7.NS.A.2b 7th Grade The Number System

Dividing Integers

Understand that integers can be divided, that the quotient of integers is a rational number, and how the sign of a quotient is determined.

How to explain it

Students divide integers by dividing absolute values and applying the sign rules (same signs positive, different signs negative), connect every quotient to its related multiplication fact, explain why a quotient of integers exists whenever the divisor is not zero and why division by zero is undefined, and interpret integer quotients in real-world contexts.

The anchor students hold onto: MAPS works for division too: Multiply or DIVIDE the absolute values · Ask if the signs match · Positive if same · Switch to negative if different.

Worked examples

Example 1 Different Signs

(−42) ÷ 6

Step 142 ÷ 6 = 7

Step 2Signs differ → negative

Step 3Check: (−7) × 6 = −42

Step 4A: −7

Answer−7

Example 2 Same Signs

(−24) ÷ (−8)

Step 124 ÷ 8 = 3

Step 2Same signs → positive

Step 3A: 3

Answer3

Common mistakes

What students write Two negatives make a negative quotient: (−42) ÷ (−6) = −7

The fix Same signs ALWAYS give a positive quotient: (−42) ÷ (−6) = +7

Try this Mara says (−42) ÷ (−6) = −7 because "the negatives stay negative." Find her mistake, then show the correct work using MAPS.

What students write You can divide by zero: 9 ÷ 0 = 0

The fix 0 ÷ 9 = 0, but 9 ÷ 0 is UNDEFINED — no number times 0 makes 9

Try this Jonah says 0 ÷ 9 = 0 and 9 ÷ 0 = 0 because "anything with zero is zero." One statement is wrong. Explain which one, then give the correct value of each expression.

Teacher tip

Head off the two predictable errors before they happen. First: Same signs ALWAYS give a positive quotient: (−42) ÷ (−6) = +7 Second: 0 ÷ 9 = 0, but 9 ÷ 0 is UNDEFINED — no number times 0 makes 9