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Math Domain Topic Review Guide

Fractions, Decimals & Number Operations

Master fraction arithmetic, decimal conversions, mixed numbers, and non-calculator computation strategies.

🎯 Core Competencies Covered

  • Finding Least Common Denominators (LCD) for addition and subtraction.
  • Applying Keep-Change-Flip (KCF) for fraction division.
  • Converting between fractions, decimals, and percentages.
  • Mental arithmetic strategies for non-calculator testing.

Understanding Fraction Operations on the ParaPro

Fractions represent one of the most frequently tested concepts on the Mathematics subtest. Because calculators are prohibited, mastering common denominators, fraction reduction, and mixed number arithmetic is essential for achieving a high scaled score.

1. Adding and Subtracting Fractions (Finding the LCD)

Fractions cannot be combined until they share a common denominator. The Least Common Denominator (LCD) is the smallest multiple shared by both denominators:

  • Example: 1/4 + 2/3
  • Common denominator of 4 and 3 is 12.
  • Convert: (1*3)/(4*3) = 3/12 and (2*4)/(3*4) = 8/12
  • Add numerators: 3/12 + 8/12 = 11/12

2. Dividing Fractions (Keep, Change, Flip)

Dividing by a fraction is mathematically identical to multiplying by its reciprocal:

  • Keep the first fraction unchanged.
  • Change the division sign to multiplication.
  • Flip the second fraction (invert numerator and denominator).
  • Example: 3/5 ÷ 2/3 = 3/5 * 3/2 = 9/10

Step-by-Step Worked Practice Problem

Exam Sample Problem:

A teacher asks an aide to divide 5 1/4 cups of paint equally among 7 student easel trays. How many cups of paint should each tray receive?

Step-by-Step Solution:
  1. Convert mixed number 5 1/4 to an improper fraction: (5 * 4) + 1 = 21/4.
  2. Express the whole number 7 as a fraction: 7/1.
  3. Apply Keep-Change-Flip: 21/4 ÷ 7/1 = 21/4 * 1/7.
  4. Cross-simplify 21 and 7 (divide by 7): (3/4) * (1/1) = 3/4 cup.
  5. Answer: Each tray receives 3/4 cup of paint.

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Frequently Asked Questions

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator (e.g. 3 2/5 = (3*5)+2 = 17/5).

What is the fastest way to compare two fractions without a calculator?

Use cross-multiplication: to compare a/b and c/d, compare (a*d) with (b*c). For example, comparing 3/7 and 4/9: 3*9=27 vs 7*4=28. Since 28 is larger, 4/9 is greater.