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Grade 7 · Number · Fraction and Decimal Multiplication

Multiply and Divide Rational Numbers

Fraction and decimal operations are easier to trust when the calculation is connected to scaling, grouping, place value, and an estimate.

The big idea

Magnitude predicts the result

Multiplying by a positive number less than 1 scales a quantity down. Dividing by a positive number less than 1 asks how many smaller groups fit, so the result grows.

Work it through

Solve 2/3 × 3/4 and 7.05 ÷ 0.5

  1. 1. Multiply the fraction numerators and denominators: 2/3 × 3/4 = 6/12 = 1/2.
  2. 2. Estimate 7.05 ÷ 0.5 as about 7 ÷ one-half, which should be about 14.
  3. 3. Create an equivalent division statement: 7.05 ÷ 0.5 = 70.5 ÷ 5.
  4. 4. Calculate 14.1 and compare it with the estimate.