6.NS.A.1 6th Grade The Number System

Dividing Fractions by Fractions

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

How to explain it

At this standard, students compute quotients of fractions using the reciprocal (keep-change-flip) method and interpret fraction division in word-problem contexts.

The anchor students hold onto: Keep the dividend, change ÷ to ×, flip the divisor to its reciprocal — then multiply across and simplify.

Dividing fractions (6.NS.A.1) builds directly toward operations with all rational numbers, including negative fractions, in 7th grade (7.NS.A.2).

Worked examples

Example 1 Keep-Change-Flip

Find: 2/3 ÷ 5/6.

Step 1Keep 2/3, change ÷ to ×

Step 2Flip 5/6 → reciprocal is 6/5

Step 32/3 × 6/5 = 12/15

Step 4Simplify: 12/15 = 4/5

Answer4/5

Example 2 Measurement Meaning

Find: 2/3 ÷ 1/6.

Step 1How many 1/6 are in 2/3?

Step 2Keep 2/3 · flip 1/6 → 6/1

Step 32/3 × 6/1 = 12/3 = 4

Step 44 sixths fit exactly in 2/3

Answer4

Common mistakes

What students write Flipping the dividend (first fraction) instead of the divisor

The fix Always keep the first fraction exactly as written; flip ONLY the divisor (second fraction).

Try this Maria says 5/6 ÷ 1/2 = 5/12 because she multiplied straight across. Devon says 5/6 ÷ 1/2 = 5/3 because he flipped the divisor first. Who is correct? What mistake did the other student make?

What students write Thinking dividing by a fraction less than 1 gives a smaller result

The fix Dividing by a fraction less than 1 makes the quotient LARGER — more pieces fit into the dividend.

Teacher tip

Head off the two predictable errors before they happen. First: Always keep the first fraction exactly as written; flip ONLY the divisor (second fraction). Second: Dividing by a fraction less than 1 makes the quotient LARGER — more pieces fit into the dividend.