Chapter A, Problem 1DE

Write a fraction expression equivalent to $\frac{2}{3}$ with a denominator of 12.

To determine

To calculate: The fraction expression which is equivalent to $\frac{2}{3}$ with a denominator of $12$.

Answer to Problem 1DE

Solution:

The fraction expression which is equivalent to $\frac{2}{3}$ with a denominator of $12$ is $\underset{\_}{\frac{8}{12}}$.

Explanation of Solution

Given information:

The provided fraction is $\frac{2}{3}$.

Formula used:

Equivalent expression can be found out by using two properties of numbers. These properties are:

1. The identity property of 0 (Additive identity)

For any number a,

$a+0=a$

2. The identity property of 1 (Multiplicative identity)

For any number a,

$a\cdot 1=a$

Calculation:

Consider the expression $\frac{2}{3}$ and solve as below:

Since,

$12=3\cdot 4$

It is required to find out the fraction notation for $\frac{2}{3}$ that has a denominator of $12$, but the denominator 3 is missing a factor of 4. Therefore, the equivalent expression of $\frac{2}{3}$ can be computed by using multiplicative identity property of 1 as below,

$\frac{2}{3}=\frac{2}{3}\cdot 1$

Use $\frac{4}{4}$ for 1,

$\begin{array}{c}\frac{2}{3}=\frac{2}{3}\cdot 1\\ =\frac{2}{3}\cdot \frac{4}{4}\end{array}$

Now, multiply numerators and denominators,

$\begin{array}{c}\frac{2}{3}=\frac{2}{3}\cdot 1\\ =\frac{2}{3}\cdot \frac{4}{4}\\ =\frac{8}{12}\end{array}$

Hence, the equivalent expression of $\frac{2}{3}$ with denominator of 12 is $\frac{8}{12}$.