ACT Math Pre-Algebra: Numbers, Ratios and Percents

ACT Math tests pre-algebra and number skills mainly through the Integrating Essential Skills category. Questions ask you to operate on integers, fractions, and decimals, set up ratios and proportions, apply percent increase and decrease, and convert between units inside word problems. ACT builds the category around skills learned before higher math and asks you to apply them to more complex problems, so expect the arithmetic to arrive inside multi-step setups.

This guide breaks down each skill area with the operations tested, common problem setups, and original practice examples. Work through the sections in order if number skills feel shaky, or jump straight to the topic slowing you down. Two free drills wait at the end of this guide: Pre-Algebra and Number Basics, and Proportions and Percents, each built to isolate the skill you are practicing.

Where Pre-Algebra and Number Questions Fit on the ACT Math Test

ACT Math has 45 questions in 50 minutes, and a calculator is allowed for the entire section. Of those 45 questions, 41 count toward your score and 4 are unscored field-test items mixed in without a label. Every scored question sorts into one of two weighted content categories, and the ACT weights below apply to scored content. ACT also reports Modeling as a third reporting category drawn from questions in the other two, so it overlaps them and carries no separate weight of its own.

The table below breaks down each category, its weight, and its subcategories.

Integrating Essential Skills, worth 20 percent of scored questions, is the direct home of pre-algebra arithmetic, ratios, percents, and unit conversions. The same category also carries area, surface area and volume, averages and medians, and expressing numbers in different ways, so the topics in this guide take up part of the 20 percent rather than all of it. Treat the 20 percent as a ceiling for arithmetic and percent work, not a floor.

Number and Quantity is a separate category at 10 to 12 percent of scored questions, and it covers real and complex number systems, integer and rational exponents, and vectors and matrices. Those topics belong to the advanced algebra side of ACT Math, not to the arithmetic, ratio, and percent work in this guide. Keep the two apart when you plan study time: number sense drills here, exponent and matrix review on the higher math side.

Integer, Fraction, and Decimal Operations

These operations show up as standalone questions and buried inside longer word problems. Speed and accuracy here free up time for the harder algebra and geometry questions later in the section. A single sign error or misplaced decimal turns a correct setup into a wrong answer, so build the habit of checking each step before you move on.

Order of Operations and Signed Numbers

PEMDAS sets the order for every expression: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. A negative sign multiplies or divides like any other signed number, and a negative times a negative gives a positive result. Adding a negative is the same as subtracting a positive, which keeps signed sums simple. Work one operation at a time and rewrite the full expression after each step.

Example: solve negative 5 plus 4 times the quantity 2 minus 8. Evaluate the parentheses first: 2 minus 8 equals negative 6. Then multiply: 4 times negative 6 equals negative 24. Then add: negative 5 plus negative 24 equals negative 29.

Fraction Operations

Four rules cover every fraction operation on the test.

• Add or subtract: find a common denominator, then combine the numerators.
• Multiply: multiply the numerators together and the denominators together.
• Divide: flip the second fraction and multiply.
• Simplify: divide the numerator and denominator by their greatest common factor.

Example: two thirds divided by four ninths becomes two thirds times nine fourths. Multiplying across the top and bottom gives eighteen over twelve. Dividing both parts by their greatest common factor of 6 leaves three halves.

Decimals and Place Value

Line up decimal points before adding or subtracting. Count the total decimal places in both factors before placing the decimal point in a product. Move the decimal point the same number of places in the divisor and dividend before dividing whole numbers. Example: 4.5 divided by 0.15 becomes 450 divided by 15 once both numbers are multiplied by 100, giving an answer of 30.

Ratios and Proportional Reasoning

A ratio compares two quantities, and a proportion sets two ratios equal to solve for a missing value. ACT ratio questions often hide inside word problems about mixtures, recipes, or scaled drawings. Read the wording closely, because a part to part ratio and a part to whole ratio lead to different setups and different answers.

Setting Up a Ratio

Write a ratio in the same order the question states it, and keep the units attached while you set it up. A class with 12 boys and 18 girls has a boy to girl ratio of 12 to 18, which simplifies to 2 to 3. The total parts in a ratio problem equal the sum of the ratio terms, useful for splitting a whole amount into ratio parts.

Solving a Proportion

Cross multiply to solve a proportion: set two fractions equal, multiply each numerator by the opposite denominator, then solve for the unknown. Example: a recipe uses 2 cups of flour for every 3 cups of sugar, and the question asks how much flour pairs with 12 cups of sugar. Set up 2 over 3 equals x over 12. Cross multiplying gives 3x equals 24, so x equals 8 cups of flour.

Percent Increase and Percent Decrease

Percent change questions show up as price changes, population changes, and measurement changes. The same formula solves every version once you identify the original value and the new value. The original value always sits in the denominator, so swapping the two values flips the result and lands you on a trap answer choice.

The Percent Change Formula

Percent change equals the amount of change divided by the original value, then multiplied by 100. A price rising from $40 to $50 changes by $10. Dividing the $10 change by the original value of $40 gives 0.25, or 25 percent. The table below sets out the formula for both directions.

Working Backward to an Original Value

Some questions give the final value after a percent change and ask for the original number. Set up an equation instead of guessing. A $60 jacket on sale for 25 percent off sells at 75 percent of the original price: 60 times 0.75 equals a sale price of $45.

Reverse the process when the original price is missing: divide the sale price by the remaining percent, expressed as a decimal. A sweater sells for $51 after a 15 percent discount, so $51 equals 85 percent of the original price. Divide 51 by 0.85 to get an original price of $60. Check the result: 60 times 0.15 equals a $9 discount, and 60 minus 9 equals $51.

Unit Conversion Word Problems

Unit conversion questions ask you to switch between units of length, weight, time, or volume inside a word problem. Set up the conversion with a factor equal to 1, and the wrong units cancel out on their own. Answer choices often include the number you get from multiplying when the setup calls for dividing, so let the units decide the direction of the fraction.

Single-Step Conversions

A conversion factor is a fraction built from two equal quantities in different units. Arrange the fraction so the unit you are removing sits opposite a matching unit and cancels. The unit left standing after cancellation is the fastest check on whether you built the fraction right side up. The list below holds the conversions worth memorizing before test day.

• 1 foot equals 12 inches
• 1 yard equals 3 feet
• 1 hour equals 60 minutes
• 1 pound equals 16 ounces

Multi-Step Conversions

Chain multiple conversion factors together when a problem skips a unit, such as converting inches directly to yards. Example: convert 90 inches to yards. First convert inches to feet: 90 divided by 12 equals 7.5 feet.

Then convert feet to yards: 7.5 divided by 3 equals 2.5 yards. Track the units at each step. A leftover unit in the answer signals a setup error before you finish.

Practice Pre-Algebra and Number Questions on 10exam

Two free drills on 10exam target the skills in this guide. The Pre-Algebra & Number Basics drill covers integer, fraction, and decimal operations. The Proportions & Percents drill covers ratios, percent change, and proportional word problems. Both drills are free and untimed, with instant explanations, and no signup is required.

For full length, timed Math practice under real test conditions, take one of our free practice tests on the ACT exam page. Review every missed pre-algebra or number question, then return to the matching drill above. Once ratios and percents feel solid, move on to our guide on linear equations, inequalities and systems. See our ACT Math section guide for the full format, calculator rules, and content breakdown across every category.

Sources

• The ACT Test for Students | ACT
• Description of Math Test | ACT