Adding and Subtracting Fractions - TutorOne USA

Adding and Subtracting Fractions

Adding and Subtracting Fractions Concept Explanation:

When adding and subtracting fractions, the main idea is to have the same denominator. If the denominators are different, find the least common denominator (LCD) before adding or subtracting.

Adding fractions:

$\frac{a}{d} + \frac{b}{d} = \frac{a + b}{d}$

If the denominators are not the same, find the LCD and rewrite each fraction:

$\frac{a}{x} + \frac{b}{y} = \frac{a \cdot y}{x \cdot y} + \frac{b \cdot x}{y \cdot x}$

Subtracting fractions:
Similar to addition, but subtract the numerators.

Diagram:

Example: Adding $\frac{3}{4} + \frac{2}{5}$

$\begin{array}{c} \begin{aligned} &\frac{3}{4} = \frac{15}{20} \ &\frac{2}{5} = \frac{8}{20} \ &\frac{15}{20} + \frac{8}{20} = \frac{23}{20} = 1 \frac{3}{20} \end{aligned} \end{array}$

Hard Questions:

Q1: Add $\frac{5}{6} + \frac{3}{4}$ .

Step-by-Step Solution:

Find the LCD of 6 and 4, which is 12.
Rewrite the fractions:

$\frac{5}{6} = \frac{10}{12}, \quad \frac{3}{4} = \frac{9}{12}$

Add the fractions:

$\frac{10}{12} + \frac{9}{12} = \frac{19}{12} = 1 \frac{7}{12}$

Answer:

The sum is $1 \frac{7}{12}$ .

Q2: Subtract $\frac{7}{9} - \frac{5}{12}$ .

Step-by-Step Solution:

Find the LCD of 9 and 12, which is 36.
Rewrite the fractions:

$\frac{7}{9} = \frac{28}{36}, \quad \frac{5}{12} = \frac{15}{36}$

Subtract the fractions:

$\frac{28}{36} - \frac{15}{36} = \frac{13}{36}$

Answer:

The difference is $\frac{13}{36}$ .

Q3: Add $\frac{3}{5} + \frac{4}{7}$ .

Step-by-Step Solution:

Find the LCD of 5 and 7, which is 35.
Rewrite the fractions:

$\frac{3}{5} = \frac{21}{35}, \quad \frac{4}{7} = \frac{20}{35}$

Add the fractions:

$\frac{21}{35} + \frac{20}{35} = \frac{41}{35} = 1 \frac{6}{35}$

Answer:

The sum is $1 \frac{6}{35}$ .

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