Listen & Learn PRESENTED BY LOVE2LEARN

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1 Number Sense and Numeration Fractions Multiplication and PRESENTED BY LOVE2LEARN Mathematics, Grade 8 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping NOT the Chat Room Your questions Satisfaction Meter 1

2 What you will learn At the end of this presentation, you will be able to Solve problems involving the multiplication and division of fractions Simplify fractions to their lowest terms Agenda Background Multiplying and Dividing Fractions Multiplying Fractions Dividing Fractions Applications Practice 2

3 Agenda Background Multiplying and Dividing Fractions Multiplying Fractions Dividing Fractions Applications Practice Background How many whole and part apples are there in 5 half apples? How do you divide half an apple into 3 equal pieces? These questions can be answered by multiplying or dividing fractions. 3

4 Agenda Background Multiplying and Dividing Fractions Multiplying Fractions Dividing Fractions Applications Practice Fraction A part of something. The splitting up of an item into parts. Example: A piece of a pie. If we cut a pie in 4 pieces and ate 1 piece, the fraction that we ate would be ¼. 4

5 Numerator/Denominator The numerator is the top number in the fraction. The denominator is the bottom number in the fraction. Numerator Denominator The numerator tells us how many parts we actually have, while the denominator tells us how many parts we could have if we had them all. Numerator Denominator 5

6 Equivalent fractions Fractions that remain the same size even when the numbers are different. These fractions are all shown as being half of something, but each fraction is showing that the item (e.g., a pie) is cut up into a different number of pieces. Fractions should be written in lowest form to make them easy to work with. Lowest form 6

7 We can solve for the lowest form by dividing the numerator and the denominator by the same number. 16 goes into 16 one time 16 goes into 32 two times We cannot find another common multiple to go into both, so we now have the lowest form of the fraction. The reciprocal of a fraction is the fraction upside down. The numerator moves to the bottom and the denominator moves to the top. You will learn to use this in the division of fractions. Reciprocal 7

8 Review of signs 3 x 3 = 9 Two positives make a positive. ( 3) x ( 3)= 9 Two negatives make positive. ( 3) x 3 = 9 Only one positive makes a negative. 3 x ( 3) = 9 Only one positive makes a negative. The same signs are used with fractions. A pie is divided into 9 pieces and Bill eats 3 pieces. What fraction represents how much Bill eats? 8

9 A pie is divided into 9 pieces and Bill eats 3 pieces. What fraction represents how much Bill eats? A pie is divided into 9 pieces and Bill eats 3 pieces. What fraction represents how much pie is left? 9

10 A pie is divided into 9 pieces and Bill eats 3 pieces. What fraction represents how much pie is left? The reciprocal of is d) 10

11 The reciprocal of is d) Find an equivalent fraction to 11

12 Find an equivalent fraction to When multiplying or dividing fractions, two negative signs make a positive negative 12

13 When multiplying or dividing fractions, two negative signs make a positive negative Agenda Background Multiplying and Dividing Fractions Multiplying Fractions Dividing Fractions Applications Practice 13

14 Multiplying Fractions In order to multiply fractions, we multiply the numerators together and then we multiply the denominators together. Multiply: Multiply the top numbers together Multiply the bottom numbers together Multiplying Fractions Remember to check if your solution can be reduced to lowest terms. Multiply: Lowest terms 14

15 Multiplying Fractions Remember the sign rules when multiplying fractions. Dividing Fractions To divide fractions, we flip the second fraction, change the sign to multiplication, and solve using multiplication. Flip the second term (write its reciprocal). 15

16 Agenda Background Multiplying and Dividing Fractions Multiplying Fractions Dividing Fractions Applications Practice Applications Using Multiplication: If three friends each bring ½ a pie to a party, how much pie is there? Therefore, there would be one and a half pies total. 16

17 Applications Using : If John cut a pie into 8 pieces and then he divided one piece into 2, what fraction of the pie would one of these small pieces be? Therefore, one of the small pieces would be of the pie. Agenda Background Multiplying and Dividing Fractions Multiplying Fractions Dividing Fractions Applications Practice 17

18 Practice Solve Practice Solution Multiply the numerators Multiply the denominators 18

19 Practice Solve Practice Solution Remember to flip the second fraction and change the sign to multiplication. 19

20 Practice Solve Practice Solution Remember, the answer needs to be reduced to lowest terms. 20

21 Practice Solve Practice Solution One positive and one negative makes a negative sign. Remember to reduce to lowest terms. 21

22 Practice Solve Practice Solution 22

23 Fractions - Multiplication and Resources Edhelper.com Fractions 23