GRE Arithmetic: Integers, Fractions, Decimals and Exponents

By Muntasir Jul 26, 2026 10 min read

TL;DR

GRE arithmetic questions test four related skills: integer properties, fraction and decimal conversion, order of operations, and exponent and root rules. ETS groups all of it under Arithmetic, one of four content areas in Quantitative Reasoning, alongside Algebra, Geometry and Data Analysis.

Know your divisibility rules, prime numbers below 20, and sign rules for odd and even numbers.
Convert fractions to decimals and back without a calculator for common values like halves, thirds, quarters and fifths.
Memorize the core exponent rules: zero exponent, negative exponent, and fractional exponent as a root.
A single on-screen calculator covers the whole Quant section, but most questions reward number sense over button-pressing.

GRE Arithmetic: Integers, Fractions, Decimals and Exponents

Integers, fractions, decimals, exponents and roots make up the arithmetic foundation of GRE Quantitative Reasoning. Almost every quant question leans on at least one of these skills, whether the question is a straightforward calculation or a multi-step algebra or geometry problem wrapped around a number-property trap. Weak arithmetic habits cost you time on questions you already know how to solve.

This guide walks through the rules ETS expects you to know cold: integer properties, fraction and decimal operations, order of operations with mixed number forms, exponent rules, and root simplification. Each section gives you the rule first and a worked example second. It closes with the traps showing up most often in this content area and where to drill each skill.

Where This Topic Fits on the GRE

ETS organizes the GRE Math Review into four parts, and Part 1, Arithmetic, covers exactly this material: integers, fractions, exponents and roots, decimals, real numbers, ratio and percent. Quantitative Reasoning questions draw on this arithmetic content area alongside algebra, geometry and data analysis. Arithmetic also sits underneath the other three areas, since algebra and geometry answers still come down to number work at the final step.

Our full GRE Quantitative Reasoning guide covers the section structure, timing and all four question formats. Percent, ratio and proportion questions build on the same fraction skills covered here and get their own treatment in our guide to GRE percents, ratios and proportions. Start with this page if fractions and exponents slow you down, then move to the percent material.

Integer Properties

Integer questions test whether you know the rules, not whether you are able to do long division. Three areas come up again and again: primes and factors, divisibility, and the sign and parity rules for odd and even numbers. Each one rewards recall, so drill them until the answers arrive without calculation.

Prime Numbers and Factors

A prime number has exactly two positive factors: 1 and itself. The number 1 is not prime, and 2 is the only even prime. The prime numbers below 20 are 2, 3, 5, 7, 11, 13, 17 and 19, worth memorizing since they appear constantly in factor and divisibility questions.

Every integer greater than 1 breaks down into a unique product of primes, its prime factorization. Finding the prime factorization of a number is the fastest route to its full list of factors, its greatest common factor with another number, and its least common multiple. Break 84 into 2 times 2 times 3 times 7, and every factor of 84 falls out of those four primes.

Divisibility Rules

Divisibility rules let you check whether one integer divides another without doing the division. They save time on factor questions, remainder questions and quantitative comparisons where the exact quotient never matters. The table below covers the rules tested most often.

Divisor	Rule
2	Last digit is even
3	Sum of digits is divisible by 3
4	Last two digits form a number divisible by 4
5	Last digit is 0 or 5
6	Divisible by both 2 and 3
8	Last three digits form a number divisible by 8
9	Sum of digits is divisible by 9
10	Last digit is 0

Odd, Even and Sign Rules

Odd and even outcomes follow fixed patterns under addition and multiplication. Even plus even stays even, odd plus odd also lands on even, and odd plus even gives odd. For multiplication, the product is even whenever at least one factor is even, and odd only when every factor is odd.

Sign rules follow the same kind of pattern. A product or quotient of two negative numbers is positive, and a product or quotient with one negative and one positive term is negative. Zero is even, and it is neither positive nor negative, a distinction showing up directly in trap answer choices.

Fractions and Decimals

Fraction and decimal fluency saves time on nearly every quant question, since converting between forms mid-problem is often faster than working through one form to the end. Decimals suit addition, subtraction and quick size comparisons. Fractions suit multiplication, division and any expression where terms cancel.

Converting Between Fractions and Decimals

Memorizing the common conversions below removes a step from many problems and lets you check numeric entry answers fast. Thirds repeat forever, so round them only at the final step of a calculation. The other values in this table terminate and are safe to use mid-problem.

Fraction	Decimal
1/2	0.5
1/3	0.333...
2/3	0.666...
1/4	0.25
3/4	0.75
1/5	0.2
1/8	0.125

Fraction Operations

Three rules cover almost all fraction work on the GRE. Treat them as fixed procedures so the arithmetic runs without a decision at each step. Apply them in this form:

Add or subtract only after rewriting both fractions over a common denominator.
Multiply straight across: numerator times numerator, denominator times denominator, then simplify.
Divide by a fraction by multiplying by its reciprocal, so dividing by 2/3 is the same as multiplying by 3/2.

Simplify fractions by dividing the numerator and denominator by their greatest common factor before doing more work on them. A fraction reduced early stays smaller and easier to manage through the rest of the problem, and it matches numeric entry answer formats expecting the simplest form. Cancelling common factors before you multiply keeps the numbers small enough to handle by hand.

Order of Operations with Mixed Number Forms

Order of operations follows one fixed sequence, and GRE problems complicate it by mixing fractions, decimals and negative numbers inside the same expression. Work the four steps in order every time, moving left to right within a step. Jumping ahead to the easy-looking operation is where most sign and grouping errors start.

Parentheses and any other grouping symbols.
Exponents and roots.
Multiplication and division, left to right.
Addition and subtraction, left to right.

Treat a fraction bar as a grouping symbol. Everything above the bar and everything below it gets fully simplified before the division happens. In an expression like (3 + 5) / (2 squared minus 2), work out the numerator and the denominator completely first, then divide the two results.

Negative signs need the same care. Squaring a negative number in parentheses, such as (-3) squared, gives a positive result, while a negative sign written outside the parentheses, as in negative 3 squared, applies the negative only after the squaring and stays negative. The first expression equals 9 and the second equals negative 9, so read the parentheses before you compute.

Exponent Rules

Exponent rules are fixed identities, and GRE quant questions reward speed at applying them over deriving them from scratch each time. Most exponent questions combine two or three of the rules inside a single expression. The table below lists the rules worth memorizing, each with a worked example.

Rule	Example
a to the 0 equals 1, for a not equal to 0	7 to the 0 equals 1
a to the negative n equals 1 over a to the n	2 to the negative 3 equals 1/8
a to the m times a to the n equals a to the (m + n)	2 cubed times 2 squared equals 2 to the 5th, or 32
a to the m divided by a to the n equals a to the (m minus n)	5 to the 6th divided by 5 squared equals 5 to the 4th
(a to the m) to the n equals a to the (m times n)	(3 squared) cubed equals 3 to the 6th
(ab) to the n equals a to the n times b to the n	(2 times 5) squared equals 4 times 25, or 100

Negative and Zero Exponents

A negative exponent sends the base to the denominator of a fraction, it does not make the value negative. So 2 to the negative 3 equals 1/8, a positive number smaller than 1, not negative 8. Any nonzero number raised to the power 0 equals 1, including large or fractional bases.

Fractional Exponents

A fractional exponent describes a root. The exponent 1/n means the nth root, so 8 to the 1/3 equals the cube root of 8, which is 2. An exponent of m/n means the nth root of the base raised to the m power, so 16 to the 3/4 equals the fourth root of 16 raised to the third power, which is 2 cubed, or 8.

Root Simplification and Estimation

Simplify a square root by pulling out the largest perfect square factor. The square root of 72 splits into the square root of 36 times the square root of 2, which simplifies to 6 times the square root of 2, since 36 is the largest perfect square factor of 72. Knowing the perfect squares through 225 makes the right split obvious at a glance.

Estimate a square root outside the perfect squares by locating it between two consecutive perfect squares. The square root of 50 falls between the square root of 49 and the square root of 64, so it sits between 7 and 8, close to 7.1. This estimate is enough to answer many quantitative comparison and estimation questions without a calculator.

The On-Screen Calculator

ETS provides one basic on-screen calculator for the entire Quantitative Reasoning measure, not a separate calculator per question type, and it is not available during Verbal Reasoning or Analytical Writing. The on-screen calculator supports the four basic operations and square root, plus memory buttons and a Transfer Display button sending a computed result straight into a Numeric Entry answer box. The same tool sits on every Quant question, so there are no per-topic calculator rules to track.

ETS designed most Quant questions to reward number sense over heavy computation, so the calculator works best as a check on work done by hand rather than a replacement for the rules in this guide. Relying on it for every step costs time you need for reading and reasoning. Save it for messy decimal arithmetic and square roots, and keep fraction and exponent work on paper.

Common GRE Traps in This Area

The same handful of traps reappear across integer, fraction and exponent questions. Most of them punish an assumption carried over from positive integers into fractions or negative numbers. Watch for these before you commit to an answer.

1 is not prime, and 2 is the only even prime, a fact tested directly in factor and divisibility questions.
Zero is even and neither positive nor negative, so an "odd or negative" answer choice built around zero is wrong.
A negative base raised to an even exponent turns positive, while an odd exponent keeps the negative sign, a frequent quantitative comparison setup.
Squaring a proper fraction between 0 and 1 makes it smaller, not larger, the opposite of what squaring does to integers above 1.
A negative exponent produces a small positive fraction, never a negative number.
Dividing a positive number by a fraction between 0 and 1 increases the value, the reverse of the usual effect of division. The same division makes a negative number smaller, since negative 4 divided by 0.5 equals negative 8.

These rules turn into speed once you drill them with a clock running. We offer three difficulty levels of free drills for each arithmetic topic. Start at the level where you miss about one question in four, then work up.

Integers and number properties: easy, medium, hard
Fractions and decimals: easy, medium, hard
Exponents and roots: easy, medium, hard

Every set is free with no signup required. Full-length practice tests and Quant section practice sit on our GRE practice page. Run your results through our GRE score calculator to see how a stronger arithmetic score moves your Quant total.