Number Operations on the GED Math Test

Marks go missing here for small reasons. Reading 8 + 5 × 3 left to right gives 39 instead of 23, and 39 will be among the answer choices. A temperature starting at −6°F that rises 10 degrees ends at 4°F, but a dropped minus sign puts it at 16°F, another choice. The practice set here is built from those slips.

On the score report this topic sits in "quantitative problem solving with rational numbers", weighted by GED Testing Service at 25% of the test. That category also holds fractions, decimals, percents, ratios and exponents, so the whole group is eleven or twelve of the roughly 46 questions, and two to four of those on number operations is our arithmetic rather than an official count.

Skills in this set: Order of operations · Evaluating expressions with integers · Adding and subtracting signed numbers · Sign rules for signed numbers · Absolute value and distance on a number line · Rounding and estimating · Least common multiple and greatest common factor · Converting units within a measurement system

What the test asks

Several indicators in the Assessment Guide for Educators cover this topic. Q.2.a is arithmetic with rational numbers, here meaning integers and the sign rules. Q.2.e is multi-step arithmetic problems from real life, where the order of operations lives, since a two-step word problem is an expression in disguise. Q.1.b is factors and multiples, including LCM and GCF; Q.1.d is absolute value as distance from zero. Unit conversions sit inside Q.3.c, the ratio indicator, which names them outright.

The contexts are ordinary: temperatures below zero, an overdrawn checking account, a diver below sea level, an attendance figure to round, two buses on different schedules, a board measured in feet and inches. About half of all items are written at depth-of-knowledge level 2, which here means two or three moves rather than one bare calculation.

This is the topic to expect in the opening no-calculator section. The test starts with about five questions GED Testing Service describes as mental math, and its math content specialist lists non-calculator items among the four areas where test-takers are weakest, so the by-hand items in this set deserve slow attention. After the three-minute break the on-screen TI-30XS handles the remaining forty or so questions.

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. Before you calculate an expression, number the operations in the order you will do them, the order many people memorize as PEMDAS: parentheses, exponents, multiplication and division, addition and subtraction. Cross each one off as you go. It is slow at first and automatic soon after.
2. Do every signed-number problem on a number line until you stop needing it: mark the start, draw an arrow right for each increase and left for each decrease, and read off where you land. The direction of the arrow is all the sign rules are about.
3. Decide which question a factor-or-multiple word problem is asking before you touch the numbers. Two cycles that need to line up again is a least common multiple: list multiples, take the first match. One pile to split into identical groups is a greatest common factor: list factors, take the largest match.
4. Say conversions as two-step chains, 3 feet is 36 inches plus 7 is 43, and then check the direction. Feet to inches makes the number much bigger and minutes to hours much smaller, so a result that moves the wrong way is wrong before you check the arithmetic.