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 written as a fraction without 0 on the bottom. This includes decimals that can be written as fractions. 0.5 = 5 10 = 1 2 Oct 9 9:07 AM 1
Place Value 5 2 1 4. 3 7 8 9 Oct 14 9:12 AM Converting from decimals (non-repeating) to fractions: Step 1: Take the number after the decimal and put it on top of the fraction. Step 2: Put a 1 on the bottom of the fraction, followed by as many 0s as there are spots after the decimal. Step 3: Simplify. 0.75 0.081 2.15 Oct 10 9:15 AM 2
Divisibility Rules Refresher: 1 It goes into everything!!! 2 It goes into all EVEN numbers 3 Add all the digits in the number up and if that is divisible by 3 then the original number is divisible by 3 Oct 24 10:08 AM 4 Look at the last two digits of a number. If they are divisible by 4, then the whole number is divisible by 4 5 All numbers that end in 0 or 5 are divisible by 5 6 Any number divisible by BOTH 2 and 3 are divisible by 6 Oct 24 10:09 AM 3
7 No rule. :'( 8 Look at the last three digits of a number. If they are divisible by 8, then the whole number is divisible by 8 9 Add all the digits in the number up and if that is divisible by 9 then the original number is divisible by 9 10 All numbers that end in 0 are divisible by 10 11 It's complicated... Oct 24 10:09 AM Converting from decimals (repeating) to fractions: Step 1: Take the repeating number after the decimal and put it on top of the fraction. Step 2: Put as many 9s on the bottom as there are spots after the decimal. Step 3: Simplify. 0.47 0.3 1.023 Oct 10 9:28 AM 4
Rounding: 4 5 4.5 4.25 4.75 Is 4.8 closer to 4 or 5? Round 4.8 to the nearest whole number. Oct 14 8:58 AM Round 8.7 to the nearest whole number. Round 8.78 to the nearest tenth. When rounding, 0.5 to 0.9 rounds and everything under 0.4 rounds. Round 8.2 to the nearest whole number. Oct 14 9:09 AM 5
Round 2.8473 to the nearest hundredth. Round 4.75243 to the nearest tenth. Round 9.95 to the nearest tenth. Round 4.749 to the nearest tenth. Oct 14 9:20 AM Converting from fractions to decimals: Step 1: Divide numerator by denominator. 2 4 7 9 Oct 9 9:18 AM 6
Oct 25 10:28 AM If a fraction is negative, where do I put the sign? Which one is correct? - 2 5-2 5 2-5 -2-5 Oct 14 9:38 AM 7
less than greater than less than or equal to greater than or equal to equal to Oct 17 9:23 AM Marshall has $1.8 billion. He spends $2.7 billion on a new skyscraper. He got a loan to cover the extra costs. How much will he owe the bank? Use a number line to represent the two numbers. Oct 20 8:57 AM 8
Converting Between Mixed Numbers and Improper Fractions Nov 30 10:24 AM Improper Fractions to Mixed Numbers Mixed Numbers to Improper Fractions Sep 18 9:21 AM 9
Converting Whole Numbers to Fractions Sep 18 9:27 AM Equivalent Fractions To make equivalent fractions, multiply the top and the bottom by the same number. Nov 23 10:18 AM 10
Simplifying Fractions Find the largest factors that divide evenly into both the numerator and the denominator Nov 23 10:36 AM Writing a rational number between two given numbers: Write a rational number between 1 and 2. Find a rational number between -3 and -4. Oct 15 9:02 AM 11
Find a rational number between 1.25 and -3.26. Find a rational number between -0.25 and -0.26. Oct 15 9:11 AM Find a rational number between and. Oct 15 9:34 AM 12
Ordering rational numbers in decimal OR fraction form Use a number line to order these numbers from least to greatest: 0.35 2.5-0.6 1.7-3.2-0.6 Oct 16 9:03 AM Use a number line to order these numbers from least to greatest: - 3 8 5 9-10 4-1 1 4 7 8 10 3 Oct 16 9:17 AM 13
Ordering Rational Numbers in Fraction and Decimal Form Steps: Convert to either ALL or ALL. Place on the number line, using the number form. Order these rational numbers from least to greatest: 1.13-10 3-3.4 3 2.7-2 2 7 5 Oct 17 9:10 AM Nov 2 9:57 AM 14
Studying for Math Tests I CAN study for a math test. Again. 1. Use your. 2. Find examples. 3. Copy the questions on piece of paper. 4. Try the question looking at your notes. 5. to see if you are right! 6. If you're right, move on to the question. 7. If not, find your, it, and then try. 8. If you don't understand what went wrong, even after checking for your error, then look over the in your notes, ask a who is confident about the topic, or the teacher. Nov 5 9:04 AM What happens now? Study Notes Chapter 3a Test Nov 23 3:10 PM 15
3.2 Adding Rational Numbers Sep 15 9:32 AM Sep 15 9:42 AM 16
Steps: Find a common denominator. Use equivalent fractions to set this up. Add the numerators. DON'T FORGET ABOUT THE +/- SIGNS!!! 1. Find a common denominator 2. Multiply both top and bottom of fraction(s) to make them equivalent 3. Add tops 4. Leave bottoms the same 5. Convert to mixed number answer, if needed Oct 20 9:39 AM Oct 21 9:00 AM 17
Oct 21 9:05 AM Oct 21 9:13 AM 18
Oct 21 9:16 AM At the beginning of June, The Frosty Snow Blower Company was $235.46 in debt. By the end of August, the company had increased its debt by $156.71. How much are they in debt for at the end of August? Oct 23 8:57 AM 19
3.3 Subtracting Rational Numbers Same process as adding but we take away instead. Convert mixed numbers to improper fractions. Find the lower common denominator (LCD). Make equivalent fractions so that the fractions have the same denominator. Subtract (just the numerator - top). Reduce. Convert any improper fractions to mixed numbers. Dec 4 10:31 AM Oct 23 9:42 AM 20
-2.3-(-3.9) -2.3+(-3.9) Oct 29 9:04 AM Oct 30 8:56 AM 21
A diver jumps off a cliff that is 14.7 m above sea level. After hitting the water, he plunges 3.8 m below the surface of the water before returning to the surface. a) Use rational numbers to represent the difference in heights from the top of the cliff to the bottom of his dive (use +/- decimals to write out the expression). Oct 30 9:35 AM b) The water is 5.6 m deep. What is the distance from the ocean floor to the bottom of the dive? Oct 21 4:40 PM 22
What happens now? Study Notes Chapter 3b Test Nov 23 3:10 PM 3.4 Multiplying Rational Numbers Part A - Fractions Steps: Convert any mixed # to improper fractions Multiply the tops straight across Multiply the bottoms straight across Check your signs to make sure you did it right Reduce Optional: You can cross cancel before Step 2, if you would like to skip Step 5 Nov 12 9:10 AM 23
Jan 5 9:52 AM Nov 12 9:24 AM 24
Part B: Decimals When multiplying by decimals, sometimes you get a answer than you expect. When multiplying by a number between and or and, your answer will be smaller than the original number. Nov 13 8:50 AM Nov 13 9:09 AM 25
Part C: Word Problems On February 5, 2008, the price of a share in CIBC changed by -$1.640. A person owns 35 shares. By how much did those shares change in value that day? Nov 14 8:58 AM The Commutative Property of Addition and Multiplication This means: When you multiply or add, the order of the numbers doesn't matter. This does not work for subtraction and division. Jan 11 10:31 AM 26
3.5 Dividing Rational Numbers Part A - Fractions Steps: 1. Convert any mixed numbers to improper fractions. 2. Flip the second fraction and change the division sign to multiplication. 3. Cross-cancel (if you like). 4. Multiply denominators and multiply numerators. 5. Simplify and convert to mixed, if necessary. Jan 11 9:51 AM Nov 20 9:01 AM 27
Jan 11 9:59 AM Part B: Decimals Jan 11 10:03 AM 28
Part C: Word Problems A person has 54 shares in WestJet Airlines. On February 6, 2008, these shares lost $17.28 in value. How much was the change in value of 1 share? Nov 24 9:15 AM 3.6 Order of Operations with Rational Numbers Brackets Exponents Division Multiplication Addition Subtraction Watch the process, then copy down the example: Nov 26 9:05 AM 29
Be careful when using different operations with fractions! If you are adding/subtracting = find a denominator. If you are multiplying/dividing = use - or your answer before continuing. Jan 19 10:49 AM Nov 28 8:53 AM 30
To convert a temp. in degrees F to degrees C, we use the formula: Using this formula, find the temp. in degrees C in Fort Simpson, NWT, if the temp. is -9.4 degrees F. Hint: Start with writing out the formula. Jan 19 10:55 AM A can of soup is a cylinder with a radius of 3.5 cm and a height of 11.5 cm. Nov 28 9:26 AM 31