Question

find each number.
increase the number $5\frac{3}{7}$ by $\frac{2}{19}$ of it.

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \( 5\frac{3}{7} \) to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So for \( 5\frac{3}{7} \), we have \( \frac{5\times7 + 3}{7}=\frac{35 + 3}{7}=\frac{38}{7} \).

Step2: Find \( \frac{2}{19} \) of \( 5\frac{3}{7} \)

Now, find \( \frac{2}{19} \) of \( \frac{38}{7} \). To find a fraction of a number, we multiply them. So \( \frac{2}{19}\times\frac{38}{7} \). Simplify \( \frac{38}{19}=2 \), so this becomes \( \frac{2\times2}{7}=\frac{4}{7} \).

Step3: Add the result to the original number

Now, we need to increase \( 5\frac{3}{7} \) (which is \( \frac{38}{7} \)) by \( \frac{4}{7} \). So we add them: \( \frac{38}{7}+\frac{4}{7}=\frac{38 + 4}{7}=\frac{42}{7}=6 \).

Answer:

\( 6 \)