Equivalent Fractions

Grade 3 · fractions · 70 practice problems · read aloud

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Equivalent Fractions: The Fun of Finding Twins! 🧑🤝🧑

Equivalent fractions are different fractions that name the same amount, just like two different names for the same person! They are useful because they help us compare, add, and subtract fractions easily.

How to Find Equivalent Fractions

  1. Step 1: Start with a fraction, like 1/2.
  2. Step 2: Pick a number to multiply the top (numerator) and bottom (denominator) by. You must use the same number for both!
  3. Step 3: Multiply. The new fraction is equivalent to the first one!

Visual Examples

Example 1: Find a fraction equivalent to 1/2.

Let's multiply the top and bottom by 2.

1 × 2 = 2
2 × 2 = 4

So, 1/2 = 2/4. Both fractions represent half of a whole! 🥧

Example 2: Find a fraction equivalent to 2/3.

Let's multiply the top and bottom by 3.

2 × 3 = 6
3 × 3 = 9

So, 2/3 = 6/9.

Common Mistakes to Avoid 🚫

Only adding or multiplying the top number. Remember, the golden rule is that whatever you do to the top, you MUST do to the bottom!

Using different numbers. If you multiply the top by 2, you must multiply the bottom by 2, not by 3.

Tips & Tricks

💡 Think of it like a scale that must always stay balanced!

💡 Use a multiplication chart to help you find numbers to use.

💡 If you can divide the numerator and denominator by the same number, you can also find equivalent fractions that way (this is called simplifying!).

How to Practice

  • Use fraction strips or pie charts to see the fractions visually.
  • Play online math games that ask you to match equivalent fractions.
  • Create your own "Fraction Wall" on a big piece of paper, showing many equivalent fractions for 1/2, 1/3, and 1/4.
  • Ask a friend: "Can you find three fractions that are equivalent to 3/4?"

Practice problems

6 of the 70, worked through step by step — try them before opening the answer.

1 2/4 = ?/2

Hint: Think about how to make the fraction simpler by dividing both the top and bottom by the same number.

Show the answer

Answer: 1

  1. Simplify the left side. 2/4 = 1/2 So the equation becomes: 1/2 = ?/2
  2. Compare both sides. Since the denominators are the same (both are 2), the numerators must be equal. Therefore: ? = 1 Final answer: 1

We start with the equation: 2/4 = ?/2

2 2/4 = ?/8

Hint: Think about what number you multiply the denominator by to get the new denominator, then multiply the numerator by the same number.

Show the answer

Answer: 4

  1. Notice that both sides are fractions. The left side is 2/4, which can be simplified. 2/4 simplifies to 1/2.
  2. So now we have: 1/2 = ?/8
  3. To find the missing number, observe that the denominators are 2 and 8. Since 8 is 4 times 2, we can multiply the numerator and denominator of 1/2 by 4 to make the denominator 8.
  4. Multiply numerator and denominator: (1 × 4)/(2 × 4) = 4/8
  5. So the missing number is 4. Final answer: 4

We start with the equation: 2/4 = ?/8

3 3/4 = ?/8

Hint: To find equivalent fractions, multiply both the numerator and denominator by the same number to make the denominators equal.

Show the answer

Answer: 6

  1. Look at the denominator of the first fraction, which is 4. We want the new denominator to be 8.
  2. Ask: What number do I multiply 4 by to get 8? 4 × 2 = 8.
  3. Since we multiplied the denominator by 2, we must also multiply the numerator by 2 to keep the fractions equal.
  4. Multiply the numerator: 3 × 2 = 6.
  5. The equivalent fraction is 6/8.

The answer is 6.

4 2/3 = ?/6

Hint: Think about what number you multiply the denominator by to get the new denominator, and multiply the numerator by the same number.

Show the answer

Answer: 4

  1. Look at the denominators. The first fraction has a denominator of 3, and the second fraction has a denominator of 6.
  2. To go from 3 to 6, you multiply by 2 (because 3 × 2 = 6).
  3. To find the equivalent fraction, you must do the same to the numerator. The first numerator is 2.
  4. Multiply the numerator by 2: 2 × 2 = 4.
  5. The equivalent fraction is 4/6.

The answer is 4.

5 2/3 = ?/9

Hint: To find equivalent fractions, multiply both the numerator and denominator by the same number. For example, to find what 1/2 equals in fourths, multiply both parts by 2.

Show the answer

Answer: 6

  1. Look at the denominators: 3 and 9
  2. Determine what number multiplied by 3 equals 9: 3 × 3 = 9
  3. Multiply the numerator by the same number: 2 × 3 = 6
  4. Write the equivalent fraction: 2/3 = 6/9
  5. The missing numerator is 6

The answer is 6.

6 3/4 = ?/12

Hint: Think about what number you multiply the denominator by to get the new denominator, then multiply the numerator by that same number.

Show the answer

Answer: 9

  1. Look at the denominators. The first fraction has a denominator of 4, and the second fraction has a denominator of 12.
  2. Find what number you multiply 4 by to get 12. 4 × 3 = 12.
  3. Multiply the numerator by the same number. 3 × 3 = 9.
  4. The equivalent fraction is 3/4 = 9/12.

The answer is 9.

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