Question

Two students use different methods to solve this multiplication problem: 1/2 • -4 4/5

Answer 1

Solution:

$\frac{1}{2}\times-4 \frac{4}{5}$

As one of the fraction is a proper fraction and another one is Mixed fraction.

There are two methods of solving it.

1. $\frac{1}{2}\times-4 \frac{4}{5}=\frac{1}{2} \times \frac{-24}{5}=\frac{-12}{5}=-2\frac{2}{5}$

2. $\frac{1}{2}\times-4 \frac{4}{5}=\frac{1}{2}[-4-\frac{4}{5}]=\frac{1}{2}\times (-4)+\frac{1}{2}\times\frac{-4}{5}=-2+\frac{-2}{5}=\frac{-10-2}{5}=\frac{-12}{5}=-2\frac{2}{5}$→→Here i have used Distributive property with respect to addition and Subtraction i.e a×(b+c)= a ×b + a×c or a×(b-c)=a×b-a×c

Now, you can fill the blanks by yourself.