Problem of the Week

Updated at Jun 22, 2026 8:57 AM

How can we solve the equation \(\frac{4(\frac{y}{5}+2)}{5}=\frac{56}{25}\)?

Below is the solution.



\[\frac{4(\frac{y}{5}+2)}{5}=\frac{56}{25}\]

1
Multiply both sides by \(5\).
\[4(\frac{y}{5}+2)=\frac{56}{25}\times 5\]

2
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[4(\frac{y}{5}+2)=\frac{56\times 5}{25}\]

3
Simplify  \(56\times 5\)  to  \(280\).
\[4(\frac{y}{5}+2)=\frac{280}{25}\]

4
Simplify  \(\frac{280}{25}\)  to  \(\frac{56}{5}\).
\[4(\frac{y}{5}+2)=\frac{56}{5}\]

5
Divide both sides by \(4\).
\[\frac{y}{5}+2=\frac{\frac{56}{5}}{4}\]

6
Simplify  \(\frac{\frac{56}{5}}{4}\)  to  \(\frac{56}{5\times 4}\).
\[\frac{y}{5}+2=\frac{56}{5\times 4}\]

7
Simplify  \(5\times 4\)  to  \(20\).
\[\frac{y}{5}+2=\frac{56}{20}\]

8
Simplify  \(\frac{56}{20}\)  to  \(\frac{14}{5}\).
\[\frac{y}{5}+2=\frac{14}{5}\]

9
Subtract \(2\) from both sides.
\[\frac{y}{5}=\frac{14}{5}-2\]

10
Simplify  \(\frac{14}{5}-2\)  to  \(\frac{4}{5}\).
\[\frac{y}{5}=\frac{4}{5}\]

11
Multiply both sides by \(5\).
\[y=\frac{4}{5}\times 5\]

12
Cancel \(5\).
\[y=4\]

Done
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