GED and HiSET mathematics — signed numbers, absolute value and order of operations

Negative numbers show up everywhere in adult life: a bank balance that dips below zero, a January morning at eight below, a business month that ends in a loss, a basement floor below street level. On the GED Mathematical Reasoning test and the HiSET Mathematics test they appear both in word problems and inside longer calculations, where one dropped sign turns a right method into a wrong answer. This material trains the rules for signed numbers and the order of operations until they are automatic.

The twelve quiz questions each cover a different situation. You find how many degrees the temperature rose from $-8$ to 15 degrees Fahrenheit, follow a checking account through a withdrawal into an overdraft, and multiply and divide negatives in one expression. You measure the distance between two points on a number line and evaluate an expression with absolute value bars. You put negative fractions and decimals in order, choose the number that lies between $-5$ and $-4$, and compute the height difference between a diver below sea level and a hiker on a hill. The order-of-operations questions include an exponent applied to a negative result inside parentheses, a fraction bar that groups a whole numerator, and the classic trap of $-3^2$ against $(-3{)}^2$. The last question averages four months of business results, two profits and two losses.

Each wrong option comes from a real slip: subtracting a negative instead of adding, reading $-\frac{2}{3}$ as smaller than $-0.75$, treating $|-4|$ as $-4$, squaring before the parentheses are finished, or getting the right size with the wrong sign. The explanation after each answer shows where that slip happens.

The flashcards review the sign rules for multiplication and division, absolute value, opposites, how the number line orders numbers, the order of operations, subtracting a negative, and the fraction bar as a grouping symbol.

The written work asks you to show your steps on paper for account balances, temperature swings, ordering numbers, absolute value and multi-step expressions, and to explain why each rule works. The oral exam asks one question at a time and expects you to talk through the signs, the way you would check a bank statement out loud.

The material is independent practice written by Zestly, based on the published content of the GED and HiSET mathematics tests; it is not produced or endorsed by GED Testing Service or ETS.

• Add, subtract, multiply and divide signed numbers in real situations
• Use absolute value as the distance between two numbers
• Order integers, negative fractions and decimals on the number line
• Apply the order of operations with exponents, parentheses and fraction bars
• Distinguish -a^2 from (-a)^2
• Interpret negative results as overdrafts, losses or positions below a reference point

Practice material written by Zestly, based on the published content of the GED Mathematical Reasoning test (quantitative problem solving: rational numbers, absolute value, order of operations) and the HiSET Mathematics test (number and operations).