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 and.00 are equal. Is she correct? Explain. a Make 0 5. Find an equivalent fraction, using the fewest possible tiles. b You will need: fraction tiles 6 Make 0. Find an equivalent fraction, using the fewest possible tiles. Simplify these fractions: a b c d??? 8 0 =?? 8 =?? 0 5 =?? Imagine what each number would look like if you made it with decimal tiles. 6 00 =?? 4?? Word fact: Equivalent means the same size. 79
4 Copy and complete this table of equivalent fractions, decimals, and percentages. Fraction Decimal Percentage??? 0.5??? 75% 5?? You should know these from memory. If you don t, use fraction, decimal and percentage magnets to help you work them out. Then try to memorize them. 5 Write each of these mixed numbers as decimals: a b 4 c 5 d 4 Use your answers to Q4 to help you. Main Exercise 6 Copy and complete to write equivalent fractions with a denominator of 0: a b c d 5 =???? 0 5 =? 0 4 5 =? 0 =??? 7 Write each fraction in Q6 as a decimal. 0.5 0.5 50% 50% Word fact: A mixed number has a whole number part and a fraction part.? 0 80
8 Copy and complete to write equivalent fractions with a denominator of 00: a b c d 5 = 50 =?? 00 4 5 =? 00 7 0 =?? e??? 00 9 5 =??? 00 9 a Write each fraction in Q8 as a decimal.? 00 b Use a calculator to check your answers to part a. is the same as 5, so press: 5 0 Write each decimal as a fraction with a denominator of 0, 00 or 000: a 0.7 b 0.49 c 0.7 d 0. e 0.6 f 0.04 g 0. h 0.6 i 0.05 j 0.5 Simplify each fraction in Q0. Simplify in your head if possible, or draw an arrow diagram. 8
You need to be able to convert between any fractions, decimals and percentages. Where the numbers are tidy, you should convert by hand. Where the numbers are more difficult, you can use a calculator. There are two main strategies: To change between decimals and percentages, multiply / divide by 00. For example: a Convert 0.5 to a percentage. 0.5 00 = 5% b Convert 45% to a decimal. 45 00 =.45 To change between either a decimal or a percentage, and a fraction, use fractions with denominators of 0, 00, or 000. For example: a b c d??? 0 / 00 / 000 Decimals Convert 0 to a decimal. We need to make a denominator of 0, 00 or 000. 0 = 00 5 Now write this as a decimal. 5 hundredths = 0.5 Convert 9 50 to a percentage. We need to make a denominator of 00 (because percentages are out of 00). 9 50 = 00 8 Now write this as a percentage. 8 hundredths = 8% Convert 0.4 to a fraction. 0.4 is 4 tenths. We can write this as: Simplify the fraction (if possible). Convert % to a fraction. Fractions % is out of 00.We can write this as: Simplify the fraction (if possible). Percentages??? 0 / 00 / 000 Decimals Decimals 4 0 4 0 = 5 00 00 = 5 8 Fractions 00 00 Percentages Percentages Math fact: If you are converting to a percentage, remember to include the % sign in your answer. If you are converting to a decimal the answer will not have a % sign. 8
TALK a Find the three pairs of matching decimal and fraction cards, and write them in your notebook. 0 0.45 b Which fraction is left? Write a decimal to match this fraction. c Which decimal is left? Write a fraction to match this decimal. Here are some fractions: Write each fraction as: a an equivalent fraction with a denominator of 00. b a decimal c a percentage d Does it matter if you have a zero on the end of the decimal in part b? How does the zero help you write the percentage in part c? 4 Look at the fractions written as decimals in Q. Now compare these with the percentages in Q. a Explaining What do you do to change a decimal to a percentage? Use a decimal slider to help you explain. b Explaining What do you do to a percentage to change it to a decimal? Explain. 5 Here are some decimals: Write each decimal as: a a percentage. 6 Here are some percentages: Write each percentage as: 7 5 0.55 0.9 50 0 5 0 8 0 7 50 50 50 4 5 9 5 9 5 Write a decimal in the decimal slider. What do you need to do to get the percentage? 0. 0.8 0.6 0.75 0.465 0.05.8.65.5 Percent (%) means out of 00. So 00? =?%. slide 0 7 Multiply by 00. Use a decimal slider to help you. b a fraction or mixed number. Simplify if possible. 9% 8% 49% 6% % 9% 0%, 5% 75% 0.8 9 0 a a decimal b a fraction or mixed number. Simplify if possible. 8
TALK TALK 7 Here are some mixed numbers: Write each mixed number as: a a decimal b a percentage c What do you notice about all the percentages? Copy and complete this sentence: The percentages are all more than?, because mixed numbers and decimals are all more than?. 8 A sports coach tells his team to give 0%. What do you think this means? 9 a Write 5 as: i an equivalent fraction with a denominator of 00 ii a decimal iii a percentage b Use a calculator to work out 5. What do you notice? c Multiply your answer in part b by 00. What do you notice? 0 a Write each of these fractions as: i an equivalent fraction with a denominator of 00 ii a decimal 8 0 7 40 iii a percentage 6 5 9 50 Work out your answer mentally if possible. Otherwise, use a calculator. b Which denominators (bottom numbers) in fractions could you easily work with mentally? Write these fractions, decimals, and percentages from smallest to largest: 4 5 0. 75% 0.4 50% Which of these is smallest? 7 8 88% 0.8 0 5 0 9 4 7 7 0 5 4 5 5 0 7 50 The whole number part will go in the ones column. Change all of them to decimals to make it easier to compare. 84
TALK Which shape has the biggest area: the parallelogram or the triangle? Show your working. 4 a What fraction of an hour is 4 minutes? Simplify your fraction. b What percentage of an hour is 4 minutes? 5 Mira says,.5 hours is hours and 5 minutes. Laila says,.5 hours is hours and 5 minutes. Who is right? Explain. 6 This table shows students favorite sports: Football Tennis Cricket Other Number of students 0 6 a What fraction of students chose football? Simplify your fraction. b What percentage of students chose football? c What percentage of students chose tennis? d What percentage of students chose cricket? e What percentage of students chose another sport? f 0.68 m 5 8 m.5 is a decimal. What is this as a fraction? How many minutes in an hour? Use your answer to part a. How many students in total? Explaining How did you work out the answer to part e? Was there more than one way? 85
HANDS ON ACtiVITY 7 Gathering and Recording Information Work out the percentage of students in your class whose favorite sport is football. Example Faisal earns a salary of 0 000 AED. His salary is increased to 000 AED. Work out the percentage increase. Answer Step Work out the size of the increase. Increase is 000 0 000 = 000 Step Step Think how you will collect and record the information. You may use a calculator to help you work out the percentage. Write the increase as a fraction of the original salary. = 000 0 000 Make an equivalent fraction with a denominator of 00. = 000 0 000 = 00 0 Step 4 Write the fraction as a percentage. % increase = 0% 8 An airline was very successful in 04. In 05, it increased its staff s monthly salaries: Original salary in 04 New salary in 05 Pilot AED 50 000 AED 55 000 Co-pilot AED 40 000 AED 44 000 Cabin crew AED 8 000 AED 0 000 a Work out the size of the salary increase for each job title. b Who received the biggest actual increase? c Work out the percentage increase for each person s salary. Math fact: To find a percentage increase, we write the increase amount as a percentage of the original amount. Write the size of each increase as a fraction of the original salary in 04. Then change your fractions into percentages. 86
TALK TALK d Who received the biggest percentage increase? e Compare your answers to parts b and d. Are they the same? Explain. 9 The table shows the price a car salesman pays for some cars (cost price) and the price he sells them for (selling price). Cost price (AED) Selling price (AED) Jeep Wrangler 70 000 84 000 Mini Cooper 00 000 000 Range Rover 50 000 7 500 The profit on each car is the difference between the cost price and the selling price. a What is the profit in AED for each car? b For each car, work out the percentage profit. c Did the car with the greatest profit in AED give the greatest percentage profit? A recurring decimal does NOT end. The digits after the decimal point repeat forever. A dot is placed on top of the number that repeats to show that it is a recurring decimal. For example, these are recurring decimals: 0. means the is repeating: 0.....4 means the 4 is repeating:.444444... 0. 8 means the and the 8 are repeating: 0.88888... 9. 05 means is the first repeating number and 5 is the last repeating number: 9.050505... 0 In these recurring decimals, which digits are repeating? a 0. b 0. c 0. Look at these decimals: 0.5 0. 0. 0..6 0. 4 First, find the profit as a fraction of the cost price. a List the recurring decimals. b List the decimals that are not recurring. 87
TALK Write these recurring decimals using dots above the number or numbers that repeat. Place the dots carefully. a 0. b.4 c.4444 d 0.040404 The fraction 7 as a decimal is: 0.485748574857 Write this as a recurring decimal. 4 a Use a calculator to write as a decimal. i Write all the numbers from your calculator display. ii Write your answer using the dot above the recurring digit. b Explaining Why is your answer to part a a recurring decimal? Explain. c Write as a percentage to decimal places. 5 a Use a calculator to write as a decimal. Write all the numbers from your calculator display. b What do you notice about the last digit on your calculator display? still a recurring decimal? c Is Multiply your decimal by 00. Which numbers are repeating? Write your answer using the dot above the recurring digit. d Write as a percentage to decimal places. Math fact: Calculators round recurring decimals, so if the recurring digit is more than 5 the last digit on the calculator display will be rounded up, e.g. 0.8 would show as 0.8888888889 Multiply your decimal by 00. Don t forget to round up your last decimal place carefully. 88
THINK 6 a Use a calculator to work out 9 as a recurring decimal and a percentage to decimal places. b Use a calculator to work out 9 as a recurring decimal and a percentage to decimal places. c Identifying Patterns Predict 4 9 as a recurring decimal and percentage to decimal places. d Use a calculator to check your prediction for part c. 7 Look at these fraction, decimal, and percentage cards. A B C D E F G 66.67% ( d.p.) H I J K L M 5 0.67 a Which cards are equivalent? b Which card is the odd one out? 0.6 0% 0..% ( d.p.) c Explaining Look at card A. Why is it 66.67% and not 66.66%? 8 a Use a calculator to work out, and as recurring decimals. b Identifying Patterns What do you notice about your answers to part a? c Use your answer to part b to predict 4 and 5 as recurring decimals. Check on your calculator. 60% 0 0.6 0. Equivalent means they have the same value: = 9? ; = 9?... Which card does not match any of the others? 89
.0 Percentages In this section you will calculate the percentage of a quantity, including working with a percentage increase and a percentage decrease. Exercise.0 Warm Up Work out: a 0. b 0.5 c 0.5 Work out: a 5 b.5 c 80 0 d 0 0 e 00 00 f 65 0 Work out: a 5 00 b 45 00 c.5 00 d.5 00 4 In your notebook, write the percentage or fraction for each letter on this double number line. 5 Work out: Use a number line to help you: 0 B C D 0 0 a 50% of 0 cm c 75% of 80 fils 0 0. 0. 0. 0.4 0.5 0.6 0.7 0.8 0.9 b % of 4 kg Use a decimal slider to help you. 0% 0% A 5%.% 40% E F G 70% I 80% K 00% 6 Copy and complete these number sentences in your notebook. a 40% = 0%? b 5% = 0%? c % = 00%? d % = %? e 0.5% = %? 6 0 H 4 J 9 0 Use the double number line in Q4 to help you. 90
READ Not 7 Work out: a 0% of 80 g b 40% of 80 g c 5% of 80 g d % of 900 AED e % of 900 AED f 0.5% of 900 AED 8 Look at these patterns. Decide whether each one is increasing or decreasing. a 5, 0, 5, 0, 5,... b 4 C, C, 0 C, C, 4 C c Height (cm) 0 0 0 Main Exercise 0 9 Work out: a 5% of 80g b 45% of 80g Height of plant 4 5 Week c.5% of 900 AED 0 Huda and Laila are working out.5% of 00 AED. Huda s Method 0% = 0. To find 0% or 0 you can divide by 0. Use your answer to Q6a and Q7a. d 5% = 0% + 5%. Use your answers to Q7a and Q7c. Use your answers to Q7e and Q7f. for sale or Laila s Method Step Find %. Step Find 0%. Step Use % to find %. Step Use 0% to find 5%. Step Use % to find 0.5%. Step Use 5% to find.5%. Step 4 Add together answers in Step 4 Add together answers step and step. in step and step. 9
TALK Not a Follow Huda s method to work out the answer. b Follow Laila s method to work out the answer. c Do you get the same answer? Are both methods correct? d Making Decisions Whose method do you like best? Why? Is there any other method you can think of? Example Use a calculator to work out 7% of 850 AED. Answer Step Change 7% to a decimal. I know that 7% = 0.7 Step Of means multiply. Write the question as 0.7 850 Step Put this in the calculator. Step 4 Write the answer. 44.5 Step 5 Write the units. Remember you 44.50 AED need decimal places for money. a Use a calculator to work out: i 5% of 870 g iii.5% of 900 AED ii 45% of 80 g iv.5% of 00 AED b Explaining Explain to a friend how to work out a percentage of an amount using a calculator. Use a calculator to work out: a 8% of 0 m c 7% of 50 g b.5% of 650 AED d 0.5% of 750 AED Use a close and easy percentage to estimate: a % of 65 m c.8% of AED 500 b 47% of 40 km d Compare your estimates with a friend. Did you use the same close, easy percentages?.5% is 0.05 as a decimal. % is close to 0%. for sale or 4 a Use a calculator to work out the percentages in Qa c. Show your working. THINK b How do your estimates in Qa c help you to decide if your answers are correct? 9
5 Saif earns 5 000 AED per month. He donates 0.9% to charity. a Estimate how much he donates to charity. b Work out how much he donates to charity. 6 Three babies were born in a hospital on the same day. Each baby s body length was recorded when they were born. As they grow, their lengths are marked on number lines, showing their starting lengths as 00%. At birth, baby Hamdan measures 50 cm. 00% 50 cm a After month, his length had increased by 0%. Copy and complete this number line to show 0%: b Use your number line to show baby Hamdan s length now, like this: 0% 00% 0%? cm 50 cm? cm c At birth, baby Mansour measures 60 cm. Draw a number line to show his length. What whole number is 0.9% close to? Be careful working out 0.9 00. 0 0% 00%? cm 50 cm 0 00% + 0% = 0% 50 cm +? cm =? cm Show his starting length as 00%. d After month, Mansour s length increases by 5%. On your number line, show 5%. Show 0% first, to help you find 5%. 9
TALK READ e Use your number line to show Mansour s length now. Extend your number line to show 00% +?%. f At birth baby Rashid measures 40 cm, and this increases by 5% after month. Use the same method to show his length after month. 7 a Increase 00 g by 0%. b Increase 4 000 AED by 5%. c Increase 40 km by 5%. d Increase 450 kg by 0%. e Increase 60 cm by 5%. f Increase 70 500 AED by 5%. 8 a Work out: i.0 00 ii.05 4 000 iii.5 40 b Compare your answers with Q7a c. What do you notice? c What is an easy way to work out a percentage increase? Explain to a friend. 9 Match these increases (a c) to the percentages and calculations: Percentages: 06% 0.6% 6% a 400 AED increased by 6% b 400 AED increased by 6% c 400 AED increased by.6% Calculations:.6 400.06 400.06 400 0 Read this article and then answer the questions. Held each year in July, the Liwa Date Festival celebrates the role that the date palm plays in Emirati culture. The date competition is at the center of the festival. About 00 Emirati farms compete to win the title of Best Date Grower. Prizes are given away for the top dates in each category. The prizes keep getting bigger and better, with new competitions added each year, to encourage owners to improve the quality of their dates and their farms. In 0 the total value of all the prizes was 5 million AED, but this was increased by 0% in 04. Festival organizers visit all participating farms three times during the year, before awarding the prizes to the best entries at the Festival. a What was the total value of the prizes in 04? b Explaining Explain to a friend how you worked it out. Did you need to write all the zeros in 5 million? 94
Cost price is the original price a store pays for something. A store adds a charge to the cost price before selling. This is the profit the store makes. The Selling price is the final price we pay in the store after they have added their profit. Selling price = cost price + profit. A bicycle store pays a cost price of 500 AED for a bicycle. The store wants to make a 9% profit. a Estimate the profit amount using a close, easy percentage. Write down the easy calculation you use. b Use your answer to part a to estimate the selling price. c Work out the exact selling price. Was your estimate close? a Faisal earns 50 000 AED. His salary increases by 6%. What is his new salary? b Mansour earns 40 000 AED. His salary increases by 7%. What is his new salary? c Who had the biggest salary increase? Faisal or Mansour? a A car salesman buys Jeeps for 50 000 AED. He wants to make a profit of 8% on each Jeep. How much should he sell each Jeep for? b He decides to increase his profit to 4%. What will he now sell each Jeep for? 4 A price is decreased by 5%. The original price was 480 AED. We can show this on a number line as 00% 00% 480 AED a Copy and complete this b Use your number line to work out number line to show 5%: a decrease of 5%. 5%? AED? 00% 480 AED - 5% 5% 75% 00%? AED? AED - 5%? 480 AED 95
READ TALK 5 a Decrease 00 g by 0%. b Decrease 4 000 AED by 5%. c Decrease 40 km by 5%. d Decrease 450 kg by 0% e Decrease 60 cm by 5% f Decrease 70 500 AED by 5% 6 Huda and Laila are working out a 0% decrease of 00 AED. Huda s Method Laila s Method Step Draw a number line and mark Step 0% decrease means 00 AED as 00%. 00% 0%. Step Find 0% of 00 by dividing by Step Find 80% of 00 AED by 5 and mark it on the number line. first finding 0% then multiplying it by 8. Step Take the answer in step away from 00 AED. a Follow Huda s method to work out the answer. b Follow Laila s method to work out the answer. c Do you get the same answer? Are both methods correct? d Making Decisions Whose method do you like best? Why? Is there any other method you can think of? 7 a Decrease: i 80 by 5% ii 60 by 0% iii 40 by 0% You can use Huda s method or Laila s method. b Explaining Explain to a friend how to work out a percentage decrease. c Use a calculator to check your answers to part a. 75% of 480 =... G8-8-N.0-5 -calculator keys Use a number line like those in Q4.... 96
TALK HANDS ON 8 Match these decreases (a c) to the percentages and calculations: Percentages: 96% 98.6% 86% a 00 g decreased by 4% b 00 g decreased by 4% c 00 g decreased by.4% 9 Suhail was paying a monthly charge of 5 AED for his mobile phone. He changed his deal so his monthly charge was reduced by 6%. a Estimate the new monthly charge. Show your working. You can use a number line to help you. What easy percentage is close to 6%? b Compare your estimate with your friends. Did you estimate in the same way? c Work out the monthly charge. 0 Decide if these statements are true or false: Calculations: 0.96 00 g 0.86 00 g 0.986 00 g a To increase an amount by 0%, we can multiply it by.0. b To increase an amount by 5%, we can just divide it by 4. c To increase an amount by %, we can multiply it by.. d To decrease an amount by 5% we can multiply it by.05. e To decrease an amount by 0% we can multiply by 0.75. You will need: blank cubes whiteboard marker Word fact: Reduced means the same as decreased. ACtiVITY 97
Work in pairs or small groups. On the faces of one cube write an amount on each face (e.g. 500 kg, 50 AED, 0 cm...etc). On the faces of the second cube write a percentage increase or decrease (e.g. +0%, 0%...etc). Take turns rolling the two cubes, and working out the calculation that shows up. Score one point for each correct answer. Mansour says, If prices are reduced by 40% in a sale, that means that the sale price is 60% of the original price. Is he correct? Explain. Example Eman buys a new mobile phone. It is on sale, reduced by 5%. She pays 90 AED for the phone. Work out the normal selling price of the phone if it is not on sale. Answer Step Work out what percentage of the Eman paid 75% of the normal full price Eman paid. price. Step Step Step 4 Show this on a double number line. Divide by to get an easy % that you will be able to multiply up to 00% later. Find 00% (the full price). 75% 00% 90 AED? AED Sale price Sale price Full price 5% 75% 00% 40 AED 90 AED? AED Full price 4 5% 75% 00% 40 AED 90 AED 70 AED Sale price Full price 4 Normal selling price = 70 AED 98
TALK THINK Salem books a desert safari in Rub al Khali at a reduced price of 40% off. He pays 40 AED. a What percentage of the full price did Salem pay? b Draw a double number line. Mark on it: The price Salem paid (percentage and AED). Where 00% is (we don t know the AED value yet). c We know 60%. Divide this by or 6 to find an easy percentage. Mark the new percentage and price on your number line. d Use this value to help you find 00%. e Copy and complete: The full price of the desert safari was?. 4 a Maitha buys a bracelet for 640 AED. She buys it in a sale where everything has already been reduced by 0%. What was the full price of the bracelet? b Maitha works out the full price of the bracelet like this: Maitha s Method Step 0% discount means I paid: 00% 0% = 80% 640 AED is 80% Step It is easy to find 0% from 80%: Step Full price is 00% (80% + 0%) 640 AED 4 = 60 AED 640 + 60 = 900 AED Read each line of Maitha s working. Do you understand each line? c Is Maitha s working correct? Use the final line of her working to find the full price on a calculator. Do you get the same answer as in part a? 5 a In a sale a car is sold for 44 000 AED. This is a reduction of 0%. What was the full price of the car? b In the same 0% sale, a motor bike is sold for 99 000 AED. What was the full price of the motor bike? 6 a Solve this number puzzle: I am thinking of a number. If I reduce my number by 5% I get the answer 54. What is my number? b Defining Problems Write a number puzzle like the one in part a for a partner to solve. 99
Summary Integers positive number or positive number = positive number + + + negative number or positive number = negative number + positive number or negative number = negative number + negative number or negative number = positive number + Powers and Roots tells us to write the number down two times, and multiply them together: 5 is 5 squared. 5 = 5 5 = 5 tells us to write the number down three times, and multiply them together: 5 is 5 cubed. 5 = 5 5 5 = 5 4 tells us to write the number down four times, and multiply them together: 5 4 is 5 to the power 4. 5 4 = 5 5 5 5 = 65 squared cubed to the power 4 5 5 5 5 5 65 square root cube root 4 You can use calculators to work out powers and roots of numbers. To work out: 6 press 6 x = 8 8 x = 5 4 5 4 = 69 69 = x SHIFT 8 x 8 = (The key is above the cubed key. x We need to press SHIFT first.) SHIFT 5 4 5 4 = (First tell the calculator which root you want, e.g. the 5th root. Then type the number under the root sign.) 00
Calculations with Fractions and Decimals When calculating with numbers, estimate first. This helps you check if your answer is sensible. You can only add or subtract fractions with the same denominator. When adding mixed numbers, add the whole numbers, then add the fractions. When subtracting mixed numbers, first subtract the whole numbers, then the fraction parts. To multiply two fractions, multiply the numerators and multiply the denominators. To divide a whole number or fraction by a fraction, turn the second fraction in the calculation upside-down and then multiply. To multiply or divide mixed numbers, change the mixed number to an improper fraction. When multiplying decimals or dividing by decimals, think about the areas of rectangles to help you. When dividing by decimals, you can multiply all the numbers in the calculation by 0 or 00 to make it an easier calculation, e.g. 0.6 0.4 has the same answer as.6 4, which is easier to work out. Rounding You can round numbers to decimal places. 0. 0.5 = 0.5 To solve 0.8 0., think about how many blocks of 0. can fit inside 0.8. Round to one decimal place ( d.p.) means round so there is one number after the decimal point. Round to two decimal places ( d.p.) means round so there are two numbers after the decimal point. You can also round numbers to significant figures. The first significant figure is the one with the highest place value. Starting from the left, this is the first digit that is not zero, e.g. In the number 0.00405, the red digits are all significant; is the first significant figure, 4 is the second significant figure, then 0 is the third, and so on. 0
To show you have rounded to one significant figure write ( s.f.) after the rounded numbers. To show you have rounded to two significant figures, write ( s.f.) after the rounded number. If you are solving a word problem where some measurements are given, you should give your answer to the same degree of accuracy as the measurements in the problem. Percentages, Fractions and Decimals To change between decimals and percentages, multiply / divide by 00. Decimals To change between either a decimal or a percentage, and a fraction, use fractions with denominators of 0, 00, or 000.??? 0 / 00 / 000 Decimals To convert a fraction to a decimal on a calculator, divide the numerator by the denominator. e.g. 8 = 8 = 0.75 Some decimals have a fixed number of digits. e.g. 0.5 only has decimal digits. A recurring decimal does not end. The digits after the decimal point repeat forever. We use dots to show recurring decimals. e.g. 0... is written as 0. 0.999... is written as 0. 9 0.066... is written as 0.0 6 Percentages can be more than 00%. 00 00 Fractions Percentages??? 0 / 00 / 000 Percentages You can add or subtract percentages from 00% to find a percentage increase (or profit) or a percentage decrease (or loss or reduction). A double number line helps you do this. 0
Review Work out. Do not use a calculator. a 8 b 0 9 c 7 6 d 40 4 e 5 7 f 56 8 Work out without using a calculator. a 6 b 9 c d 0 e 6 f 49 g Use your calculator to work out: 8 h 64 a 5 b 4 c 8 d 44 e 4 f 6 79 4 Work out. Do not use a calculator. a + 5 6 b 4 5 c 5 Work out. Do not use a calculator. Give your answers as mixed numbers. 4 a + b 6 5 + 7 0 c 4 8 4 6 Work out. Do not use a calculator. Simplify your answers if possible. a 7 0 b e 5 0 f 5 8 8 6 c 5 6 7 d 5 4 7 Work out. Solve as many as you can without using a calculator. a 6 4 b 8 c 4 8 d e 5 6 f g 4 5 0 8 Saif spends 5 of his salary on rent. He spends of what is left on food. What fraction of his salary does he spend on food? 9 Some beads are 0 7 cm long. How many beads can fit on a string 7 cm long? 5 4 0 Work out. Solve as many as you can without using a calculator. a 0.7 0.7 b 5. 6. c. 0.04 d 0.. e 0.8 0. f 4. 0.7 g 0. 0.4 7 0 0
Put it all together Round each of these numbers to: i decimal places ( d.p.) ii significant figures ( s.f). a 8.54 b 0.0768 c.0 A pack of sweets costs 5.75 AED. There are 7 sweets in the pack. How much does each sweet cost? Copy and complete this table: Decimal Percentage Fraction or mixed number (simplified if possible) 0.6?? 0.6??.??? 45%?? 4%?? 04%??? 0?? 4 5?? 5 8 4 a There are 5 students in a class. 0 of them ride the bus to school. What percentage ride the bus to school? b A movie ticket costs 40 AED. The movie theatre increases the price by 5%. What is the new ticket price? 5 Hamda bought a laptop for 000 AED. When she bought it, the laptop was on sale for 0% off. What is the full selling price of the laptop? 6 Copy and complete with the missing terms in each sequence: a, 6,?, 4, 48 b,?, 9, 6,? c 6,,,?,?, Change all the fractions to equivalent fractions? 6. 04
Put it all together Put it all together d e 4,, 4,?,?, 4, 4, 8,?, f 900, 90, 9,?,? g For each sequence, explain how you get from one term to the next term. 7 A square field has an area of. km. One eighths of the field is to be grazed by sheep, five eighths of the field is to be grazed by camels, the rest is to be given to goats. a What percentage of the field is to be grazed by goats? b What area of the field is to be grazed by goats? 8 Here are three prisms: 7 cm 8 cm A B C a Match the name to the prism: cube rectangular prism triangular prism b Work out the volume of the rectangular prism. G8-8-N.review-fig c The cube has a volume that is 6 of the volume of the rectangular prism. What is the volume of the cube? d Work out the length of a side of the cube. cm How many eighths are to be grazed by goats? Draw a diagram. Give your answer in km. A B C 0.8 cm? cm cm? cm Change all your measurements to decimals. Give your answer in cm volume of cube = length length length. 05
e The triangular prism has a volume that is 75% more than the cube. What is the volume of the triangular prism? f 75% more means it has increased by 75%, so the volume of the triangular prism = 00% + 75% of the volume of the cube. What is the height of the triangular prism? Volume of triangular prism = (length x height x width). I can statements What can you do? I can multiply and divide with positive and negative numbers. I can find squares, cubes and higher powers of numbers. I can find square roots, cube roots and higher roots of numbers. I can add and subtract fractions and mixed numbers. I can multiply with fractions, whole numbers and mixed numbers. I can divide with whole numbers, fractions and mixed numbers. I can multiply with decimals. I can divide with decimals. I can round to a given number of decimal places. I can round to a given number of significant figures. I can decide on sensible rounding. I can convert between fractions, decimals and percentages. I can work with recurring decimals. I can write one quantity as a percentage of another. I can work out percentage increases and decreases (including profit and loss). 06
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