Arithmetic (Beginner) · Quick Reference

Fractions Cheat Sheet

Arithmetic (Beginner) · Lesson 8/21

In one line: a fraction represents a part of a whole, written as numerator over denominator.

Key Ideas

1Numerator and Denominator. In a/b, a (numerator) is the number of parts taken, b (denominator) is the total number of equal parts.

2Proper, Improper, Mixed. Proper: numerator < denominator (3/4). Improper: numerator ≥ denominator (7/4). Mixed: a whole number plus a fraction (1 3/4).

3Equivalent Fractions. Fractions that represent the same value, found by multiplying or dividing top and bottom by the same number.

4Simplifying. Divide numerator and denominator by their greatest common factor to reduce a fraction.

5Adding/Subtracting Fractions. Fractions need a common denominator before adding or subtracting.

Worked Examples

Simplify 12/16.

3/4

Add 1/4 + 1/3.

7/12

Multiply 2/3 x 3/5.

2/5

Formulas

a/b + c/d = (ad + bc) / bd

a/b x c/d = ac/bd

a/b ÷ c/d = a/b x d/c

Practice Yourself

Simplify 8/12.

2/3

Convert 7/2 into a mixed number.

3 1/2

Add 1/2 + 1/6.

2/3