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Unit 3: Fractions Dividing Fractions and Whole Numbers
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Main Ideas: Models like number lines and fractions circles can be used to demonstrate the meaning of division of fractions. Models like number lines and fractions circles can be used to demonstrate the meaning of division of fractions. Dividing a whole number by a fraction relates to the notion of grouping. Dividing a whole number by a fraction relates to the notion of grouping. Dividing a fraction by a whole number relates to the notion of sharing. Dividing a fraction by a whole number relates to the notion of sharing.
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20 ÷ 5 Think of dividing as sharing. For example, this math question says to share 20 items equally among 5 sets. Think of dividing as sharing. For example, this math question says to share 20 items equally among 5 sets. Or you can think of dividing as groups. For example, this math questions says how many groups of 5 fit into 20? Or you can think of dividing as groups. For example, this math questions says how many groups of 5 fit into 20? The answer, in both cases, is 4. The answer, in both cases, is 4.
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Divide a whole number by a fraction: 6 ÷ 1GROUPING! 6 ÷ 1GROUPING! 3 Think: How many thirds are in 6? Think: How many thirds are in 6? Use a number line: (see p. 130 in textbk) Use a number line: (see p. 130 in textbk) You make 18 jumps on the number line. You make 18 jumps on the number line. There are 18 thirds in 6; therefore, the answer is 18. There are 18 thirds in 6; therefore, the answer is 18.
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Another example: 6 ÷ 4 6 ÷ 4 3 Think: Think: –How many four-thirds go into 6? Use a number line: (see pg 130 in textbk) Use a number line: (see pg 130 in textbk) You make four and a half jumps on the number line. You make four and a half jumps on the number line. There are 4½ four-thirds in 6; therefore, the answer is 4½. There are 4½ four-thirds in 6; therefore, the answer is 4½.
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Divide a Fraction by a Whole Number: 1 ÷ 3SHARING! 1 ÷ 3SHARING! 2 Think: Share ½ into 3 equal parts. Think: Share ½ into 3 equal parts. Use a number line (see pg 131 in textbk): Use a number line (see pg 131 in textbk): –Mark ½ on the line –Divide the interval 0 to ½ into 3 equal parts. –Each part is equal to 1 6 –Therefore, ½ ÷ 3 = 1/6
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Another example: 3 ÷ 2 3 ÷ 2 4 Think: Think: –Share ¾ into 2 equal parts. Use a number line: (see pg 131 in textbk) Use a number line: (see pg 131 in textbk) –Mark ¾ on the number line –Divide the interval 0 to ¾ into 2 equal parts. –To label this point, divide the fourths into eighths. –Each part is 3/8. –Therefore, ¾ ÷ 2 = 3/8
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Fraction Circles 5 ÷ 3 5 ÷ 35 Think: How many 3/5 are in 5 wholes? Think: How many 3/5 are in 5 wholes? Use fraction circles in fifths to model 5 (see p. 132 in textbk) Use fraction circles in fifths to model 5 (see p. 132 in textbk) Count groups of three-fifths. There are 8. there is 1 fifth left over. Count groups of three-fifths. There are 8. there is 1 fifth left over. 1/5 is 1/3 of 3/5. 1/5 is 1/3 of 3/5. Therefore, 5 ÷ 3/5 = 8 1/3 Therefore, 5 ÷ 3/5 = 8 1/3
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