Subtracting Fractions

What You’ll Learn

In this lesson you’ll learn how to subtract fractions step by step, first with the same denominator, then different ones, and handling mixed numbers when borrowing is needed. This builds directly on adding fractions.

The Concept

Subtracting fractions with the same denominator is straightforward. Just subtract the numerators:

$$\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}$$

For example: $\frac{5}{8} - \frac{2}{8} = \frac{3}{8}$

Subtracting fractions with different denominators requires a common denominator, just like adding. The least common denominator (LCD) is the smallest number that both denominators divide into evenly.

The general formula is:

$$\frac{a}{b} - \frac{c}{d} = \frac{a \times d - c \times b}{b \times d}$$

After subtracting, always check whether the result can be simplified by dividing the numerator and denominator by their greatest common factor.

Mixed numbers (whole + fraction): Subtract whole numbers first, then fractions. If the first fraction is smaller than the second, borrow 1 from the whole number. This adds $\frac{d}{d}$ (a full “1” in fraction form) to the fraction part.

Example: $3 \frac{1}{4} - 1 \frac{3}{4}$ Can’t do $\frac{1}{4} - \frac{3}{4}$, so borrow: $2 \frac{5}{4} - 1 \frac{3}{4} = 1 \frac{2}{4} = 1 \frac{1}{2}$

Worked Examples

Let’s subtract $\frac{3}{4} - \frac{1}{6}$ step by step.

1. Find the LCD. The denominators are 4 and 6. The smallest number both divide into is 12.

2. Convert each fraction.

$$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$$ $$\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}$$

3. Subtract the numerators.

$$\frac{9}{12} - \frac{2}{12} = \frac{7}{12}$$

4. Simplify if possible. 7 and 12 share no common factors, so $\frac{7}{12}$ is already in simplest form.

Now a mixed number example: $4 \frac{2}{3} - 2 \frac{5}{6}$

1. Find the LCD. Denominators are 3 and 6. LCD is 6.
2. Convert: $4 \frac{4}{6} - 2 \frac{5}{6}$
3. Can’t subtract $\frac{4}{6} - \frac{5}{6}$, so borrow: $3 \frac{10}{6} - 2 \frac{5}{6}$
4. Subtract: $3 \frac{10}{6} - 2 \frac{5}{6} = 1 \frac{5}{6}$

Real-World Applications

Subtracting fractions appears in cooking (subtracting used amounts from a recipe), budgeting (remaining time/money after spending part), or measurements (cutting material). Example: You have $2 \frac{3}{4}$ yards of fabric and use $1 \frac{1}{2}$ yards → $2 \frac{3}{4} - 1 \frac{1}{2} = 1 \frac{1}{4}$ yards left. Or a tank has $\frac{5}{8}$ full gas and you use $\frac{1}{4}$ → $\frac{5}{8} - \frac{2}{8} = \frac{3}{8}$ remaining.

You’ve Got This

Subtracting fractions is just like adding but in reverse. Find the common ground (denominator) and take away. When borrowing feels tricky, remember it’s like trading a dollar for quarters to make change. Practice a few problems, check by adding back, and it’ll click quickly.

Quiz

What is 5/6 - 2/6?

• A.3/6
• B.7/6
• C.3/12
• D.7/12

Subtract 3/4 - 1/8. What is the result?

• A.5/8
• B.2/8
• C.4/8
• D.6/8

A recipe calls for 2 1/3 cups of flour. You have 3 1/2 cups. How much more do you have?

• A.1 1/6 cups
• B.1 1/3 cups
• C.1 1/2 cups
• D.2/3 cup

Subtract 4 5/12 - 2 7/12. What is the result?

• A.2 2/12
• B.1 10/12
• C.2 10/12
• D.1 8/12

What is 7/8 - 3/8?

• A.4/8
• B.1/2
• C.10/8
• D.4/16