Lesson 15: Equivalent Fractions, Reducing Fractions, Part 1

New Concept

Equivalent fractions are different ways to write the same value. They are made by multiplying or dividing by a fraction equal to 1.

Different fractions that name the same number are called equivalent fractions.

What’s next

This card is your foundation. Soon, you'll tackle worked examples on finding equivalent fractions and reducing them to their lowest terms.

Property

Different fractions that name the same number are equivalent. You can create them by multiplying the original fraction by a form of 1, like $\frac{a}{a}$.

Examples

"To give $\frac{2}{3}$ a denominator of 12: $\frac{2}{3} \times \frac{4}{4} = \frac{8}{12}$."
"Create another equivalent for $\frac{1}{2}$: $\frac{1}{2} \times \frac{5}{5} = \frac{5}{10}$."

Explanation

Think of it as giving a fraction a disguise! Multiplying it by a fancy '1' changes its look but not its value. This is key for getting common denominators before adding or subtracting.

Property

To reduce a fraction, divide both terms by a common factor. For lowest terms, divide by the greatest common factor (GCF) in one step.

Examples

"Reduce $\frac{18}{24}$ using the GCF of 6: $\frac{18 \div 6}{24 \div 6} = \frac{3}{4}$."
"For $3\frac{8}{12}$, reduce the fraction part: $3\frac{8 \div 4}{12 \div 4} = 3\frac{2}{3}$."

Explanation

Think of reducing as decluttering! You divide the top and bottom numbers by the biggest factor they share to simplify the fraction to its most basic form. The value stays the same, it just looks much cleaner.