Question

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

Read each of their methods below and then enter numbers to correctly complete their work.

Answer 1

Answer:Barbara writes each number as a fraction and then multiplies.

-24/5 -12/5

Answer:Christopher writes the mixed number as a sum and uses the distributive property.

-4 -4/5 -2 -2/5

Answer:Barbara's and Christopher’s answers will be equal. Write the answer as a mixed number in simplest form.

-2 2/5

Explanation:

Answer 2

`(1)/(2)*-4 (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.
`(1)/(2)*-4 (4)/(5)=(1)/(2) * (-24)/(5)=(-12)/(5)=-2(2)/(5)`

2.
`(1)/(2)*-4 (4)/(5)=(1)/(2)[-4-(4)/(5)]=(1)/(2)* (-4)+(1)/(2)*(-4)/(5)=-2+(-2)/(5)=(-10-2)/(5)=(-12)/(5)=-2(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.