L3 · Proportions: stating equivalence

Learning goal

“I can state a proportion - two equal ratios written as fractions, a/b = c/d - and find a missing term by spotting the scale factor between the two ratios.”

Proportion — a statement that two ratios are equal, written like 2/3 = 4/6.

Term (of a proportion) — each of the four numbers in a proportion.

Missing term — the unknown value in a proportion, often written as n, to be found by scaling.

Worked example

3 pens cost $6. A pack of 6 of the same pens costs $12. Step 1: Write each deal as a ratio in fraction form, keeping the same order (pens over dollars): 3/6 and 6/12. Step 2: The deals are the same value - 6/12 scales down to 3/6 - so state the equivalence: 3/6 = 6/12. That statement is a proportion. Step 3: Read it in words: '3 pens for $6 is the same rate as 6 pens for $12.' On the double number line, pens 0, 3, 6 align with dollars 0, 6, 12 - the pairs line up because the ratios are equal. A proportion is a sentence that says 'this ratio equals that ratio,' and the order of quantities must match on both sides.

Check yourself — explain it

A proportion is a statement that...

Paired problem — example still visible

5 apples cost $10; 10 of the same apples cost $20. Write the proportion (apples over dollars) -> 5/10 = 10/20

Faded completion — last step is yours

"4/5 = ___/15" -> 12

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

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