Product of fractions
Find the product of these mixed numbers
Age
11 to 14
Challenge level
Problem
Can you find an efficient way of calculating the product below, without using a calculator?
$$1\frac23\times1.8\times1\frac17\times1.75\times1\frac56$$
This problem is taken from the World Mathematics Championships
Student Solutions
Answer: $11$
$$\begin{align}1\frac23\times1.8\times1\frac17\times1.75\times1\frac56&=
1\frac23\times1\frac45\times1\frac17\times1\frac34\times1\frac56\\
&\ \\
&=\ \frac53\ \times\ \frac95\ \times\ \frac87\ \times\ \frac74\ \times\ \frac{11}6\\
&\ \\
&=\quad \ \ \ \ 3\ \quad \ \ \ \times\ \quad \ \ 2\quad \ \ \ \ \times\ \ \frac{11}6\\
&\ \\
&=11\end{align}
$$