GED and HiSET mathematics — number, ratio and percent

Roughly half of the mathematics paper is number sense: percentages, ratios, rates and fractions, applied to money, time, weight and distance. These twelve are all of that kind, and all of them are calculations someone might actually do standing in a shop or reading a work sheet.

The percentage questions are built around the thing that makes percentages hard, which is that the base changes under your feet. A shirt costs forty dollars, rises by ten percent and then falls by ten percent — and ends at thirty-nine dollars sixty, because the fall was taken from forty-four while the rise was taken from forty. A pair of shoes is sixty dollars after twenty-five percent off, and the original price is found by dividing rather than by adding the same percentage back. A discount is followed by a sales tax, and the tax is charged on what is actually being paid.

Two more are about comparison. Coffee comes in a twelve-ounce bag at nine dollars and a twenty-ounce bag at fourteen: seventy-five cents an ounce against seventy, so the bigger bag costs more in total and less per ounce at once, which is exactly what a unit price on a shelf label exists to show. And three pieces of trim — three-quarters of a foot, a half, five-eighths — have to be counted in the same size of piece before they can be added at all. The wrong answer there is nine-fourteenths, from adding the tops and the bottoms separately; it is worth seeing named, because it produces a total shorter than the shortest piece in the sum, which gives it away without any arithmetic.

The rest is the everyday machinery: a prize split three to two, a recipe scaled from four people to ten, an hourly rate across a thirty-two-hour week, miles per gallon, two hundred and fifty minutes turned into hours and minutes, fifteen dollars saved out of sixty expressed as a percent, and a ten-percent fee estimated from a rounded figure in your head.

Everything is written in plain words and digits, with no notation to decode and no charts to read — sums can be done on paper or aloud.

Zestly is an independent study tool. It is not affiliated with GED Testing Service, which owns the GED test, or with the HiSET program, and it is not a test centre.

• Compare two package sizes by price per unit
• Apply a percentage rise and then a fall, keeping track of which base each is taken from
• Find a price before a discount, and apply a discount followed by a sales tax
• Share an amount in a given ratio, and scale a recipe by a unit rate
• Work out earnings from an hourly rate, and fuel use in miles per gallon
• Convert minutes into hours and minutes
• Add fractions by rewriting them over a common denominator, and see why adding tops and bottoms fails
• Express one quantity as a percent of another, and check a fee mentally using round numbers

Written for this exercise, in plain words and digits with no notation. From the bank: "A shirt is priced at 40 dollars. The price first rises by 10 percent, and then the new price falls by 10 percent. What is the final price?" It is 39 dollars 60, not 40 — the rise is taken from 40 and the fall from 44, and one of the offered answers is the intuition that the two cancel.