Sixth Grade · Math · week 10

Dividing fractions by fractions

Divide a fraction by a fraction using keep-change-flip (multiplying by the reciprocal) and explain why it works.

Dividing by a fraction means asking "how many of this fraction fit into that amount?" For example, 1 ÷ 1/4 asks how many fourths fit in 1 whole - the answer is 4.

The reliable method: KEEP the first fraction, CHANGE divide to multiply, FLIP the second fraction to its reciprocal. Then multiply straight across.

The reciprocal of a fraction flips its numerator and denominator - the reciprocal of 2/3 is 3/2. Multiplying a number by its reciprocal always gives 1.

📋 For the teacher
Teach it (10–15 min):
  • Say the chant together - "keep, change, flip" - every time until it is automatic.
  • Connect back to whole-number division they already know: 8 ÷ 2 asks "how many 2s are in 8?" Fraction division asks the same kind of question.
  • Have them check one answer by asking "does this many pieces make sense?" using a picture or fraction strips.
  • Remind them to simplify the final fraction and convert to a mixed number if that is the expected form.
Talk about it:
  • What does "keep, change, flip" mean, step by step?
  • Why does dividing by a fraction less than 1 give a bigger answer?
  • How can you check a fraction-division answer using multiplication?

Mastery looks like: They divide fraction-by-fraction problems using keep-change-flip and simplify the result correctly.

Common stumbles: Flipping the first fraction instead of the second; forgetting to simplify or convert to a mixed number.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

FractionsSlice bars and circles into equal parts and compare them.try →MultiplicationEqual groups and arrays make products finally click.try →DivisionShare fairly and build equal groups.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
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