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4TH GRADE MATH · FREE LESSON

How to find equivalent fractions

One half and two fourths look different on paper, but they can describe exactly the same amount. Learn how to rename a fraction without changing its value, then explain the change with a drawing.

Start the lesson
BEFORE YOU BEGIN

A quick starting check.

  • Recognize the numerator as the number of selected parts.
  • Recognize the denominator as the number of equal parts in one whole.
  • Multiply and divide small whole numbers.
UNDERSTAND THE IDEA

Build the method, one step at a time.

Start with the same whole

A fraction describes equal parts of a whole. In 2/32/3, the whole has three equal parts and two are selected. Equivalent fractions describe the same value, even when the number and size of those parts change.

For a fair picture comparison, use the same whole or equal-sized wholes. Half of a small sandwich and half of a large sandwich are both one half, but they are not the same amount of food. Keep the size of the whole fixed while you change its partitions.

Split every part in the same way

Draw two equal-length strips. Split the first into three equal sections and shade two. On the second strip, split each third into two smaller equal sections. There are now six sections and four are shaded. The shaded length has not changed: 2/3=4/62/3 = 4/6.

Both counts doubled. Multiplying the numerator and denominator by the same positive whole number renames the fraction. Algebraically, you have multiplied by a form of one: 2/3×2/2=4/62/3 \times 2/2 = 4/6. Multiplying by one leaves the value unchanged.

Use the relationship between denominators

To change thirds into twelfths, ask what multiplies 3 to make 12. The answer is 4, so multiply the numerator by 4 too. You can also work backward by dividing both numbers by a common factor.

A fraction is in simplest form when its numerator and denominator share no whole-number factor greater than 1. Simplifying makes the numbers smaller; it does not make the fraction's value smaller.

2/3
4/6
Both full strips are the same length. Splitting each third in half doubles both counts, while the shaded length stays the same.
SEE IT WORK

Two worked examples.

EXAMPLE 1

Rename 3/43/4 using twelfths

  1. Find the denominator multiplier: 4×3=124 \times 3 = 12.
  2. Multiply the numerator by the same number: 3×3=93 \times 3 = 9.
  3. Write 3/4=9/123/4 = 9/12. Each fourth has become three twelfths, so three shaded fourths become nine shaded twelfths.

Check your reasoning: Divide both 9 and 12 by 3 to return to 3/43/4. A drawing of equal-sized wholes should show the same shaded area.

EXAMPLE 2

Simplify 8/128/12

  1. Both 8 and 12 are divisible by 4. Group the smaller pieces into sets of four.
  2. Divide both numbers by 4: (8÷4)/(12÷4)=2/3(8 \div 4)/(12 \div 4) = 2/3.
  3. The numbers 2 and 3 share no factor greater than 1, so 2/32/3 is in simplest form.

Check your reasoning: Multiply 2/32/3 by 4/44/4 to get 8/128/12 again. The amount is unchanged in either direction.

YOUR TURN

Try it before you reveal it.

Write down your thinking. Open a hint if you get stuck, then compare your method with the explanation.

Practice 1

Complete the equivalent fraction: 2/5=□/152/5 = \square/15.

Show a hint

How many times as large is 15 as 5?

Show the answer and explanation

6

The denominator is multiplied by 3, so multiply the numerator by 3 too: 2×3=62 \times 3 = 6. Therefore 2/5=6/152/5 = 6/15.

Practice 2

Write 9/129/12 in simplest form.

Show a hint

Look for a whole number that divides both 9 and 12.

Show the answer and explanation

3/43/4

Divide both numbers by 3: 9÷3=39 \div 3 = 3 and 12÷3=412 \div 3 = 4. Three and four have no common factor greater than 1.

Practice 3

Are 3/53/5 and 6/156/15 equivalent? Explain your decision.

Show a hint

Rename 3/53/5 using fifteenths before comparing.

Show the answer and explanation

No. 3/5=9/153/5 = 9/15, not 6/156/15.

Multiplying the denominator 5 by 3 requires multiplying the numerator 3 by 3 too. Six fifteenths simplifies to 2/52/5, which is less than 3/53/5.

KEEP THIS IDEA

What to take with you.

Explain what happened to both the selected parts and all the parts. The same factor must change both counts while the whole stays fixed.

Try explaining one example without looking at the steps. If a step is hard to explain, revisit that part before moving on.

A PROMPT TO TRY IN STUDY

I am practicing equivalent fractions. Give me a fraction-strip question and ask me to explain the scale factor before you reveal the answer.

Eligible students ages 13 and older with Study access can sign in and use this prompt for more practice. Check AI explanations against your class materials.

Continue in Study

Written by FutureSteps for study and review. This lesson expands a topic in our Texas starter collection. Course reference: Texas TEKS · Grade 4 Mathematics (§111.6(b)(3)(C)). These references do not imply endorsement, complete standard coverage or assessed mastery. Follow your school’s materials and course sequence.

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