Explain how many times one quantity is another

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Explain how many times one quantity is another

If A: B = 3: 2, then A = (3/2)B and B = (2/3)A. The multiplier depends on which direction the comparison is made. A verbal description such as “A is one and a half times B” expresses the first relationship.

A difference describes an additive relationship, while a ratio describes a multiplicative one. For positive quantities with ratio 3: 2, the difference changes as the overall scale changes even though the ratio remains fixed.

Use the multiplier to move from a known value to its corresponding value. Check by forming the ratio again. Avoid translating “three times as much” into “three more”, which changes the model.

Worked example: A: B = 3: 2 and B = 10. Find A.

A is 3/2 times B.

Calculate (3/2) × 10.

Answer: 15.

Check your understanding: If both quantities double, does their ratio change?

Answer: No.

Why: The common multiplier cancels from the comparison.