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PEAZIT Aha card

Dividing fractions: how many pieces fit?

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3/4 ÷ 1/8 asks how many eighths fit in three quarters. Divide by a nonzero fraction by multiplying by its reciprocal.

Three quarters are six eighths.
ExpressionMeaning
3/4 ÷ 1/8Count eighth-sized pieces.
3/4 × 8/1Invert only the divisor.
24/4 = 6Six eighths fit in three quarters.

One worked example

  1. 3/4 ÷ 1/8Count eighth-sized pieces.
  2. 3/4 × 8/1Invert only the divisor.
  3. 24/4 = 6Six eighths fit in three quarters.

Watch out: Division by zero is undefined. Invert only the divisor, not both fractions.

Goal, prerequisites and card origin

What you will learn: Divide by a fraction using its reciprocal.

What you need first: Fraction multiplication and reciprocals.

An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1

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3/4 ÷ 1/8 asks how many eighths fit in three quarters. Divide by a nonzero fraction by multiplying by its reciprocal.

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