Solve ratio and rate problems, including unit rate. | Ratios, rates, proportional relationships, and units | SAT Math

核心知识

A unit rate is a rate with denominator 1. To find it, divide the numerator quantity by the denominator quantity: $t o t a l q u a n t i t y t o t a l u n i t s = r a t e p e r 1 u n i t$ .

深入理解

Unit rate is the "per 1" version of a rate.

Ratios compare same-kind quantities; rates compare different kinds.
Divide total quantity by total units to get the unit rate.
If the problem asks for a different amount, multiply the unit rate back up.
Trap: a part-to-part ratio like 3:5 is not the same as a part-to-whole fraction.

分步讲解

Identify the two quantities being compared.
Write them as a fraction with the 'per' quantity in the denominator.
Divide to get the rate per 1 unit.
If the problem asks for a different number of units, multiply the unit rate by that number.

常见误解

Confusing part-to-part ratio (3:5) with part-to-whole fraction $38$ .
Putting quantities in the wrong position — always check which unit should be 'per.'
Forgetting that 'miles per hour' means miles in the numerator, hours in the denominator.

题目

示例解析

A machine produces 84 widgets in 3.5 hours. At this rate, how many widgets does the machine produce per hour?

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