L2 · Equivalent ratios

Learning goal

“I can make an equivalent ratio by multiplying or dividing BOTH terms by the same number, use a ratio table to find missing terms, and judge whether two ratios are equivalent - and I know adding the same number to both terms does NOT work.”

Equivalent ratios — ratios that describe the same comparison (2 : 3 and 6 : 9).

Ratio table — a table that lists pairs of terms in the same ratio, row by row.

Scale factor — the number both terms are multiplied or divided by to move between equivalent ratios.

Worked example

Lemonade mixes 2 cups of concentrate with 3 cups of water: ratio 2 : 3. Step 1: To make a double batch, multiply BOTH terms by 2: 4 : 6. Same taste - same ratio. Step 2: Build the ratio table: concentrate 2, 4, 6, 8 over water 3, 6, 9, 12. Step 3: Scaling by 4 from the first row: 2 x 4 = 8 and 3 x 4 = 12, so 2 : 3 = 8 : 12. On the double number line, every pair of aligned marks is the same ratio. Multiplying only ONE term changes the comparison - both terms scale, or the ratio changes.

Check yourself — explain it

Why is 6 : 9 the same ratio as 2 : 3?

Paired problem — example still visible

Scale 3 : 5 by 2 -> 6 : 10

Faded completion — last step is yours

"4 : 7 scaled by 3 is 12 : ___" -> 21

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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