Subtracting of Proper and Mixed Fractions

Subtracting fractions is easier than you think! The key is finding a common denominator. Below, you’ll find clear explanations, examples, and a calculator to help verify your calculations.

Result

\[ \frac{3}{10}\]

Core Principle

The denominators must be the same to subtract fractions—that’s the fundamental rule of fraction subtraction!

Practical Uses

Fraction subtraction is useful in everyday life—from cooking recipes to budgeting.

Basics of Fraction Subtraction

Subtracting fractions relies on a simple principle: the denominators must be the same to subtract the numerators. If the fractions have different denominators, you need to find a common denominator first.

When denominators are the same:

\( \large \frac{5}{7} - \frac{2}{7} = \frac{5 - 2}{7} = \frac{3}{7} \)

Subtract only the numerators (top numbers), while the denominator (bottom number) stays the same.

When denominators are different:

You need to find a common denominator:

\( \large \frac{3}{4} - \frac{1}{3} \)

Find the common denominator (12), convert the fractions, and subtract the numerators.

Formula for subtracting fractions with different denominators:

\( \huge \frac{a}{b} - \frac{c}{d} = \frac{a \times d - c \times b}{b \times d} \)

5 Simple Steps to Subtract Fractions

1

Check the denominators—are they the same or different?

2

Find a common denominator if they’re different (usually the LCM).

3

Convert the fractions to the common denominator.

4

Subtract the numerators and keep the common denominator.

5

Simplify the result to its simplest form.

How to Find a Common Denominator?

To find a common denominator:

  1. Determine the least common multiple (LCM) of the denominators.
  2. Convert each fraction to the new denominator by multiplying both numerator and denominator by the appropriate value.

Example: For fractions \( \large \frac{2}{3} \) and \( \large \frac{3}{5} \), LCM(3, 5) = 15

\( \large \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \)
\( \large \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \)

Practical Examples

Fraction Subtraction Examples

Example 1: Fractions with the same denominator

\[ \frac{7}{8} - \frac{3}{8} \]
  1. The denominators are the same (8), so subtract directly.
  2. Subtract the numerators: \( 7 - 3 = 4 \).
  3. Result: \( \large \frac{7}{8} - \frac{3}{8} = \frac{4}{8} = \frac{1}{2} \).

Example 2: Fractions with different denominators

\[ \frac{3}{4} - \frac{2}{3} \]
  1. The denominators are different (4 and 3), so find LCM(4, 3) = 12.
  2. Convert the first fraction: \( \large \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \).
  3. Convert the second fraction: \( \large \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \).
  4. Subtract the numerators: \( \large \frac{9}{12} - \frac{8}{12} = \frac{1}{12} \).

Example 3: Subtraction with a negative result

\[ \frac{1}{3} - \frac{2}{3} \]
  1. The denominators are the same (3), so subtract directly.
  2. Subtract the numerators: \( 1 - 2 = -1 \).
  3. Result: \( \large \frac{1}{3} - \frac{2}{3} = \frac{-1}{3} = -\frac{1}{3} \).

Common Mistakes to Avoid

Don’t subtract the denominators!

Wrong: \( \large \frac{3}{4} - \frac{1}{2} = \frac{3-1}{4-2} = \frac{2}{2} = 1 \) ❌

Correct: \( \large \frac{3}{4} - \frac{1}{2} = \frac{6}{8} - \frac{4}{8} = \frac{2}{8} = \frac{1}{4} \) ✓

Incorrect common denominator

Always find the LCM of the denominators, don’t just multiply them (unless that’s the LCM).

Incorrect fraction conversion

Remember to multiply both numerator and denominator by the same number.

Not simplifying the result

Always check if the result can be simplified by dividing numerator and denominator by their common factor.

Issues with negative signs

If you subtract a larger fraction from a smaller one, the result is negative—don’t forget the minus sign!

Tips and Advice for Students

Practice regularly

Consistent practice is key. Start with simple examples and progress to more complex ones.

Visualize fractions

Drawing fractions on paper (e.g., as parts of a circle or rectangle) helps understand their meaning.

Break it down

Divide the problem into smaller steps—find the common denominator, convert fractions, subtract numerators.

Check your work

Use a fraction calculator to verify your answers and identify mistakes.

Practice Problems—Test Your Skills

Solve on your own:

Task 1: Subtract fractions with the same denominator

  • \( \large \frac{5}{6} - \frac{1}{6} \)
  • \( \large \frac{9}{10} - \frac{4}{10} \)
  • \( \large \frac{7}{8} - \frac{5}{8} \)

Task 2: Subtract fractions with different denominators

  • \( \large \frac{2}{3} - \frac{1}{4} \)
  • \( \large \frac{5}{6} - \frac{3}{10} \)
  • \( \large \frac{7}{12} - \frac{2}{9} \)

Task 3: Real-world applications

  • A recipe calls for \( \large \frac{3}{4} \) cup of flour, but you only have \( \large \frac{1}{2} \) cup. How much more flour do you need?
  • From a piece of fabric measuring \( 2\frac{1}{3} \) meters, \( 1\frac{1}{2} \) meters were used. How much fabric is left?

Summary

Practice with our calculator to solidify your fraction subtraction skills!

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