Multiplying and Dividing Rational Numbers
Free printable multiplying and dividing rational numbers worksheets: negative decimals and fractions, -3.6 × 0.5 and -3/4 ÷ (-1/2), with an answer key.
Each problem multiplies or divides two signed decimals or two signed fractions: -3.6 × 0.5 = -1.8, -8.4 ÷ 2 = -4.2, 2/3 × (-3/4) = -1/2 and -3/4 ÷ (-1/2) = 1 1/2. At least one number is always negative, and the sign of the answer follows the same rule as for integers.
A decimal is multiplied by a whole number from 2 to 9 or by a decimal below 10, and every division comes out exactly, with no repeating decimals. Fractions are proper and drawn stacked, with denominators up to 12, and every answer is in lowest terms. A sheet has decimals and fractions as evenly as its count allows unless the setting picks one.
What this worksheet covers
- Multiply and divide positive and negative decimals
- Multiply and divide positive and negative fractions
Common Core standards
- 7.NS.A.2 Multiply and divide rational numbers, including negative numbers.
Frequently asked questions
What is the sign rule for multiplying and dividing?
Two numbers with the same sign give a positive answer, and different signs give a negative one. -3/4 ÷ (-1/2) is positive, 1 1/2, and -3.6 × 0.5 is negative, -1.8. The rule is the same for fractions and decimals as for whole numbers.
How do you divide by a negative fraction?
Multiply by its reciprocal, keeping its sign: -3/4 ÷ (-1/2) becomes -3/4 × (-2/1), which is 6/4, or 1 1/2.
Do the decimal divisions ever repeat?
No. Each division is built backwards from its answer, so it always comes out exactly: -8.4 ÷ 2 is -4.2 with nothing left over. Repeating decimals are a separate topic.
What grade is multiplying and dividing rational numbers?
Seventh grade. It follows multiplying and dividing integers, and leans on the fraction division students meet in sixth grade.