Problem of the Week

Updated at Sep 10, 2018 3:14 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve 5×54×5z=2545\times \frac{5}{4\times \frac{5}{z}}=\frac{25}{4}?

Check out the solution below!



5×54×5z=2545\times \frac{5}{4\times \frac{5}{z}}=\frac{25}{4}

1
Simplify  4×5z4\times \frac{5}{z}  to  20z\frac{20}{z}.
5×520z=2545\times \frac{5}{\frac{20}{z}}=\frac{25}{4}

2
Invert and multiply.
5×5×z20=2545\times 5\times \frac{z}{20}=\frac{25}{4}

3
Use this rule: ab×cd=acbd\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}.
5×5z20=254\frac{5\times 5z}{20}=\frac{25}{4}

4
Simplify  5×5z5\times 5z  to  25z25z.
25z20=254\frac{25z}{20}=\frac{25}{4}

5
Simplify  25z20\frac{25z}{20}  to  5z4\frac{5z}{4}.
5z4=254\frac{5z}{4}=\frac{25}{4}

6
Multiply both sides by 44.
5z=254×45z=\frac{25}{4}\times 4

7
Cancel 44.
5z=255z=25

8
Divide both sides by 55.
z=255z=\frac{25}{5}

9
Simplify  255\frac{25}{5}  to  55.
z=5z=5

Done
Cymath foriOSAndroid