Subtract Unlike Fractions

Grade 5 · fractions · 59 practice problems · read aloud

🔊 Listen to this explanation

Subtracting Unlike Fractions

What Is It and Why Learn It?

Unlike fractions have different denominators (the bottom numbers). Before you can subtract them, you must make the denominators the same. We do this to subtract equal parts, like comparing pieces of different-sized cakes. 🎂 This skill is essential for measurements, baking, and more advanced math!

How to Subtract Unlike Fractions: Step-by-Step

  1. Find a Common Denominator. Look for the smallest number both denominators divide into evenly.
  2. Create Equivalent Fractions. Multiply the numerator and denominator of each fraction to get the new common denominator.
  3. Subtract the Numerators. Now that the denominators are the same, just subtract the top numbers. The denominator stays the same.
  4. Simplify Your Answer. Reduce the fraction to its simplest form.

Worked Examples

Example 1: 3/4 - 1/2

  1. Common Denominator: 4 (since 2 and 4 both divide into 4).
  2. Equivalent Fractions: 3/4 stays the same. 1/2 becomes (1×2)/(2×2) = 2/4.
  3. Subtract Numerators: 3/4 - 2/4 = 1/4.
  4. Simplify: 1/4 is already simple!

Answer: 1/4

Example 2: 5/6 - 1/3

  1. Common Denominator: 6.
  2. Equivalent Fractions: 5/6 stays. 1/3 becomes (1×2)/(3×2) = 2/6.
  3. Subtract Numerators: 5/6 - 2/6 = 3/6.
  4. Simplify: 3/6 = 1/2.

Answer: 1/2

Common Mistakes to Avoid

🚫 Subtracting Denominators: Never subtract the denominators! Once they are the same, they stay the same. Only subtract the numerators.

🚫 Forgetting to Convert Both Fractions: Make sure you change both fractions to have the common denominator before subtracting.

🚫 Forgetting to Simplify: Always check if your answer can be reduced to a simpler fraction.

Tips & Tricks

Butterfly Method (Shortcut): Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the numerator of the second by the denominator of the first. Subtract these two results to get the new numerator. Multiply the two denominators to get the new denominator. Simplify! 🦋

Memory Aid: "Bottom up, top down!" Find the common denominator (bottom up), then subtract the numerators (top down).

How to Practice

  • Use fraction circles or bars to see the problem visually.
  • Solve at least 5 problems each day.
  • Create your own problems and solve them.
  • Ask a friend or parent to give you problems to solve.

Practice problems

6 of the 59, worked through step by step — try them before opening the answer.

1 3/4 - 1/6 = ?

Hint: To subtract fractions with different denominators, first find a common denominator by identifying the least common multiple of the denominators.

Show the answer

Answer: 7/12

  1. Find a common denominator. The denominators are 4 and 6. The smallest number that both 4 and 6 divide into is 12. So, the common denominator is 12.
  2. Convert the first fraction, 3/4, to have a denominator of 12. To change 4 into 12, you multiply by 3. You must do the same to the numerator (the top number) to keep the value of the fraction the same. So, (3 * 3) / (4 * 3) = 9/12.
  3. Convert the second fraction, 1/6, to have a denominator of 12. To change 6 into 12, you multiply by 2. You must do the same to the numerator. So, (1 * 2) / (6 * 2) = 2/12.
  4. Now subtract the new fractions. Since both fractions now have the same denominator (12), you subtract the numerators and keep the denominator. So, 9/12 - 2/12 = (9 - 2)/12 = 7/12.
  5. Check if the answer can be simplified. The fraction 7/12 is already in its simplest form because 7 and 12 have no common factors other than 1. Therefore, the final answer is 7/12.

To subtract fractions, they must have the same denominator (the bottom number). Here is the step-by-step process:

2 3/4 - 2/5 = ?

Hint: To subtract fractions with different denominators, first find a common denominator by identifying the least common multiple of the denominators.

Show the answer

Answer: 7/20

  1. Identify the denominators. The denominators are 4 and 5.
  2. Find a common denominator. The least common multiple of 4 and 5 is 20.
  3. Rewrite each fraction with denominator 20. For 3/4: Multiply numerator and denominator by 5 → (3 × 5)/(4 × 5) = 15/20. For 2/5: Multiply numerator and denominator by 4 → (2 × 4)/(5 × 4) = 8/20.
  4. Subtract the numerators while keeping the denominator 20. 15/20 − 8/20 = (15 − 8)/20 = 7/20.
  5. Check if the result can be simplified. 7 and 20 have no common factors other than 1, so 7/20 is already in simplest form. Final answer: 7/20

To subtract fractions, they must have the same denominator. Here are the steps:

3 5/6 - 1/4 = ?

Hint: To subtract fractions with different denominators, first find a common denominator by identifying the least common multiple of the denominators.

Show the answer

Answer: 7/12

  1. Identify the denominators. The denominators are 6 and 4.
  2. Find a common denominator. The smallest number that both 6 and 4 divide into is 12. This is the Least Common Denominator (LCD).
  3. Rewrite each fraction with the common denominator of 12. - For 5/6: Ask, "What number multiplied by 6 gives 12?"
  4. Perform the subtraction. Now that both fractions have the same denominator, subtract the numerators and keep the denominator: 10/12 - 3/12 = (10 - 3)/12 = 7/12.
  5. Check if the result can be simplified. Look for the greatest common factor of 7 and 12. The number 7 is prime and does not divide into 12, so the fraction 7/12 is already in its simplest form. Therefore, the final answer is 7/12.

To subtract fractions, they must have the same denominator. Here is the step-by-step process: The answer is 2. Multiply both the numerator and denominator by 2: (5 * 2) / (6 * 2) = 10/12. - For 1/4: Ask, "What number multiplied by 4 gives 12?" The answer is 3. Multiply both the numerator and denominator by 3: (1 * 3) / (4 * 3) = 3/12.

4 7/8 - 2/5 = ?

Hint: To subtract fractions with different denominators, first find a common denominator by identifying the least common multiple of the denominators.

Show the answer

Answer: 19/40

  1. Find a common denominator for 8 and 5. The least common multiple of 8 and 5 is 40.
  2. Convert 7/8 to have denominator 40: (7 × 5)/(8 × 5) = 35/40
  3. Convert 2/5 to have denominator 40: (2 × 8)/(5 × 8) = 16/40
  4. Subtract the fractions: 35/40 - 16/40 = 19/40
  5. Check if the fraction can be simplified: 19 and 40 have no common factors other than 1, so 19/40 is already in simplest form.

The answer is 19/40.

5 7/8 - 2/3 = ?

Hint: To subtract fractions with different denominators, first find a common denominator by identifying the least common multiple of the denominators.

Show the answer

Answer: 5/24

  1. Find the least common multiple of 8 and 3. The multiples of 8 are 8, 16, 24, 32... The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24... The LCM is 24.
  2. Convert 7/8 to have denominator 24: (7 × 3)/(8 × 3) = 21/24
  3. Convert 2/3 to have denominator 24: (2 × 8)/(3 × 8) = 16/24
  4. Subtract the fractions: 21/24 - 16/24 = 5/24
  5. Check if the fraction can be simplified: 5 and 24 have no common factors other than 1, so 5/24 is already in simplest form.

The answer is 5/24.

6 5/6 - 3/8 = ?

Hint: To subtract fractions with different denominators, first find a common denominator. For example, to subtract 2/3 - 1/4, you would find a common denominator of 12.

Show the answer

Answer: 11/24

  1. Find a common denominator for 6 and 8. The least common multiple is 24.
  2. Convert 5/6 to have denominator 24: (5 × 4)/(6 × 4) = 20/24
  3. Convert 3/8 to have denominator 24: (3 × 3)/(8 × 3) = 9/24
  4. Subtract the fractions: 20/24 - 9/24 = 11/24
  5. Check if the fraction can be simplified: 11 and 24 have no common factors, so 11/24 is already in simplest form.

The answer is 11/24.

Practise this topic — 10 free problems, no signup →