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Praxis Core · Mathematics (5733)

Praxis Core: Number and Quantity Concepts

Importance ★★★★★ · 36% (estimate)

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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.

Overview

This chapter is the largest part of the Math test. It covers integers, fractions, decimals, place value, ratios and proportions, percents, rates, and units of measurement. These skills also show up inside problems in every other chapter.

Fractions, decimals, and percents are three ways to write the same amount, so being able to switch between them quickly saves time. To find a percent of a number, change the percent to a decimal and multiply.

Ratios compare two amounts, and a proportion says two ratios are equal, which you can solve by cross-multiplying. Rates, such as miles per hour, are ratios with different units. Always convert to the same unit before you add, subtract, or compare measurements.

Key concepts

  • Percent of a number

    Change the percent to a decimal by dividing by 100, then multiply. For example, 15% of 80 = 0.15 × 80 = 12.

    Memory tip"Of" means multiply.

  • Percent change

    Percent change = (new value − old value) ÷ old value × 100. A positive result is an increase; a negative result is a decrease.

    Memory tipAlways divide by the ORIGINAL amount.

  • Proportion

    Two equal ratios, such as a/b = c/d. Solve by cross-multiplying: a × d = b × c, then divide to find the missing value.

    Memory tipKeep the same units in the same positions on both sides.

  • Rate and unit rate

    A rate compares two different units, like miles per hour. A unit rate gives the amount for one unit. Distance = rate × time.

    Memory tip"Per" means divide.

  • Fraction, decimal, percent

    The same value in three forms: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%. To turn a fraction into a decimal, divide the top by the bottom.

    Memory tipDecimal to percent: move the point two places right.

  • Unit conversion

    Multiply by a conversion factor equal to 1, such as 12 inches/1 foot or 60 minutes/1 hour, so the unwanted units cancel.

    Memory tipConvert first, then calculate.

  • Order of operations

    Do parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

    Memory tipPEMDAS: Please Excuse My Dear Aunt Sally.

Often tested

  • To find a percent of a number, change the percent to a decimal and multiply.
  • Set up a proportion as two equal ratios and cross-multiply.
  • Convert units before you add or compare measurements.
  • For percent change, divide the change by the original value.
  • Multiplication and division are done left to right, as are addition and subtraction.

3 sample questions

Verified practice questions from this unit.

Practice questionReviewedMathematics (5733) › Number and Quantity★★★★★

Question 1. What is 3/4 + 2/3?

  1. ① 5/7
  2. ② 11/12
  3. ③ 17/12
  4. ④ 1/2
  5. ⑤ 1/12
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Answer: ③ 17/12

Key point: Add fractions by first rewriting them with a common denominator.

  1. The common denominator of 4 and 3 is 12.
  2. 3/4 = 9/12 and 2/3 = 8/12.
  3. 9/12 + 8/12 = 17/12 (which is 1 and 5/12).

Check: 0.75 + 0.667 ≈ 1.417, and 17 ÷ 12 ≈ 1.417.

Wrong choices

  • "5/7": This adds the tops and the bottoms (3 + 2 and 4 + 3). Fractions need a common denominator first.
  • "11/12": This changes 3/4 to 9/12 correctly but writes 2/3 as 2/12 without multiplying the top by 4.
  • "1/2": This is the product 3/4 × 2/3 = 6/12, not the sum.
  • "1/12": This is the difference 9/12 − 8/12, not the sum.
Practice questionReviewedMathematics (5733) › Number and Quantity★★★★★

Question 2. What is 35% of 240?

  1. ① 84
  2. ② 156
  3. ③ 840
  4. ④ 275
  5. ⑤ 8.4
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ① 84

Key point: Percent of a number: change the percent to a decimal and multiply.

  1. 35% = 0.35.
  2. 0.35 × 240 = 84.

Check: 10% of 240 is 24, so 30% is 72 and 5% is 12; 72 + 12 = 84.

Wrong choices

  • "8.4": This moves the decimal one place too far. 35% is 0.35, not 0.035.
  • "156": This is 240 − 84, the part that is NOT 35%.
  • "840": This uses 3.5 instead of 0.35.
  • "275": This simply adds 35 and 240.
Practice questionReviewedMathematics (5733) › Number and Quantity★★★★★

Question 3. In a class of 40 students, the ratio of boys to girls is 3 to 5. How many girls are in the class?

  1. ① 15
  2. ② 24
  3. ③ 8
  4. ④ 20
  5. ⑤ 25
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ⑤ 25

Key point: A ratio a:b splits a total into a + b equal parts.

  1. Total parts: 3 + 5 = 8.
  2. Each part: 40 ÷ 8 = 5 students.
  3. Girls: 5 parts × 5 = 25.

Check: boys = 3 × 5 = 15, and 15 + 25 = 40.

Wrong choices

  • "15": 15 is the number of boys, not girls.
  • "24": This finds 3/5 of 40. The girls are 5 out of 8 total parts, not 3/5.
  • "8": 8 is the total number of ratio parts (3 + 5), not the number of girls.
  • "20": This splits the class in half, ignoring the 3-to-5 ratio.
Practice 5 questions from this unit →