Add and Subtract Fractions

This tutorial provides comprehensive coverage of adding and subtracting of fractions based on Common Core (CCSS) and State Standards and its prerequisites. Students can navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs. This simple tutorial uses appropriate examples to help you understand adding and subtracting of fractions in a general and quick way.

Audience

This tutorial has been prepared for beginners to help them understand the basics of adding and subtracting of fractions. After completing this tutorial, you will find yourself at a moderate level of expertise in adding and subtracting of fractions, from where you can advance further.

Prerequisites

Before proceeding with this tutorial, you need a basic knowledge of elementary math concepts such as number sense, addition, subtraction, multiplication, division, whole numbers, fractions, equivalent fractions, least common denominator and so on.

Definition

Fractions that have exact same denominators are called like fractions.

Fractions such as 15$\frac{1}{5}$ and 45$\frac{4}{5}$ are like fractions because they have a common denominator 5.

In other words, fractions with like denominators are categorized as like fractions. Performing any mathematical operations on like fractions is comparatively easier as we can make use of the common denominator for fraction operations like addition and subtraction.

Adding like fractions − Formula

If fractions with same denominators are to be added, we need to add the numerators only and keep the same denominator.

• We add the numerators.
• We keep the common denominator.
• Then the Sum of the fractions = (Sum−of−the−Numerators)(Common−Denominator)$\frac{(Sum-of-the-Numerators)}{(Common-Denominator)}$
• Sum of the fractions = ac$\frac{a}{c}$ + bc$\frac{b}{c}$ = (a+b)c$\frac{(a+b)}{c}$, where a, b and c are any three real numbers.

Subtracting like fractions − Formula

If fractions with same denominators are to be subtracted, we need to subtract the numerators only and keep the same denominator.

• We subtract the numerators.
• We keep the common denominator.
• Then the Difference of the fractions = (Difference−of−the−Numerators)(Common−Denominator)$\frac{(Difference-of-the-Numerators)}{(Common-Denominator)}$
• Difference of the fractions = ac$\frac{a}{c}$ − bc$\frac{b}{c}$ = (a−b)c$\frac{(a-b)}{c}$, where a, b and c are any three real numbers

Problem 1:

Add 37$\frac{3}{7}$ + 27$\frac{2}{7}$

Solution

Step 1:

Here, the denominators are the same 7. We add the numerators 3 + 2 = 5 and put the result 5 over the common denominator 7 to get the answer.

37$\frac{3}{7}$ + 27$\frac{2}{7}$ = (3+2)7$\frac{(3+2)}{7}$ = 57$\frac{5}{7}$

Step 2:

So, 37$\frac{3}{7}$ + 27$\frac{2}{7}$ = 57$\frac{5}{7}$

Problem 2:

Subtract 56$\frac{5}{6}$ − 46$\frac{4}{6}$

Solution

Step 1:

Here, the denominators are the same 6. We subtract the numerators; 5 − 4 = 1 and put the result 1 over the common denominator to get the answer.

56$\frac{5}{6}$ − 46$\frac{4}{6}$ = (5−4)6$\frac{(5-4)}{6}$ = 16$\frac{1}{6}$

Step 2:

So, 56$\frac{5}{6}$ − 46$\frac{4}{6}$ = 16

Adding like fractions and simplification − Formula

If fractions with same denominators are to be added, we add the numerators only and keep the same denominator. If necessary, we simplify the resulting fraction to lowest terms.

• Sum of the fractions = ac$\frac{a}{c}$ + bc$\frac{b}{c}$ = (a+b)c$\frac{(a+b)}{c}$, where a, b and c are any three real numbers.

Subtracting like fractions and simplification − Formula

If fractions with same denominators are to be subtracted, we subtract the numerators only and keep the same denominator. If necessary, we simplify the resulting fraction to lowest terms.

• Difference of the fractions = ac$\frac{a}{c}$ − bc$\frac{b}{c}$ = (a−b)c$\frac{(a-b)}{c}$, where a, b and c are any three real numbers.

Problem 1:

Add 38$\frac{3}{8}$ + 18$\frac{1}{8}$

Solution

Step 1:

Add 38$\frac{3}{8}$ + 18$\frac{1}{8}$

Here, the denominators are the same 8. Since this is an addition operation,

We add the numerators 3 + 1 = 4 and put the result 4 over the common denominator to get the answer.

So 38$\frac{3}{8}$ + 18$\frac{1}{8}$ = (3+1)8$\frac{(3+1)}{8}$ = 48$\frac{4}{8}$

Step 2:

Reducing the fraction to lowest terms

48$\frac{4}{8}$ = 12$\frac{1}{2}$

So, 38$\frac{3}{8}$ + 18$\frac{1}{8}$ = 12$\frac{1}{2}$

Problem 2:

Subtract 56$\frac{5}{6}$ − 16$\frac{1}{6}$

Solution

Step 1:

Subtract 56$\frac{5}{6}$ − 16$\frac{1}{6}$

Here, the denominators are same 6. Since this is a subtraction operation, we subtract the numerators, 5 − 1 = 4 and put the result 4 over the common denominator 6.

So 56$\frac{5}{6}$ − 16$\frac{1}{6}$ = (5−1)6$\frac{(5-1)}{6}$ = 46$\frac{4}{6}$

Step 2:

Simplifying to the lowest terms,

46$\frac{4}{6}$ = 23$\frac{2}{3}$

So, 56$\frac{5}{6}$ − 16$\frac{1}{6}$ = 23

$\frac{\mathrm{<br>}}{}$

$\frac{\mathrm{<br>}}{}$

$\frac{\mathrm{<br>}}{}$