Year 4 Maths · Number strand

Equivalent Fractions with Crafting Recipes

Fill Minecraft crafting grids to discover when two fractions are the same amount — just cut into different-sized pieces.

Section 1 · Equivalent fractions

Crafting Grid Fractions

By the end of this section I can represent, simplify and prove equivalent fractions using crafting grids — so I can recognise when two recipes yield the same amount.

Success criteria 0 / 4 ticked

Tick each one when you can do it without help.

1A Fractions on a Crafting Grid

A crafting grid is a perfect fraction model. A 3×3 grid has 9 cells — that is your denominator. The cells you fill are your numerator. Fill 6 of 9 and you have 6/9 of the grid crafted.

Key terms

numerator denominator simplify equivalent

The numerator (top) counts filled cells. The denominator (bottom) counts all cells. To simplify, divide both by the same number. Two fractions are equivalent if they simplify to the same thing.

Simplify 6/9 from a 3×3 grid

Grid: 9 cells total, 6 filled → 6/9
Both 6 and 9 divide by 3 → GCD = 3 greatest common divisor
6 ÷ 3 = 2,   9 ÷ 3 = 3 → 2/3
So 6/9 = 2/3 simplest form — no further simplifying

Interactive · tap cells to fill the crafting grid

Check yourself

A 3×3 crafting grid has 9 cells. You fill 3 cells, then simplify. What fraction is filled? 3/9 = ?

Find the biggest number that divides into both 3 and 9, then divide top and bottom by it.
Both 3 and 9 divide by 3.   3 ÷ 3 = 1, 9 ÷ 3 = 3.   So 3/9 = 1/3.

A 2×4 crafting grid has 8 cells. You fill 4 cells, then simplify. What is the simplified fraction? 4/8 = ?

Both 4 and 8 divide by 4 — try dividing top and bottom by that.
Both 4 and 8 divide by 4.   4 ÷ 4 = 1, 8 ÷ 4 = 2.   So 4/8 = 1/2.

A 3×4 crafting grid has 12 cells. You fill 9 cells, then simplify. What is the simplified fraction? 9/12 = ?

Find the greatest common divisor of 9 and 12 — it is 3.
Both 9 and 12 divide by 3.   9 ÷ 3 = 3, 12 ÷ 3 = 4.   So 9/12 = 3/4.

1B Proving Equivalent Fractions

Two crafting grids with different numbers of cells can show the same amount. If you fill 4 of 6 cells on one grid and 6 of 9 on another, both simplify to 2/3 — the recipes are equivalent.

Prove 4/6 = 6/9

Grid A (2×3 = 6 cells): fill 4 → 4/6
Simplify: 4 ÷ 2 = 2,   6 ÷ 2 = 3 → 2/3
Grid B (3×3 = 9 cells): fill 6 → 6/9
Simplify: 6 ÷ 3 = 2,   9 ÷ 3 = 3 → 2/3
Both equal 2/3, so 4/6 = 6/9 equivalent ✓

Interactive · fill both grids, then check equivalence

Grid A — 2×4 (8 cells)
Grid B — 3×4 (12 cells)

Check yourself

Complete the equivalent fraction: 1/3 = ?/9

Ask: what do you multiply 3 by to get 9? Multiply the numerator by the same number.
3 × 3 = 9, so multiply the top by 3 as well: 1 × 3 = 3.   So 1/3 = 3/9.

Complete the equivalent fraction: 2/5 = ?/10

What do you multiply 5 by to get 10? Do the same to the numerator.
5 × 2 = 10, so multiply the top by 2: 2 × 2 = 4.   So 2/5 = 4/10.

Are 4/6 and 6/9 equivalent? Type yes or no.

Simplify both fractions and check if they give the same result.
4/6: divide by 2 → 2/3.   6/9: divide by 3 → 2/3.   Both simplify to 2/3, so yes, they are equivalent.

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