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& dding ubtracting ractions

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Adding & Subtracting Fractions with Same Denominators

Steps; 1) Add or subtract the numerators 2) Keep the denominator the same 3) Simplify by reducing to lowest terms

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Adding & Subtracting Fractions with Different Denominators

Steps; 1) Find a common denominator List multiples Multiply the denominators 2) Make equivalent fractions 3) Add or subtract the numerators 4) Keep the denominator the same 5) Simplify by reducing to lowest terms

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We need a common denominator to add these fractions. +

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+ We need a common denominator to add these fractions. Count by 2’s 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Count by 7’s 7, 14, 21, 28, 35…

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Count by 2’s 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Count by 7’s 7, 14, 21, 28, 35… The first number IN COMMON that appears on both lists becomes the common denominator

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7 6 13 = = + 7 + 6 = 13 x 7 X 7 x 2 x 2 Make equivalent fractions.

Add the numerators = + 7 + 6 = 13 x 2 13

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+ We need a common denominator to add these fractions. Count by 7’s 7, 14, 21, 28, 35, 42, 49, 56, 63 Count by 5’s 5, 10, 15, 20, 25, 30, 35, 40, 45

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15 7 22 = + = 15 + 7 = 22 x 5 X 5 x 7 x 7 Make equivalent fractions.

Add the numerators = x 7 = 22 22

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We need a common denominator to add these fractions. + Count by 7’s 7, 14, 21, 28, 35, 42, 49, 56, 63 Count by 8’s 8, 16, 24, 32, 40, 48, 56, 64, 72

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32 21 53 32 + 21 = 53 = + = x 8 x 8 x 7 x 7 Make equivalent fractions.

Add the numerators x 7 + = 53 = x 7 53

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+ We need a common denominator to add these fractions. Count by 3’s 3, 6, 9, 12, 15, 18, 21, 24, 27 Count by 5’s 5, 10, 15, 20, 25, 30, 35, 40, 45

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x 3 9 Add the numerators = X 3 = 19 x 5 10 + = x 5 19

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+ We need a common denominator to add these fractions. Count by 3’s 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 Count by 11’s 11, 22, 33, 44, 55, 66, 77…

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15 22 37 = + = 15 + 22 = 37 x 3 X 3 x 11 x 11 Make equivalent

fractions. = X 3 x 11 Add the numerators 22 + = = 37 x 11 37

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+ We need a common denominator to add these fractions. Count by 3’s 3, 6, 9, 12, 15, 18, 21, 24, 27 Count by 6’s 6, 12, 18, 24,…

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4 1 5 4 + 1 = 5 = + = x 2 X 2 x 1 x 1 Make equivalent fractions.

Add the numerators = x 1 4 + 1 = 5 5

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+ We need a common denominator to add these fractions. Count by 11’s 11, 22, 33, 44, 55, 66, 77… 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

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18 11 29 = + = 18 + 11 = 29 x 6 X 6 x 11 x 11 Make equivalent

fractions. = X 6 x 11 11 + Add the numerators. = = 29 x 11 29

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We need a common denominator to add these fractions. +

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+ We need a common denominator to add these fractions. Count by 5’s 5, 10, 15, 20, 25, 30, 35, 40, 45 Count by 9’s 9, 18, 27, 36, 45, 54, 63, 72, 81

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Count by 5’s 5, 10, 15, 20, 25, 30, 35, 40, 45 Count by 9’s 9, 18, 27, 36, 45, 54, 63, 72, 81 The first number IN COMMON that appears on both lists becomes the common denominator

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x 9 36 Make equivalent fractions. Make equivalent fractions. = x9 x 5 35 Add the numerators. Add the numerators. + = = 71 = 71 x 5 71

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+ We need a common denominator to add these fractions. Count by 12’s 12, 24, 36, 48, 60, 72, 84, 96 Count by 8’s 8, 16, 24, 32, 40, 48, 56, 64, 72, 79, 80, 88, 96

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10 9 19 10 + 9 = 19 = + = x 2 x 2 x 3 x 3 Make equivalent fractions.

Add the numerators. + = = 19 x 3 19

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– We need a common denominator to subtract a fraction from another. Count by 5’s 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 Count by 11’s 11, 22, 33, 44, 55, 66, 77…

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15 11 4 15 – 11 = 4 = = – x 5 x 5 x 11 x 11 Make equivalent fractions.

Subtract. = = 4 – x 11 4

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– We need a common denominator to subtract one fraction from another. Count by 2’s 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 … Count by 10’s 10, 20, 30…

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5 3 2 5 – 3 = 2 = – = x 5 x 5 x 1 x 1 Make equivalent fractions.

Subtract. – = 5 – 3 = 2 x 1 2

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Try These A D E B F C

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Try These Answers 10 9 17 27 A D 41 28 13 12 B E 19 20 26 21 C F

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