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ATI TEAS: Numbers and Algebra Concepts

Importance ★★★★★ · 53% (estimate)

Overview

This chapter covers the number skills used in everyday math: fractions, decimals, and percents, ordering numbers, ratios and proportions, and solving simple equations and inequalities. Many questions are word problems, so turning sentences into math is a key skill.

Fractions, decimals, and percents are three ways to write the same amount. To change a fraction to a decimal, divide the top by the bottom; to change a decimal to a percent, multiply by 100. When solving a problem with several operations, follow the order of operations: parentheses, exponents, multiplication and division from left to right, then addition and subtraction from left to right.

A ratio compares two amounts, and a proportion says two ratios are equal. You can solve a proportion by cross-multiplying. To solve an equation, do the same operation to both sides until the variable is alone. Inequalities work the same way, except that multiplying or dividing both sides by a negative number flips the inequality sign.

Key concepts

  • Fraction, decimal, percent

    Three forms of the same value. Divide numerator by denominator to get a decimal, then multiply by 100 to get a percent. Example: 3/4 = 0.75 = 75%.

    Memory tipPercent means per hundred.

  • Order of operations

    The agreed order for solving expressions: parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right).

    Memory tipPEMDAS, but do multiply/divide and add/subtract left to right.

  • Ratio

    A comparison of two quantities, written as 3:4, 3 to 4, or 3/4.

    Memory tipKeep the order of the words in the order of the numbers.

  • Proportion

    An equation stating that two ratios are equal, such as 2/5 = x/20. Solve by cross-multiplying: 2 x 20 = 5x, so x = 8.

    Memory tipLine up matching units on top and bottom before you cross-multiply.

  • Percent change

    How much an amount went up or down compared with where it started: (new - original) / original x 100.

    Memory tipAlways divide by the original amount.

  • Solving an equation

    Getting the variable alone by doing inverse operations to both sides. Example: 3x + 4 = 19, subtract 4 to get 3x = 15, divide by 3 to get x = 5.

    Memory tipUndo addition or subtraction first, then multiplication or division.

  • Inequality sign flip

    When you multiply or divide both sides of an inequality by a negative number, the sign reverses. Example: -2x > 6 becomes x < -3.

    Memory tipNegative multiply or divide = flip the sign.

Often tested

  • To compare fractions, decimals, and percents, change them all to decimals first.
  • "Of" in a percent problem usually means multiply: 20% of 50 = 0.20 x 50 = 10.
  • Check an equation's answer by putting it back into the original equation.
  • In word problems, "is" usually means equals, and "more than" means add.

3 sample questions

Verified practice questions from this unit.

Practice questionReviewedMathematics › Numbers and Algebra★★★★★

Question 1. What is 3/4 written as a percent?

  1. ① 34%
  2. ② 7.5%
  3. ③ 75%
  4. ④ 43%
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ③ 75%

Key point: Fraction → percent: divide, then multiply by 100

To change a fraction to a percent, divide and then multiply by 100.

  1. 3 ÷ 4 = 0.75
  2. 0.75 × 100 = 75%

Check: 75% of 4 is 3, so 3/4 = 75%.

Wrong choices

  • 34%: This just puts the 3 and 4 side by side; it is not a conversion.
  • 7.5%: The decimal point is in the wrong place; 0.75 × 100 = 75, not 7.5.
  • 43%: This reverses the digits and does not convert the fraction.
Practice questionReviewedMathematics › Numbers and Algebra★★★★★

Question 2. What is 0.6 written as a fraction in simplest form?

  1. ① 3/5
  2. ② 6/100
  3. ③ 1/6
  4. ④ 3/50
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ① 3/5

Key point: Decimal → fraction: use place value, then simplify

0.6 means six tenths.

  1. 0.6 = 6/10
  2. Divide top and bottom by 2: 6/10 = 3/5

Check: 3 ÷ 5 = 0.6.

Wrong choices

  • 6/100: 0.6 is six tenths, not six hundredths (0.06).
  • 1/6: 1/6 is about 0.17, not 0.6.
  • 3/50: 3/50 equals 0.06, not 0.6.
Practice questionReviewedMathematics › Numbers and Algebra★★★★★

Question 3. Which list orders these numbers from least to greatest? 0.45, 1/2, 3/8, 40%

  1. ① 40%, 3/8, 0.45, 1/2
  2. ② 1/2, 0.45, 40%, 3/8
  3. ③ 3/8, 0.45, 40%, 1/2
  4. ④ 3/8, 40%, 0.45, 1/2
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ④ 3/8, 40%, 0.45, 1/2

Key point: To compare, change all numbers to decimals

Change every number to a decimal, then compare.

  1. 0.45 = 0.45
  2. 1/2 = 0.50
  3. 3/8 = 0.375
  4. 40% = 0.40

Least to greatest: 0.375, 0.40, 0.45, 0.50 → 3/8, 40%, 0.45, 1/2.

Wrong choices

  • 40%, 3/8, 0.45, 1/2: 3/8 is 0.375, which is less than 40% (0.40).
  • 1/2, 0.45, 40%, 3/8: This is greatest to least, the reverse order.
  • 3/8, 0.45, 40%, 1/2: 0.45 is greater than 40% (0.40), so they are out of order.
Practice 5 questions from this unit →

AI-written · Verified · Written by AI. Only units that passed a separate AI check (re-reading facts and numbers) are published. Tell us if you find a mistake.