Ratios and Proportions on the GED Math Test

The wrong answers here are rarely arithmetic slips. They come from a wrong idea about how the numbers move: adding 5 to the price because the count went up by 5, assuming the biggest bag is the best deal, dividing a map distance when real life should be the bigger number. The practice set writes each of those ideas into the answer choices.

Ratios and proportions belong to "quantitative problem solving with rational numbers", weighted by GED Testing Service at 25% of the test and shared with number operations, fractions, decimals, percents and exponents: eleven or twelve of about 46 questions for the group. Two to four of them on ratios is our arithmetic, with no official count published.

Skills in this set: Unit rates · Solving a proportion for a missing value · Scaling a recipe up or down · Scale drawings, maps and models · Comparing unit prices to find the better buy · Distance, rate and time with d = rt

What the test asks

Three indicators in the Assessment Guide for Educators carry this topic. Q.3.a is unit rates, with the examples the guide itself gives: price per item, speed, population density. Q.3.b is scale factors, converting between a scale drawing and real dimensions in both directions. Q.3.c is multi-step real-life problems with ratios or proportions, some of which need a unit conversion along the way. The formula sheet prints d = rt and total cost = number of units × price per unit, which is the better-buy comparison as a formula.

The settings are everyday: three sizes of one product in a price table, a rice recipe scaled for a crowd, a commuter train at a steady speed, a floor plan where one inch is 4 feet. Items can be grouped two or three to one stimulus, so a price table may carry more than one question. Our recipe items use drag-and-drop, with leftover amounts that come from adding instead of multiplying.

A proportion with friendly numbers fits the opening no-calculator section, where the first five or so questions are done by hand: $36 for 4 tickets, for instance. In the calculator part, better-buy comparisons and d = rt problems with decimal times lean on the TI-30XS, and the skill becomes setting the division up the right way round.

The mistakes this set is built to catch

Each wrong answer in the practice set is the result of one specific slip, and the explanation names it. These are the ones that come up most in this topic.

A worked example

How to practice it

1. Solve every proportion two ways until they agree by reflex: find the amount for one and multiply by the new count, then write two equal fractions with matching units in matching positions and check that the cross products match. When the two disagree, you have found a mistake before the test did.
2. Practice unit prices with a grocery flyer: pick any product sold in two sizes, divide each price by its weight, and say which is cheaper per ounce before you look at the sizes.
3. For scale and map questions, write the scale as a ratio with units, 1 inch : 20 miles, and decide the direction before you compute. Drawing to real life multiplies, real life to drawing divides, and the answer should land on the bigger or smaller side accordingly.
4. With d = rt, label all three quantities before you use the formula, and turn minutes into hours when the speed is in miles per hour. Multiply for distance, divide distance by rate for time, divide distance by time for rate, and multiply back to see whether the distance returns.