Compute 1 1/2 ÷ (-7/5). Use the signed-number rules and simplify exactly.
Exact result: ____________________
CCSS 7.NS.A.2a–c · signed multiplication & division
Multiply and Divide Rational Numbers Worksheet Generator
Practice products and quotients across signed rational forms while preserving exact values. Division problems never use a zero divisor, and answers are generated from rational arithmetic instead of decimal approximations.
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Multiply & Divide Rational Numbers
Multiply & divide rational numbers · Grade 7 standard · Seed 271701
1.
2.
Compute 16/5 ÷ 1.5. Use the signed-number rules and simplify exactly.
Exact result: ____________________
3.
Compute 4 ÷ (-3 1/2). Use the signed-number rules and simplify exactly.
Exact result: ____________________
4.
Compute 3 1/3 × 27/8. Use the signed-number rules and simplify exactly.
Exact result: ____________________
5.
Compute -7/6 ÷ 5/2. Use the signed-number rules and simplify exactly.
Exact result: ____________________
6.
Compute 5 1/6 ÷ (-3.5). Use the signed-number rules and simplify exactly.
Exact result: ____________________
7.
Compute -1/5 × (-2). Use the signed-number rules and simplify exactly.
Exact result: ____________________
8.
Compute -4 ÷ (-3 3/4). Use the signed-number rules and simplify exactly.
Exact result: ____________________
9.
Compute -13/4 ÷ 31/8. Use the signed-number rules and simplify exactly.
Exact result: ____________________
10.
Compute -2 1/5 × 5/8. Use the signed-number rules and simplify exactly.
Exact result: ____________________
Exact-construction rule: operations use normalized integer numerator/denominator pairs, number-line positions use exact ticks, repeating decimals come from remainder cycles, and money contexts use exact cents. No answer depends on binary floating-point rounding.
Signs first, then the numbers
Multiplication and division of rational numbers follow a small set of rules that are easier to apply when the sign is decided separately from the magnitude. Division problems never use a zero divisor, and every answer comes from exact rational arithmetic.
Frequent mistakes with signs and reciprocals
- Flipping the dividend as well as the divisor when dividing fractions.
- Assuming a quotient is always smaller than the number divided.
- Losing track of the sign when there are three or more factors.
Products and quotients worked through
- (−2/3) × (9/10) = −18/30, which simplifies to −3/5.
- (−4.2) ÷ (−0.7) = 6, since the two negatives give a positive and 42 ÷ 7 = 6.
- −5/6 ÷ 5/12 = −5/6 × 12/5 = −60/30 = −2.
- (−2)(−3)(−1): three negative factors give a negative product, so the result is −6.
Teaching why the rules work
Ask why a negative times a negative is positive before asking students to apply it. The distributive property gives a short argument: −3 × (2 + (−2)) = 0, so −3 × (−2) must equal +6 for the total to be zero.
Note 1
Decide the sign first, then multiply or divide the absolute values.
Note 2
Count the negative factors: an even number of negatives gives a positive result, an odd number gives a negative result.
Note 3
For fraction division, multiply by the reciprocal of the nonzero divisor and flip only the divisor: -3/4 divided by 2/3 is -3/4 times 3/2 = -9/8.
Note 4
Dividing by a number between 0 and 1 makes the absolute value larger; the sign rule still applies separately.
Note 5
Use the distributive property to explain why a negative times a negative is positive rather than treating it as an unexplained rule.
Continue the 7.NS progression
Move to another Grade 7 rational-number skill
Quick answers
Can a divisor ever be zero?
No. The generator excludes zero divisors by construction.
Do challenge problems include mixed numbers?
Yes. Challenge mode uses a broader mix of signed fractions, decimals, mixed numbers, and integers.
Why does a negative times a negative equal a positive?
Because the distributive property forces it: since -3 times (2 + -2) = 0, the terms -3 times 2 = -6 and -3 times -2 must be opposites, so -3 times -2 = 6.
Which standard does this cover?
7.NS.A.2a-2c: applying and extending the properties of operations to multiply and divide rational numbers, including that the quotient of integers with a nonzero divisor is a rational number.