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PEAZIT Aha card

Equivalent fractions change the pieces, not the amount

Splitting every piece equally multiplies both the total number of pieces and the selected number. Multiply both numerator and denominator by the same non-zero number.

The selected half of the chocolate stays the same size.

Before	Change to pieces	Same amount
1/2	Split each piece into 3	3/6
3/6	Group pieces in threes	1/2

One worked example

1/2Take one of two equal parts.
(1 × 3)/(2 × 3) = 3/6Split each half into three. We now have 3 selected pieces out of 6.

Watch out: Adding the same number to numerator and denominator does not generally preserve a fraction. To simplify, divide both by a common factor.

Goal, prerequisites and card origin

What you will learn: Make equivalent fractions and simplify them without changing their value.

What you need first: Numerator and denominator; multiplying and dividing whole numbers.

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

Show connections

Fractions: equal parts of a whole

One whole — divide into 4 equal parts — Whole divided into quarters

Whole divided into quarters — select 3 equal parts — Three of four parts: 3/4

Three of four parts: 3/4 — halve each part: same value — Six of eight parts: 6/8

Six of eight parts: 6/8 — still represents three quarters of the whole — One whole

Splitting every piece equally multiplies both the total number of pieces and the selected number. Multiply both numerator and denominator by the same non-zero number.