MATHEMATICS 8 CHAPTER FRACTION OPERATIONS REVIEW: EQUIVALENT FRACTIONS AND IMPROPER FRACTIONS AND MIXED NUMBERS Date The numerator is The denominator is A proper fraction is An improper fraction is A mixed number is Equivalent fractions are Example : Shade the following fractions and indicate which fractions are equivalent. Example : Shade the following fractions and indicate what each fraction is equivalent to. = Two-halves = three-thirds = four-fourths = five-fifths = six-sixths
Example : Determine the missing value for the following equivalent fractions. a) b) c) 0 7 0 0 d) 0 Example : Compare the following fractions. Use inequality signs to indicate which of the fractions are larger. If the fractions are equivalent, use an equal sign to indicate this. Don t forget to convert to equivalent fractions first if the denominators are different. a) b) 0 8 c) 9 d) 0 7 8 Example : Reduce the following fractions to lowest terms. a) 0 b) 0 c) d) 00 Example : For each of the following, write as an improper fraction and as a mixed number. a) b) c) d) First, re-draw the diagram: First, re-draw the diagram:
HOW TO CONVERT IMPROPER FRACTIONS AND MIXED NUMBERS To convert from an improper fraction to a mixed number: Step : How many times does the denominator go into the numerator? goes into 8 7 times! This is our whole number. Step : What s left over? Think: 7 so 8. This is our numerator. Step : Write the numerator over the same denominator. 8 7 To convert from a mixed number to an improper fraction: Step : Multiply the whole number by the denominator. 7 Step : Add the numerator to the answer from Step. 8. This is our new numerator. Step : Write the numerator over the same denominator. Example 7: Convert the following improper fractions into mixed numbers. 8 a) b) 7 c) 8 d) Example 8: Convert the following mixed numbers into improper fractions. a) 7 b) c) d) 9 7
MATHEMATICS 8 CHAPTER FRACTION OPERATIONS REVIEW: ADDING FRACTIONS Date ADDING PROPER AND IMPROPER FRACTIONS Step : Make sure the denominators are the same. If not, you must convert one or maybe even both fractions to equivalent fractions first. Step : Add the numerators together. Write this over the same denominator. Step : If possible, reduce your answer to lowest terms. Step : If your answer is an improper fraction, you may need to change it to a mixed number (READ the instructions! If it is not stated, then leave your answer as an improper fraction). Example : Add the following proper and improper fractions. Where necessary, write your answer as a mixed number. a) b) 7 c) 8 d) e) f) 7
ADDING MIXED NUMBERS METHOD : CONVERT TO IMPROPER FRACTIONS Step : Convert both mixed numbers to improper fractions. Step : Make sure the denominators are the same. If not, you must convert one or maybe even both fractions to equivalent fractions first. Step : Add the numerators together. Write this over the same denominator. Step : If possible, reduce your answer to lowest terms. Step : You may need to change your answer to a mixed number (READ the instructions! If it is not stated, then leave your answer as an improper fraction). Example : Add the following mixed numbers by converting them to improper fractions first. Write your answer as a mixed number. a) b) 7 7 c) d) e) f) 7
METHOD : ADD WHOLE NUMBERS AND PROPER FRACTIONS SEPARATELY Step : Make sure the denominators are the same. If not, you must convert one or maybe even both fractions to equivalent fractions first. Step : Add the whole numbers together, then add the proper fractions together (add the numerators and write over the same denominator). Step : If the fraction is an improper fraction, you must change it to a mixed number and add this to the whole number from Step. Step : If possible, reduce your answer to lowest terms. Step : You may need to change your answer to an improper fraction (READ the instructions! If it is not stated, then leave your answer as a mixed number). Example : Add the following mixed numbers by adding the whole numbers and proper fractions separately. Write your answer as an improper fraction. a) 7 b) 8 8 c) d) e) f) 7
MATHEMATICS 8 CHAPTER FRACTION OPERATIONS REVIEW: SUBTRACTING FRACTIONS Date SUBTRACTING PROPER AND IMPROPER FRACTIONS Step : Make sure the denominators are the same. If not, you must convert one or maybe even both fractions to equivalent fractions first. Step : Subtract the numerators. Write this over the same denominator. Step : If possible, reduce your answer to lowest terms. Step : If your answer is an improper fraction, you may need to change it to a mixed number (READ the instructions! If it is not stated, then leave your answer as an improper fraction). Example : Subtract the following proper and improper fractions. Where necessary, write your answer as a mixed number. a) b) c) 0 d) 0 e) f) 9
SUBTRACTING MIXED NUMBERS METHOD : CONVERT TO IMPROPER FRACTIONS Step : Convert both mixed numbers to improper fractions. Step : Make sure the denominators are the same. If not, you must convert one or maybe even both fractions to equivalent fractions first. Step : Subtract the numerators. Write this over the same denominator. Step : If possible, reduce your answer to lowest terms. Step : You may need to change your answer to a mixed number (READ the instructions! If it is not stated, then leave your answer as an improper fraction). Example : Subtract the following mixed numbers by converting them to improper fractions first. Write your answer as a mixed number. a) 7 b) c) 7 0 d) 7 0 e) 7 f)
METHOD : SUBTRACT WHOLE NUMBERS AND PROPER FRACTIONS SEPARATELY Step : Make sure the denominators are the same. If not, you must convert one or maybe even both fractions to equivalent fractions first. Step : If the second mixed number has a fraction that is larger than the fraction of the first mixed number, your first fraction must borrow from the whole number. eg Step : Subtract the whole numbers, then subtract the fractions (subtract the numerators and write over the same denominator). Step : If possible, reduce your answer to lowest terms. Step : You may need to change your answer to an improper fraction (READ the instructions! If it is not stated, then leave your answer as a mixed number). Example : Subtract the following mixed numbers by subtracting the whole numbers and proper fractions separately. Write your answer as an improper fraction. a) 7 b) c) 9 0 d) 8 9 0 e) f) 0
MATHEMATICS 8 CHAPTER FRACTION OPERATIONS MULTIPLYING PROPER FRACTIONS (.) Date MULTIPLYING USING DIAGRAMS Example : Determine using a diagram. MULTIPLYING USING A RULE Multiply the numerators together and the denominators together. You can cross-cancel while you are multiplying or reduce your answer to lowest terms at the end. Cross-cancelling is Example : Determine the following. Express your product in lowest terms. a) 9 b) 7 0 8 c) 9 d) 8 9 e) 8 f)
g) 9 8 h) 9 0 Example : Estimate and calculate. 7 ESTIMATE CALCULATE Example : In Pet s World, three-eighths of the animals are fish, and two-fifteenths of the fish are tropical fish. What fraction of the animals in the store are tropical fish? Example : Orion had two six-sided die. Each number on the die has a chance of being rolled. What is the probability of rolling an eight? Dice Dice
MATHEMATICS 8 CHAPTER FRACTION OPERATIONS MULTIPLYING A FRACTION AND A WHOLE NUMBER (.) Date MULTIPLYING USING DIAGRAMS Example : Determine using fraction strips or pattern blocks. First, express the multiplication as a repeated addition: Count the shaded parts. Each part represents. Re-draw your diagram: Example : Determine using a number line. Express your answer in lowest terms. First, express the multiplication as a repeated addition: Draw a number line and divide each whole number into parts. Each part represents : MULTIPLYING USING A RULE First, write the whole number as an improper fraction by making the denominator. Then, multiply the numerators together and the denominators together. You can cross-cancel while you are multiplying or reduce your answer to lowest terms at the end.
Example : Determine the following. Express your product as a mixed number in lowest terms. 7 a) 8 b) c) 7 0 9 d) e) 7 f) 0 8 Example : Charles has 0 hockey cards. Hector has as many hockey cards as Charles. How many cards does Hector have? Remember: The word of often indicates multiplication! Example : Penelope has as much money as Katie. Katie has $. How much money does Penelope have?
MATHEMATICS 8 CHAPTER FRACTION OPERATIONS MULTIPLYING IMPROPER FRACTIONS AND MIXED NUMBERS (.) Date MULTIPLYING IMPROPER FRACTIONS The same rule applies for multiplying improper fractions as for multiplying proper fractions. Multiply the numerators together and the denominators together. You can cross-cancel while you are multiplying or reduce your answer to lowest terms at the end. Example : Determine the following. Express your product as a mixed number in lowest terms. 9 a) 7 b) 8 8 c) 0 7 9 d) e) 0 MULTIPLYING MIXED NUMBERS First, write the mixed numbers as improper fractions, then multiply. Express your product as a mixed number in lowest terms. Example : a) b) c) 0
7 d) e) f) 9 Example : Estimate and calculate. ESTIMATE CALCULATE Example : Complete each of the following multiplication statements using a mixed number in lowest terms. a) b) 8 c) 9 d)
MATHEMATICS 8 CHAPTER FRACTION OPERATIONS DIVIDING A FRACTION AND BY A WHOLE NUMBER (.) Date DIVIDING USING DIAGRAMS Example : Determine using fraction strips or pattern blocks. Steps:. Use a fraction strip to represent.. Cut each fourth into equal parts.. Each of the equal parts of is. So, Example : Determine using a number line. Steps:. Draw and label a number line that shows fourths.. Cut each fourth into equal parts.. Each of the equal parts of is. So, DIVIDING USING A RULE First, write the whole number as an improper fraction by making the denominator. Turn the second fraction upside down (change it into its reciprocal). Then, multiply the numerators together and the denominators together. You can cross-cancel while you are multiplying or reduce your answer to lowest terms at the end. A reciprocal is To help you remember how to divide a fraction: "Dividing fractions, as easy as pie, Flip the second fraction, then multiply. And don't forget to simplify, Before it's time to say goodbye" OR Leave me, change me, turn me over
Example : Determine the quotient for the following. a) b) 7 7 c) 9 d) 8 8 e) f) Example : Kevin can eat of a pizza in hours. How much pizza can he eat in hour? 0 Example : Luke has of a chocolate bar left, which he gives to hungry friends to share. If they share it equally, what fraction of the whole chocolate bar does each receive?
MATHEMATICS 8 CHAPTER FRACTION OPERATIONS DIVIDING FRACTIONS AND MIXED NUMBERS (.) Date There are two methods for dividing fractions: METHOD : DIVIDE USING A COMMON DENOMINATOR To divide fractions, write them with a and divide the numerators. For mixed numbers, change them into improper fractions first. Example : Determine the quotients for the following by dividing using a common denominator. Where necessary, reduce your answer to lowest terms and express as a mixed number. 8 a) 9 9 b) c) 0 0 d) e) f) 8 METHOD : DIVIDE USING MULTIPLICATION (same as last lesson) To divide by a fraction, you can by its. To help you remember how to divide a fraction: "Dividing fractions, as easy as pie, Flip the second fraction, then multiply. And don't forget to simplify, Before it's time to say goodbye" OR Leave me, change me, turn me over
Example : Determine the quotients for the following by dividing using multiplication. Where necessary, reduce your answer to lowest terms and express as a mixed number. 7 a) b) 9 c) d) e) f) Example : Estimate and calculate ESTIMATE. CALCULATE Method : Divide Using a Common Denominator Method : Divide Using Multiplication
Example : According to the package on a frozen shepherd s pie, 8 of the tray is one serving. How many servings are in five trays of shepherd s pie? Example : George is 0 cm and is as tall as his older brother, Parker. How tall is Parker?
MATHEMATICS 8 CHAPTER FRACTION OPERATIONS APPLYING FRACTION OPERATIONS (.) Date The order of operations for is the same as for and. B E D M A S Example : Calculate. a) b) c) d) 9
e) f) 0 9 g) 7 h) 7 Example : Brenda earns $/h working at the nursery. For time worked above 0 hours in a week, she earns time-and-a-half. How much does Brenda earn for working 7 hours in a week? METHOD : CALCULATE IN STAGES METHOD : EVALUATE ONE EXPRESSION Time-and-a half means to be paid for h for each hour of work done