Mixed Numbers Unlike

Grade 5 · mathematics · 86 practice problems · read aloud

🔊 Listen to this explanation

Adding & Subtracting Mixed Numbers with Unlike Denominators

🔍 What is it and Why Learn It?

Sometimes, you need to add or subtract amounts that include whole numbers and fractions, like adding 2 1/4 cups of flour to 1 1/2 cups. When the fraction parts have different bottom numbers (denominators), we need to find a common language for them before we can combine them. This is a super useful skill for cooking, building, and other real-life projects!

📝 Step-by-Step Guide

  1. Separate the whole numbers and the fractions.
  2. Check Denominators. If the fraction parts have different bottom numbers, find a common denominator (a number both denominators can divide into).
  3. Make Equivalent Fractions using the common denominator.
  4. Add or Subtract the fractions, then add or subtract the whole numbers.
  5. Simplify your answer. If the fraction is improper (top number bigger than bottom), convert it to a mixed number and add it to your whole number.

✨ Worked Examples

Example 1: Adding

Solve: 2 3/4 + 1 2/3

  1. Separate: Whole numbers: 2 + 1. Fractions: 3/4 + 2/3.
  2. Common denominator for 4 and 3 is 12.
  3. Equivalent fractions: 3/4 = 9/12    2/3 = 8/12
  4. Add: Whole numbers: 3. Fractions: 9/12 + 8/12 = 17/12.
  5. Simplify: 17/12 = 1 5/12. Final answer: 3 + 1 5/12 = 4 5/12.

Example 2: Subtracting

Solve: 3 1/2 - 1 2/5

  1. Separate: Whole numbers: 3 - 1. Fractions: 1/2 - 2/5.
  2. Common denominator for 2 and 5 is 10.
  3. Equivalent fractions: 1/2 = 5/10    2/5 = 4/10
  4. Subtract: Whole numbers: 2. Fractions: 5/10 - 4/10 = 1/10.
  5. Simplify: The fraction is already simple. Final answer: 2 1/10.

⚠️ Common Mistakes to Avoid

  • Adding Denominators: Don't add the denominators! Only find a common one. 1/2 + 1/3 is NOT 2/5.
  • Forgetting the Whole Number: Always keep track of your whole numbers separately. Don't just add the fractions and forget the wholes.
  • Not Simplifying: Always check if your final fraction can be simplified (e.g., 2/4 should be 1/2).

💡 Tips & Tricks

  • Butterfly Method: A quick way to find a common denominator is to multiply the two denominators together. (e.g., for 1/2 and 1/3, 2 x 3 = 6).
  • Double-Check with Drawing: Draw circles or rectangles, shade in the fractions to see if your answer makes sense.
  • Remember the Steps: Use a mnemonic like "Silly Cats Make Awesome Sounds" for Separate, Common denominator, Make equivalents, Add/Subtract, Simplify.

🏋️ How to Practice

  • Start with worksheets that have plenty of space to show your work for each step.
  • Create your own problems using recipes or measuring tapes.
  • Use online math games that focus on fractions and mixed numbers.
  • Practice with a friend and check each other's work—explaining your steps is a great way to learn!

Practice problems

6 of the 86, worked through step by step — try them before opening the answer.

1 3 1/4 + 2 2/3 = ?

Hint: Convert mixed numbers to improper fractions with a common denominator before adding. For example, when adding 1 1/2 and 2 1/4, you would first find a common denominator for the fractional parts.

Show the answer

Answer: 5 11/12

  1. Write the mixed numbers as sums of whole numbers and fractions. 3 1/4 = 3 + 1/4 2 2/3 = 2 + 2/3
  2. Add the whole numbers together. 3 + 2 = 5
  3. Now add the fractions: 1/4 + 2/3. To add fractions, we need a common denominator. The denominators are 4 and 3. The least common denominator is 12.
  4. Convert each fraction to have a denominator of 12. For 1/4: Multiply numerator and denominator by 3. (1 * 3)/(4 * 3) = 3/12 For 2/3: Multiply numerator and denominator by 4. (2 * 4)/(3 * 4) = 8/12
  5. Add the converted fractions. 3/12 + 8/12 = (3 + 8)/12 = 11/12
  6. Combine the result from Step 2 (the whole number sum) with the result from Step 5 (the fraction sum). 5 + 11/12 = 5 11/12 Final Answer: 5 11/12

Let's add 3 1/4 and 2 2/3 step by step.

2 2 3/4 + 1 1/6 = ?

Hint: Convert mixed numbers to improper fractions with a common denominator before adding.

Show the answer

Answer: 3 11/12

  1. Write the mixed numbers as sums of whole numbers and fractions. 2 3/4 = 2 + 3/4 1 1/6 = 1 + 1/6
  2. Add the whole numbers first. 2 + 1 = 3
  3. Now add the fractions: 3/4 + 1/6. To add fractions, we need a common denominator. The denominators are 4 and 6.
  4. Find the least common denominator (LCD). The smallest number that both 4 and 6 divide into is 12.
  5. Convert each fraction to have a denominator of 12. For 3/4: Multiply numerator and denominator by 3. (3 x 3)/(4 x 3) = 9/12 For 1/6: Multiply numerator and denominator by 2. (1 x 2)/(6 x 2) = 2/12
  6. Add the converted fractions. 9/12 + 2/12 = 11/12
  7. Combine the whole number sum and the fraction sum. 3 + 11/12 = 3 11/12 Final Answer: 3 11/12

Let's add 2 3/4 and 1 1/6 step by step.

3 3 2/5 + 1 3/4 = ?

Hint: Convert mixed numbers to improper fractions with a common denominator before adding

Show the answer

Answer: 5 3/20

  1. Convert 3 2/5 to an improper fraction: (3 × 5) + 2 = 15 + 2 = 17, so 3 2/5 = 17/5
  2. Convert 1 3/4 to an improper fraction: (1 × 4) + 3 = 4 + 3 = 7, so 1 3/4 = 7/4
  3. Find a common denominator for 5 and 4, which is 20
  4. Convert 17/5 to twentieths: 17/5 = (17 × 4)/(5 × 4) = 68/20
  5. Convert 7/4 to twentieths: 7/4 = (7 × 5)/(4 × 5) = 35/20
  6. Add the fractions: 68/20 + 35/20 = 103/20
  7. Convert back to a mixed number: 103 ÷ 20 = 5 with remainder 3, so 103/20 = 5 3/20

The answer is 5 3/20.

4 2 3/4 + 1 5/6 = ?

Hint: Convert mixed numbers to improper fractions with a common denominator before adding

Show the answer

Answer: 4 7/12

  1. Convert 2 3/4 to an improper fraction: (2 × 4 + 3)/4 = 11/4
  2. Convert 1 5/6 to an improper fraction: (1 × 6 + 5)/6 = 11/6
  3. Find a common denominator for 4 and 6, which is 12
  4. Convert 11/4 to twelfths: (11 × 3)/(4 × 3) = 33/12
  5. Convert 11/6 to twelfths: (11 × 2)/(6 × 2) = 22/12
  6. Add the fractions: 33/12 + 22/12 = 55/12
  7. Convert 55/12 to a mixed number: 55 ÷ 12 = 4 with remainder 7, so 4 7/12

The answer is 4 7/12.

5 5 3/4 + 2 2/5 = ?

Hint: Convert mixed numbers to improper fractions with a common denominator before adding

Show the answer

Answer: 8 3/20

  1. Convert 5 3/4 to an improper fraction: 5 × 4 + 3 = 23/4
  2. Convert 2 2/5 to an improper fraction: 2 × 5 + 2 = 12/5
  3. Find a common denominator for 4 and 5, which is 20
  4. Convert 23/4 to twentieths: 23/4 = 115/20
  5. Convert 12/5 to twentieths: 12/5 = 48/20
  6. Add the fractions: 115/20 + 48/20 = 163/20
  7. Convert back to a mixed number: 163 ÷ 20 = 8 remainder 3, so 8 3/20

The answer is 8 3/20.

6 5 2/3 - 2 3/4 = ?

Hint: Convert mixed numbers to improper fractions with a common denominator before subtracting

Show the answer

Answer: 2 11/12

  1. Convert 5 2/3 to an improper fraction: (5 × 3 + 2)/3 = 17/3
  2. Convert 2 3/4 to an improper fraction: (2 × 4 + 3)/4 = 11/4
  3. Find a common denominator for 3 and 4, which is 12
  4. Convert 17/3 to twelfths: (17 × 4)/(3 × 4) = 68/12
  5. Convert 11/4 to twelfths: (11 × 3)/(4 × 3) = 33/12
  6. Subtract the fractions: 68/12 - 33/12 = 35/12
  7. Convert 35/12 back to a mixed number: 35 ÷ 12 = 2 remainder 11, so 2 11/12

The answer is 2 11/12.

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