A quantity is multiplied successively by 1 1/2, 1 1/3, 1 1/4 and 1 1/5. By what total factor is it multiplied?

Learn / Library / Mental math

Chain of mixed growth factors

Mental mathHard

A quantity is multiplied successively by $1 \frac{1}{2}$ , $1 \frac{1}{3}$ , $1 \frac{1}{4}$ and $1 \frac{1}{5}$ . By what total factor is it multiplied?

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

Convert each mixed number and look for cancelling pairs.

Solution

The factors are $\frac{3}{2}$ , $\frac{4}{3}$ , $\frac{5}{4}$ and $\frac{6}{5}$ .
Multiply: $\frac{3}{2} \times \frac{4}{3} \times \frac{5}{4} \times \frac{6}{5}$ .
Every numerator cancels the previous denominator, leaving $\frac{6}{2}$ .
So the total factor is $3$ .

Answer: $3$

Next question Back to the library