandringham School Sixth Form. AS Maths. Bridging the gap
Sandringham School Sixth Form AS Maths Bridging the gap Section 1 - Factorising be able to factorise simple expressions be able to factorise quadratics The expression 4x + 8 can be written in factor form,
More informationPercents, Explained By Mr. Peralta and the Class of 622 and 623
Percents, Eplained By Mr. Peralta and the Class of 622 and 623 Table of Contents Section 1 Finding the New Amount if You Start With the Original Amount Section 2 Finding the Original Amount if You Start
More informationN5 A1.3 Fractions and Percentages - Revision
N A. Fractions and Percentages - Revision This revision pack covers the skills at Unit Assessment and exam level f Fractions and Percentages so you can evaluate your learning of this outcome. It is imptant
More informationBusiness Calculus Chapter Zero
Business Calculus Chapter Zero Are you a little rusty since coming back from your semi-long math break? Even worst have you forgotten all you learned from your previous Algebra course? If so, you are so
More informationChapter 7 BUILD YOUR VOCABULARY
C H A P T E R 7 BUILD YOUR VOCABULARY This is an alphabetical list of new vocabulary terms you will learn in Chapter 7. As you complete the study notes for the chapter, you will see Build Your Vocabulary
More information3 Ways to Write Ratios
RATIO & PROPORTION Sec 1. Defining Ratio & Proportion A RATIO is a comparison between two quantities. We use ratios every day; one Pepsi costs 50 cents describes a ratio. On a map, the legend might tell
More informationMA 1125 Lecture 12 - Mean and Standard Deviation for the Binomial Distribution. Objectives: Mean and standard deviation for the binomial distribution.
MA 5 Lecture - Mean and Standard Deviation for the Binomial Distribution Friday, September 9, 07 Objectives: Mean and standard deviation for the binomial distribution.. Mean and Standard Deviation of the
More informationPERCENTAGES M.K. HOME TUITION. Mathematics Revision Guides Level: GCSE Higher Tier
Mathematics Revision Guides Percentages Page 1 of 17 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier PERCENTAGES Version: 2.3 Date: 01-02-2014 Mathematics Revision Guides Percentages
More informationProject: The American Dream!
Project: The American Dream! The goal of Math 52 and 95 is to make mathematics real for you, the student. You will be graded on correctness, quality of work, and effort. You should put in the effort on
More informationCAHSEE on Target UC Davis, School and University Partnerships
UC Davis, School and University Partnerships CAHSEE on Target Mathematics Curriculum Published by The University of California, Davis, School/University Partnerships Program 2006 Director Sarah R. Martinez,
More informationMath 6 Unit 7 Notes: Proportional relationships
Math 6 Unit 7 Notes: Proportional relationships Objectives: (3.2) The student will translate written forms of fractions, decimals, and percents to numerical form. (5.1) The student will apply ratios in
More informationyou ll want to track how you re doing.
Investment Club Finances An Orientation for All Club Members For tonights topic, we re going to be discussing your club finances. It is very easy to do your club accounting using bivio but you need to
More informationAn Orientation to Investment Club Record Keeping
An Orientation to Investment Club Record Keeping Treasurer Training Orientation to Investment Club Accounting Monthly Treasurer Tasks Non Monthly Treasurer Tasks This presentation is part of a three part
More information1, are not real numbers.
SUBAREA I. NUMBER SENSE AND OPERATIONS Competency 000 Understand the structure of numeration systems and ways of representing numbers. A. Natural numbers--the counting numbers, 23,,,... B. Whole numbers--the
More informationMonthly Treasurers Tasks
As a club treasurer, you ll have certain tasks you ll be performing each month to keep your clubs financial records. In tonights presentation, we ll cover the basics of how you should perform these. Monthly
More informationEconS Utility. Eric Dunaway. Washington State University September 15, 2015
EconS 305 - Utility Eric Dunaway Washington State University eric.dunaway@wsu.edu September 15, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 10 September 15, 2015 1 / 38 Introduction Last time, we saw how
More information4.1 Write Linear Equations by Using a Tables of Values
4.1 Write Linear Equations by Using a Tables of Values Review: Write y = mx + b by finding the slope and y-intercept m = b = y = x + Every time x changes units, y changes units m = b = y = x + Every time
More informationChapter 9: Consumer Mathematics. To convert a percent to a fraction, drop %, use percent as numerator and 100 as denominator.
Chapter 9: Consumer Mathematics Definition: Percent To convert a percent to a decimal, drop % and move the decimal two places left. Examples: To convert a percent to a fraction, drop %, use percent as
More informationUNIT 4 VOCABULARY: FRACTIONS
º ESO Bilingüe Página UNIT VOCABULARY: FRACTIONS 0. Introduction A fraction is a number that expresses part of a unit or a part of a quantity. Fractions are written in the form b is not 0. a b where a
More informationWorking with Percents
Working with Percents Percent means parts per hundred or for every hundred Can write as 40 or.40 or 40% - fractions or decimals or percents 100 Converting and rewriting decimals, percents and fractions:
More informationChapter 12. Sequences and Series
Chapter 12 Sequences and Series Lesson 1: Sequences Lesson 2: Arithmetic Sequences Lesson 3: Geometry Sequences Lesson 4: Summation Notation Lesson 5: Arithmetic Series Lesson 6: Geometric Series Lesson
More informationLooking to invest in property? Getting smart when it comes to financing your property investment.
Looking to invest in property? Getting smart when it comes to financing your property investment. Is property the place to build your wealth? Australia is a country of homeowners. If we haven t already
More information