Question

Replace each with <, > or = to make a true sentence.

$\frac{12}{44}\cdot \frac{8}{11}$

Short answer

The true statement is $\frac{12}{44}<\frac{8}{11}$.

Step-by-step solution

Step 1. Take L.C.M of the denominators of each fraction.

$\text{L.C.Mof44and11}=44$

Step 2. Write all fractions with the same denominator.

First, make the denominators of all fractions equal to LCM by multiplying the numerator and denominator with an integer.

Here the first fraction has a denominator as LCM already but the denominator of the second fraction is not the same as LCM. So, multiply the second fraction up and down by 4 to get

$\begin{array}{c}\frac{8}{11}=\frac{8\cdot 4}{11\cdot 4}\\ =\frac{32}{44}\end{array}$

Step 3. Comparing the numerator of both fractions.

Now, since the denominators of both fractions are equal, so compare the numerators. The fraction with a larger numerator will be greater than another fraction.

Here observe that

$12<32$

Therefore, the true statement is $\frac{12}{44}<\frac{8}{11}$.