Question

What is the product of −4 1/2 and 2 1/2 ? Enter your answer as a mixed number, in simplified form, in the box.

Answer 1

let's firstly convert the mixed fractions to improper fractions and then multiply.

`\bf \stackrel{mixed}{4(1)/(2)}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}}~\hfill \stackrel{mixed}{2(1)/(2)}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{9}{2}\cdot \cfrac{5}{2}\implies -\cfrac{9\cdot 5}{2\cdot 2}\implies -\cfrac{45}{4}\implies -11(1)/(4)`

Answer 2

The product is
`-11\left((1)/(4)\right)`

Solution:

The first number is
`-4 (1)/(2)`

Now if we simplify the first number we get,
`-4 (1)/(2)=-\left(4+(1)/(2)\right)=-4-(1)/(2)`

`=(-4 * 2-1)/(2)=-(9)/(2)`

The second number is
`2\left((1)/(2)\right)`

If we simplify the second number we get,
`2 (1)/(2)=(2 * 2+1)/(2)=(5)/(2)`

Now the product of both the numbers are,

`-4 (1)/(2) * 2 (1)/(2)`

`\left(-(9)/(2)\right) * (5)/(2)`

`-\left((9 * 5)/(2 * 2)\right)`

`-\left((45)/(4)\right)`