Add/Subtract Mixed Numbers

Grade 4 · mathematics · 83 practice problems · read aloud

🔊 Listen to this explanation

Add & Subtract Mixed Numbers 🧮

Mixed numbers are numbers that have a whole number part and a fraction part, like 2 ½. We use them all the time for measurements like "one and a half cups of flour" or "two and three-quarter miles." Learning to add and subtract them helps us solve real-world problems!

How to Solve: Step-by-Step

  1. Add/Subtract the Whole Numbers: First, combine the whole number parts.
  2. Add/Subtract the Fractions: Next, combine the fraction parts. Make sure they have the same denominator (the bottom number) first!
  3. Simplify Your Answer: If your fraction is improper (top number bigger than bottom), turn it into a mixed number and add it to your whole number. Always put your fraction in simplest form.

Let's See It In Action! ✨

Example 1: Add 2 ¼ + 1 ½

  1. Whole Numbers: 2 + 1 = 3
  2. Fractions: ¼ + ½. First, make denominators the same: ¼ + 2/4 = 3/4
  3. Combine: 3 + 3/4 = 3 ¾

Example 2: Subtract 3 ⅗ - 1 ⅕

  1. Whole Numbers: 3 - 1 = 2
  2. Fractions: ⅗ - ⅕ = 2/5
  3. Combine: 2 + 2/5 = 2 ⅖

Watch Out! Common Mistakes 🚧

  • Forgetting Common Denominators: You can't add ½ and ⅓ directly! Change them to 3/6 and 2/6 first.
  • Ignoring the Whole Number: Don't just add the fractions and forget about the whole numbers you already calculated.
  • Not Simplifying: Always check if your fraction can be simplified (e.g., 2/4 should be ½).

Tips & Tricks 💡

  • Draw pictures! Circles (pizzas) or rectangles are great for visualizing mixed numbers.
  • Remember the phrase: "Wholes with wholes, parts with parts."
  • If you end up with a fraction like 5/4, you know it's the same as 1 ¼, so you can add that 1 to your whole number.

Time to Practice! 🏄‍♂️

Try solving these on your own:

  • 1 ⅓ + 2 ⅓
  • 4 ¾ - 2 ¼
  • 5 ½ + 1 ¼
  • 3 ⅞ - 1 ½

Use graph paper to keep your numbers neatly lined up. You can also practice by doubling recipes when you help cook!

Practice problems

6 of the 83, worked through step by step — try them before opening the answer.

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

Hint: First add the whole numbers, then add the fractions. If the fractions add up to 1 or more, convert that to a whole number.

Show the answer

Answer: 4

  1. Write the mixed numbers as whole numbers plus fractions. 2 1/4 means 2 + 1/4 1 3/4 means 1 + 3/4 So the problem becomes: (2 + 1/4) + (1 + 3/4)
  2. Group the whole numbers together and the fractions together. (2 + 1) + (1/4 + 3/4)
  3. Add the whole numbers. 2 + 1 = 3
  4. Add the fractions. 1/4 + 3/4 = 4/4
  5. Simplify the fraction. 4/4 = 1
  6. Add the results from Step 3 and
  7. 3 + 1 = 4 Therefore, 2 1/4 + 1 3/4 = 4

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

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

Hint: Convert mixed numbers to improper fractions before adding, then simplify the result back to a mixed number.

Show the answer

Answer: 4 1/4

  1. Write the mixed numbers separately. 2 3/4 means 2 + 3/4 1 1/2 means 1 + 1/2 So the problem is: (2 + 3/4) + (1 + 1/2)
  2. Add the whole numbers first. 2 + 1 = 3
  3. Now add the fractions: 3/4 + 1/2 To add fractions, they must have the same denominator. The denominator of 1/2 is 2. A common denominator for 4 and 2 is 4. Convert 1/2 to a fraction with denominator 4: 1/2 = 2/4
  4. Add the fractions with the common denominator. 3/4 + 2/4 = 5/4
  5. Simplify the fraction 5/4. 5/4 is an improper fraction (numerator larger than denominator). 5/4 = 1 1/4 because 4 goes into 5 one time with a remainder of 1.
  6. Combine the whole number from step 2 with the result from
  7. From step 2 we had 3. From step 5 we have 1 1/4. So 3 + 1 1/4 = 4 1/4 Final Answer: 4 1/4

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

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

Hint: First add the whole numbers together, then add the fractions together. If the fractions add up to 1 or more, remember to combine that with your whole number total.

Show the answer

Answer: 6

  1. Write the mixed numbers. 3 1/4 means 3 + 1/4. 2 3/4 means 2 + 3/4.
  2. Add the whole numbers first. 3 + 2 = 5.
  3. Add the fractions. 1/4 + 3/4 = (1 + 3)/4 = 4/4.
  4. Simplify the fraction. 4/4 = 1.
  5. Combine the results. 5 (from the whole numbers) + 1 (from the fractions) = 6. Therefore, 3 1/4 + 2 3/4 = 6.

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

4 2 3/8 + 1 5/8 = ?

Hint: Add the whole numbers and fractions separately, then combine them. Remember that when fractions add up to 1 or more, you can convert them to whole numbers.

Show the answer

Answer: 4

  1. Add the whole numbers: 2 + 1 = 3
  2. Add the fractions: 3/8 + 5/8 = 8/8
  3. Simplify the fraction: 8/8 = 1
  4. Combine the results: 3 + 1 = 4

The answer is 4.

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

Hint: When adding mixed numbers, first add the whole numbers together, then add the fractions. Remember to find a common denominator for the fractions.

Show the answer

Answer: 6 1/4

  1. Add the whole numbers: 3 + 2 = 5
  2. Add the fractions: 1/2 + 3/4
  3. Find a common denominator for 1/2 and 3/4. The common denominator is 4
  4. Convert 1/2 to 2/4
  5. Add the fractions: 2/4 + 3/4 = 5/4
  6. Convert 5/4 to a mixed number: 5/4 = 1 1/4
  7. Add the whole number results: 5 + 1 1/4 = 6 1/4
  8. The final answer is 6 1/4

6 4 3/8 + 2 5/8 = ?

Hint: When adding mixed numbers with the same denominator, first add the whole numbers, then add the fractions.

Show the answer

Answer: 7

  1. Add the whole numbers: 4 + 2 = 6
  2. Add the fractions: 3/8 + 5/8 = 8/8
  3. Simplify 8/8 = 1
  4. Add the results: 6 + 1 = 7

The answer is 7.

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