Question

Choose the correct valuefor the following expression: $1\frac{3}{4}÷2\frac{6}{7}=$

• A. $5$
• B. $\frac{1}{5}$
• C. $\frac{49}{80}$
• D. $\frac{31}{80}$

Answer 1

The correct option is C $\frac{49}{80}$

Given : $1\frac{3}{4}÷2\frac{6}{7}$

Convert the mixed fractions into improper fractions
$1\frac{3}{4}=\frac{1\times 4+3}{4}=\frac{7}{4}$

$2\frac{6}{7}=\frac{2\times 7+6}{7}=\frac{20}{7}$

We need to solve $\frac{7}{4}÷\frac{20}{7}$

Step 1: Turn the second fraction upside down (it becomes a reciprocal)
$\frac{20}{7}$ becomes $\frac{7}{20}$

Step 2: Multiply the first fraction by that reciprocal
$\frac{7}{4}\times \frac{7}{20}$

Now, we have to multiply the top numbers and the bottom numbers as follows.

$\therefore \frac{7}{4}\times \frac{7}{20}=\frac{7\times 7}{4\times 20}=\frac{49}{80}$

Step 3: Simplify the fraction

There is no common factor between numerator and denominator of the resulting fraction.

$\therefore 1\frac{3}{4}÷2\frac{6}{7}=\frac{49}{80}$