Add Unlike Fractions

Grade 5 · fractions · 52 practice problems · read aloud

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Adding Unlike Fractions

Unlike fractions are fractions with different denominators (the bottom number). Learning to add them is super useful because it helps us combine parts of different wholes, like adding a half-cup of flour to a third-cup of flour in a recipe! ✨

How to Solve: Step-by-Step Guide

  1. Find a Common Denominator: Look for the smallest number that both denominators can divide into evenly. This is called the Least Common Denominator (LCD).
  2. Make Equivalent Fractions: Change both fractions so they have this new common denominator. Remember: whatever you do to the bottom, you must do to the top!
  3. Add the Numerators: Now that the denominators are the same, just add the numerators (the top numbers). The denominator stays the same.
  4. Simplify: If possible, reduce your answer to its simplest form.

Visual Examples

Example 1: 1/2 + 1/4

  1. The denominators are 2 and 4. The LCD is 4.
  2. Convert 1/2 to 2/4. (1/2 = ?/4 → 2/4). 1/4 stays the same.
  3. Add the numerators: 2 + 1 = 3. So, 2/4 + 1/4 = 3/4.
  4. 3/4 is already in simplest form. ✅

Example 2: 2/3 + 1/6

  1. The denominators are 3 and 6. The LCD is 6.
  2. Convert 2/3 to 4/6. (2/3 = ?/6 → 4/6). 1/6 stays the same.
  3. Add the numerators: 4 + 1 = 5. So, 4/6 + 1/6 = 5/6.
  4. 5/6 is in simplest form. ✅

Common Mistakes to Avoid

🚫 Don't Add Denominators! A common mistake is to add both the top and bottom numbers: 1/3 + 1/6 does NOT equal 2/9. The denominator must stay the same once you find a common one.

🚫 Forgetting to Convert Both Fractions: Make sure you change both fractions to have the common denominator, not just one.

Tips & Tricks

Butterfly Method (Shortcut): 🦋 Multiply the denominators diagonally and add to get the new numerator. Then multiply the denominators to get the new denominator. Example: For a/b + c/d, the sum is (a*d + b*c) / (b*d). Always simplify your answer!

LCD Checklist: List the multiples of the larger denominator until you find one the smaller denominator divides into. For 3 and 5, multiples of 5 are: 5, 10, 15... 15 works because 3 goes into 15 evenly!

How to Practice

  • Start with fractions that have one denominator that is a multiple of the other (like 2 and 4).
  • Use fraction circles or bars to draw the problem and see it visually.
  • Create your own practice problems and solve them. Try using a friend's problems too!
  • Ask your teacher for worksheets or find interactive games online.

Practice problems

6 of the 52, worked through step by step — try them before opening the answer.

1 2/3 + 1/4 = ?

Hint: To add fractions with different denominators, first find a common denominator that both denominators can divide into evenly. Then convert both fractions to equivalent fractions with that common denominator before adding.

Show the answer

Answer: 11/12

  1. Find a common denominator. The denominators are 3 and 4. The smallest number that both 3 and 4 divide into evenly is 12. So, the common denominator is 12.
  2. Convert the first fraction, 2/3, to have a denominator of 12. To change the denominator from 3 to 12, we multiply it by 4. To keep the value of the fraction the same, we must also multiply the numerator (the top number) by the same amount. So, 2/3 = (2 * 4) / (3 * 4) = 8/12.
  3. Convert the second fraction, 1/4, to have a denominator of 12. To change the denominator from 4 to 12, we multiply it by 3. We must also multiply the numerator by 3. So, 1/4 = (1 * 3) / (4 * 3) = 3/12.
  4. Now add the two fractions that have the same denominator. Since both fractions now have a denominator of 12, we add the numerators and keep the denominator. 8/12 + 3/12 = (8 + 3)/12 = 11/12.
  5. Check if the answer can be simplified. The fraction 11/12 is already in its simplest form because 11 and 12 have no common factors other than 1. Therefore, the final answer is 11/12.

To add the fractions 2/3 and 1/4, we need a common denominator because the denominators (the bottom numbers) are different.

2 3/8 + 1/6 = ?

Hint: To add fractions with different denominators, first find a common denominator that both denominators can divide into evenly.

Show the answer

Answer: 13/24

  1. Find the least common denominator of 8 and 6. The multiples of 8 are 8, 16, 24, 32... The multiples of 6 are 6, 12, 18, 24, 30... The least common multiple is 24.
  2. Convert 3/8 to an equivalent fraction with denominator 24: 3/8 = (3 × 3)/(8 × 3) = 9/24
  3. Convert 1/6 to an equivalent fraction with denominator 24: 1/6 = (1 × 4)/(6 × 4) = 4/24
  4. Add the fractions: 9/24 + 4/24 = 13/24
  5. Check if the fraction can be simplified: 13 and 24 have no common factors other than 1, so 13/24 is already in simplest form.

The answer is 13/24.

3 5/6 + 3/8 = ?

Hint: To add fractions with different denominators, first find a common denominator. For example, to add 1/4 and 1/3, you would use 12 as the common denominator since it's the smallest number that both 4 and 3 divide into evenly.

Show the answer

Answer: 29/24

  1. Find the least common denominator of 6 and 8. The multiples of 6 are 6, 12, 18, 24, 30... The multiples of 8 are 8, 16, 24, 32... The least common multiple is 24.
  2. Convert 5/6 to have denominator 24: 5/6 = (5 × 4)/(6 × 4) = 20/24
  3. Convert 3/8 to have denominator 24: 3/8 = (3 × 3)/(8 × 3) = 9/24
  4. Add the fractions: 20/24 + 9/24 = 29/24
  5. The answer is 29/24, which is an improper fraction.

4 2/5 + 1/3 = ?

Hint: To add fractions with different denominators, first find a common denominator. For example, to add 1/4 and 1/6, you would find a common denominator of 12.

Show the answer

Answer: 11/15

  1. Find a common denominator for 5 and 3. The least common multiple is 15.
  2. Convert 2/5 to have denominator 15: (2×3)/(5×3) = 6/15
  3. Convert 1/3 to have denominator 15: (1×5)/(3×5) = 5/15
  4. Add the fractions: 6/15 + 5/15 = 11/15
  5. The fraction 11/15 is already in simplest form.

The answer is 11/15.

5 3/7 + 2/5 = ?

Hint: To add fractions with different denominators, first find a common denominator. For example, to add 1/4 and 1/6, you would find a common denominator of 12.

Show the answer

Answer: 29/35

  1. Find a common denominator for 7 and 5. The least common multiple is 35.
  2. Convert 3/7 to have denominator 35: (3×5)/(7×5) = 15/35
  3. Convert 2/5 to have denominator 35: (2×7)/(5×7) = 14/35
  4. Add the fractions: 15/35 + 14/35 = 29/35
  5. The fraction 29/35 is already in simplest form.

The answer is 29/35.

6 3/8 + 2/7 = ?

Hint: To add fractions with different denominators, first find a common denominator. For example, to add 1/5 and 1/4, you would find a common denominator of 20.

Show the answer

Answer: 37/56

  1. Find a common denominator for 8 and 7. The least common multiple is 56.
  2. Convert 3/8 to have denominator 56: (3×7)/(8×7) = 21/56
  3. Convert 2/7 to have denominator 56: (2×8)/(7×8) = 16/56
  4. Add the fractions: 21/56 + 16/56 = 37/56
  5. The fraction 37/56 is already in simplest form since 37 and 56 have no common factors.

The answer is 37/56.

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