Fraction Multiplication and Division

Overview

This lecture covers how to multiply and divide fractions, including step-by-step examples and how to simplify results.

To multiply fractions, multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
Example: ( \frac{7}{9} \times \frac{2}{3} = \frac{7 \times 2}{9 \times 3} = \frac{14}{27} ).
Check if the answer can be simplified; if the greatest common factor is 1, it is already in simplest form.

Divide fractions using "keep, switch, flip" (also known as "keep, change, flip").
Keep the first fraction as it is.
Switch the division sign to multiplication.
Flip (take the reciprocal of) the second fraction.
Example: ( \frac{3}{8} \div \frac{1}{4} ) becomes ( \frac{3}{8} \times \frac{4}{1} = \frac{12}{8} ).
Convert an improper fraction (( \frac{12}{8} )) to a mixed number by dividing the numerator by the denominator (( 12 \div 8 = 1 ) remainder 4), so ( 1 \frac{4}{8} ).
Simplify the fraction by dividing both numerator and denominator by their greatest common factor (( 1 \frac{4}{8} = 1 \frac{1}{2} )).

Numerator — The top part of a fraction.
Denominator — The bottom part of a fraction.
Reciprocal — A fraction flipped so the numerator becomes the denominator and vice versa.
Improper Fraction — A fraction where the numerator is greater than or equal to the denominator.
Mixed Number — A whole number combined with a fraction.
Simplest Form — When a fraction’s numerator and denominator have no common factors except 1.

Practice multiplying and dividing fractions and simplifying results.
Review how to convert improper fractions to mixed numbers and reduce to simplest form.