How to Break Fractions and Mixed Numbers Apart to Add or Subtract
TL;DR: When you add or subtract mixed numbers, you can either convert them to improper fractions first or break them into whole-number and fraction parts. Both methods work. Breaking them apart often feels more intuitive, add the whole numbers, add the fractions, then combine.
Key takeaways:
- Two methods: convert to improper fractions, OR break into whole + fraction parts.
- Breaking apart: add the whole numbers and the fractions separately, then combine.
- Always find a common denominator before adding the fraction parts.
- When subtracting, borrow from the whole number if the top fraction is smaller than the bottom.
- Simplify the final answer and convert improper fractions to mixed numbers if needed.
When you’re dealing with fractions and mixed numbers, it’s often useful to break them apart to simplify the process of adding or subtracting.
A Step-by-step Guide to Breaking Fractions and Mixed Numbers Apart to Add or Subtract
Here’s a step-by-step guide to breaking down fractions and mixed numbers to add or subtract:
Step 1: Convert mixed numbers to improper fractions
A mixed number is a whole number combined with a fraction. To convert it into an improper fraction:
- Multiply the whole number by the denominator of the fraction.
- Add the numerator of the fraction to that product.
- The result is your new numerator, with the denominator staying the same.
For example, let’s convert the mixed number \(2 \frac{3}{4}\) to an improper fraction:
- Multiply 2 (the whole number) by 4 (the denominator): 2 * 4 = 8
- Add 3 (the numerator): \(8 + 3 = 11\)
- So, \(2 \frac{3}{4}\) as an improper fraction is \( \frac{11}{4}\).
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Step 2: Make sure the fractions have a common denominator
If the fractions have different denominators, you’ll need to find the least common denominator (LCD). Multiply the numerator and denominator of each fraction by whatever number will make the denominator equal to the LCD.
For example, if you’re adding \( \frac{1}{2}\) and \( \frac{2}{3}\), the LCD is 6. Multiply the numerator and denominator of \( \frac{1}{2}\) by 3 to get \( \frac{3}{6}\), and multiply the numerator and denominator of \( \frac{2}{3}\) by 2 to get \( \frac{4}{6}\).
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For a complete fractions workbook that drills mixed-number operations alongside other grade-5 topics, the Grade 5 Common Core Math for Beginners (resource currently unavailable) walks through every fraction skill with worked examples. For state-test prep, the Grade 5 FSA Math for Beginners (resource currently unavailable) covers mixed-number arithmetic in FSA question format.
Frequently Asked Questions
How do you break apart a fraction?
Write the fraction as a sum of smaller fractions with the same denominator by splitting the numerator. For example, 5/8 = 2/8 + 3/8. This helps when adding mixed numbers: in 2 7/8 + 1 3/8, split 3/8 into 1/8 + 2/8. Then 2 7/8 + 1/8 makes 3, and the total is 3 + 1 + 2/8 = 4 2/8, which simplifies to 4 1/4.
What is break apart in math?
Breaking apart means splitting a number into easier pieces, such as place-value parts or wholes and fractions, and then working with the pieces. With mixed numbers, 3 2/5 breaks into 3 + 2/5. To add 3 2/5 + 1 1/5, add the wholes (3 + 1 = 4) and the fractions (2/5 + 1/5 = 3/5) to get 4 3/5. The same idea also makes multiplying whole numbers easier.
What are fractions and mixed numbers?
A fraction such as 3/4 names equal parts of a whole: the denominator tells how many parts make the whole, and the numerator tells how many you have. A mixed number combines a whole number and a fraction, like 2 3/4, which means 2 + 3/4. You can rewrite it as the improper fraction 11/4, because 2 × 4 + 3 = 11.
Can a fraction be a mixed number?
An improper fraction, where the numerator is at least as large as the denominator, can be rewritten as a mixed number. Divide the numerator by the denominator: 17 ÷ 5 is 3 with remainder 2, so 17/5 = 3 2/5. A proper fraction like 3/5 is less than 1, so it stays a fraction. If the division comes out even, you get a whole number, as in 10/5 = 2.
Can fractions be added?
Yes. When the denominators match, add the numerators and keep the denominator: 2/9 + 5/9 = 7/9. When they differ, rewrite both with a common denominator first: 1/4 + 1/6 = 3/12 + 2/12 = 5/12. For mixed numbers, break them apart, add the wholes and the fractions separately, and regroup if the fraction part reaches 1 or more.
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