Question

1. explain how to find a common denominator to add $\frac{2}{3}$ and $\frac{3}{4}$. show your steps.

Explanation:

Step1: Identify denominators

Denominators are $3$ and $4$.

Step2: Find least common multiple (LCM)

Multiples of $3$: $3, 6, 9, 12, ...$
Multiples of $4$: $4, 8, 12, ...$
LCM of $3$ and $4$ is $12$, so common denominator is $12$.

Step3: Rewrite fractions with common denominator

For $\frac{2}{3}$: $\frac{2 \times 4}{3 \times 4} = \frac{8}{12}$
For $\frac{3}{4}$: $\frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

Step4: Add the rewritten fractions

$\frac{8}{12} + \frac{9}{12} = \frac{8+9}{12} = \frac{17}{12}$

Answer:

The common denominator (least common denominator) of $\frac{2}{3}$ and $\frac{3}{4}$ is 12, and their sum is $\frac{17}{12}$ (or $1\frac{5}{12}$ as a mixed number).