math class 678 4-in-1 skill sheets
7.NS.A.2c 7th Grade The Number System

Multiplying & Dividing Rationals

Apply properties of operations as strategies to multiply and divide rational numbers.

How to explain it

Students multiply positive and negative fractions, mixed numbers, and decimals by multiplying absolute values and applying the sign rules, divide rational numbers by rewriting every quotient as multiplication by the reciprocal (Keep–Change–Flip), explain why a quotient of integers with a nonzero divisor is a rational number and why the divisor can never be zero, and interpret products and quotients in real-world contexts.

The anchor students hold onto: MAPS still rules the signs: Multiply or DIVIDE the absolute values · Ask if the signs match · Positive if same · Switch to negative if different. See division? KCF it first.

Worked examples

Example 1 Multiply Straight Across
(,[object Object],) × ,[object Object]
Step 1Multiply across: 2×3 = 6, 3×5 = 15
Step 2Signs differ → negative
Step 3−6/15 = −2/5
Step 4A: −2/5
Answer−2/5
Example 2 KCF a Division
(,[object Object],) ÷ ,[object Object]
Step 1KCF: (−5/6) × (12/5)
Step 2Multiply across: 60/30 = 2
Step 3Signs differ → negative
Step 4A: −2
Answer−2

Common mistakes

What students write Multiplying mixed numbers in pieces: 2 1/2 × 3 = 6 1/2
The fix Convert first: 2 1/2 = 5/2, so 5/2 × 3 = 15/2 = 7 1/2
Try this Leo says 2 1/2 × 3 = 6 1/2 because "2 × 3 = 6, and the 1/2 just comes along." Find his mistake, then show the correct work.
What students write Flipping the first fraction: (1/2) ÷ (3/4) = (2/1) × (3/4)
The fix KEEP the first — FLIP the divisor: (1/2) × (4/3) = 2/3
Try this Ava evaluates (−1/2) ÷ (3/4) by flipping the first fraction: (−2/1) × (3/4) = −3/2. Find her mistake, then show the correct work using KCF.

Teacher tip

Head off the two predictable errors before they happen. First: Convert first: 2 1/2 = 5/2, so 5/2 × 3 = 15/2 = 7 1/2 Second: KEEP the first — FLIP the divisor: (1/2) × (4/3) = 2/3