# How do you solve 5/f=35/21?

Apr 8, 2018

$f = 3$

#### Explanation:

Cross multiply:

$5 \cdot 21 = 35 \cdot f$

$35 f = 105$

$f = 3$

These two are equivalent fractions. The second fraction can be derived from the first one. In order for them to be equivalent, the numerator and denominator both have to be multiplied/divided by the same number.

5 is multiplied by 7 to get 35, so f must also be multiplied by 7 to get 21.

$7 \cdot f = 21$

$f = 3$

Apr 8, 2018

$f = 3$

#### Explanation:

$\frac{5}{f} = \frac{35}{21}$ (First, multiply both sides by f)

$5 = \frac{35}{21} f$ (Multiply both sides of the reciprocal of $\frac{35}{21}$ which is $\frac{21}{35}$)

$5 \left(\frac{21}{35}\right) = f$ (Distribute 5 to the numbers in bracket)

$\frac{21}{7} = f$ (Simplify the left side)

$3 = f$

Check the answer by plugging it into the original equation:

$\frac{5}{3} = \frac{35}{21}$ (7 if a factor for the right side to simplify it)

$\frac{5}{3} = \frac{5}{3}$