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Mathematics · Grade 7

Multiply and Divide Rational Numbers

Learners discover the sign rules for multiplication from patterns and prove (−1)(−1) = 1 with the distributive property, then divide signed numbers, see why division by zero is undefined and why −(3/4) = (−3)/4 = 3/(−4). They use long division to show that every fraction becomes a terminating or a repeating decimal, and finish by solving multi-step problems with all four operations.

  • 4 lessons
  • About 90 minutes
  • Multiplying and dividing rational numbers check: 10 questions
  • Ways to answer: choose an answer, type a fraction, match pairs, type a number, put in order and sort into groups
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What learners will discover

  • Multiply rational numbers and explain the sign rules using patterns and the distributive property, such as (−1)(−1) = 1.
  • Divide rational numbers, explain why division by zero is undefined, and recognize that −(p/q) = (−p)/q = p/(−q).
  • Convert a rational number to a decimal using long division and recognize that the decimal either terminates or repeats.
  • Solve real-world and mathematical problems involving the four operations with rational numbers.

Lessons

  1. Why a negative times a negative is positive 9 steps5 practiceabout 23 min
  2. Dividing rational numbers 9 steps6 practiceabout 22 min
  3. Fractions to decimals: terminate or repeat 8 steps5 practiceabout 22 min
  4. Four operations in context 9 steps6 practiceabout 23 min
  5. Multiplying and dividing rational numbers check 10 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Ratio KitchenScale recipes, fill ratio tables and find the better buy.
  • Coordinate CourierDrive the parcel van to the right address on the coordinate grid.

More 7th grade math

Guide for grown-ups