How to Break Fractions and Mixed Numbers Apart to Add or Subtract

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 \( \frac{11}{4}\).

Pre-Algebra for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.30 out of 5 based on 105 customer ratings

Satisfied 92 Students

The Absolute Best Book for 4th Grade Students

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 \( \frac{4}{6}\).

The Best Math Books for Elementary Students

Recommended EffortlessMath Books

For a complete fractions workbook that drills mixed-number operations alongside other grade-5 topics, the Grade 5 Common Core Math for Beginners walks through every fraction skill with worked examples. For state-test prep, the Grade 5 FSA Math for Beginners covers mixed-number arithmetic in FSA question format.

Frequently Asked Questions

Why would I break mixed numbers apart instead of converting to improper fractions?

For many students, breaking apart feels more natural — you keep the whole numbers visible the whole time. Converting to improper fractions can make the numbers larger and harder to track (\(17\frac{2}{3}\) becomes \(\frac{53}{3}\), which is unwieldy). Use whichever method clicks better for you; both are mathematically equivalent.

How do I subtract mixed numbers when the top fraction is smaller?

Borrow from the whole number. \(5\frac{1}{4} – 2\frac{3}{4}\) — the \(\frac{1}{4}\) is smaller than \(\frac{3}{4}\), so borrow 1 from the 5. Rewrite as \(4 + 1 + \frac{1}{4} = 4 + \frac{4}{4} + \frac{1}{4} = 4\frac{5}{4}\). Now subtract: \(4\frac{5}{4} – 2\frac{3}{4} = 2\frac{2}{4} = 2\frac{1}{2}\).

Can I break apart when subtracting too?

Yes. Same idea — split each mixed number into whole and fraction parts, then subtract whole from whole and fraction from fraction. The only catch is borrowing: if the first mixed number’s fraction is smaller than the second’s, you need to borrow 1 from the whole-number part to make the fraction big enough to subtract from.

What’s the alternative — converting to improper fractions?

Convert each mixed number to an improper fraction first, then add or subtract as usual. \(3\frac{1}{4} + 2\frac{1}{6} = \frac{13}{4} + \frac{13}{6}\). LCD is 12: \(\frac{39}{12} + \frac{26}{12} = \frac{65}{12} = 5\frac{5}{12}\). Same answer as the break-apart method; you just got there a different way.

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, then add the numerator. The result becomes the new numerator; the denominator stays the same. \(3\frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4}\). Use the same process every time.

How do I convert an improper fraction back to a mixed number?

Divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same. \(\frac{17}{5}\) — 17 divided by 5 is 3 with remainder 2, so \(\frac{17}{5} = 3\frac{2}{5}\).

Which method is better for tests?

Whichever feels faster for you. Most teachers accept either approach as long as your work is clear. On computer-based state tests, you just type or select the final answer — the method doesn’t matter. On the FSA, STAAR, PARCC, and similar grade-5 tests, both methods work equally well.

What if both mixed numbers have the same denominator?

The break-apart method is especially clean. \(4\frac{2}{5} + 1\frac{1}{5}\) — add whole parts: \(4 + 1 = 5\). Add fraction parts: \(\frac{2}{5} + \frac{1}{5} = \frac{3}{5}\). Combine: \(5\frac{3}{5}\). No LCD needed since the denominators already match.

Can I use this with three or more mixed numbers?

Yes. Break each one into whole and fraction parts, then add all the wholes together and all the fractions together (with a common denominator). Combine at the end. The process scales to any number of mixed numbers as long as you’re patient with the bookkeeping.

Where does this skill show up?

Throughout grade 5 and grade 6 fraction work, every state grade-5/6 math test, and any practical situation involving measurement (cups, inches, hours, miles). Mixed-number arithmetic also lays the groundwork for adding rational expressions in algebra — same logic, just with variables in the denominators.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• Add fractions with unlike denominators
• Add and subtract three fractions
• Fraction word problems
• Multiplying fractions and whole numbers
• Free Grade 5 FSA Math practice test