Add and Subtract Rational Numbers, Foundations Answer Key

Grade 7 rational numbers: adding and subtracting positive and negative fractions, mixed numbers, and decimals. Monday practice at the foundations level.

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Lesson Notes

To add or subtract fractions, the pieces must be the same size. Find a common denominator, rewrite each fraction, then add or subtract the numerators.

Same denominator: add the topsDifferent denominators: rewrite first

Worked example 1: unlike denominators

$\tfrac{3}{4} - \tfrac{1}{6}$: the smallest common denominator is 12.

$\tfrac{9}{12} - \tfrac{2}{12} = \tfrac{7}{12}$

Worked example 2: mixed numbers

$2\tfrac{1}{2} + 1\tfrac{2}{3}$: add the wholes, then the fractions.

$3 + \tfrac{3}{6} + \tfrac{4}{6} = 3 + \tfrac{7}{6} = 4\tfrac{1}{6}$

Worked example 3: decimals

Line up the decimal points. $6.5 - 2.75$ becomes $6.50 - 2.75 = 3.75$.

Signs

Same signs: add the sizes and keep the sign. $-2 + (-3) = -5$.
Different signs: subtract the sizes and keep the sign of the larger size. $-5 + 3 = -2$.
Subtracting a number is the same as adding its opposite. $5 - (-3) = 5 + 3$.

Check it. Before you write your answer, ask whether the sign and size make sense on a number line.

25 problems. Work each one on the canvas under it (pen, eraser and clear are in the canvas toolbar; drag the handle below the canvas for more room). Enter your answer in the box (the keypad under it has fractions, exponents, square roots, pi, the degree sign and the symbols < > ≤ ≥ ≠). When a Unit row is shown, tap the unit for your answer. Then press Check. Write fraction answers as improper fractions in lowest terms. Write decimal answers as decimals. The eye at the right of the row shows or hides the worked solution.