Question

Drag the tiles to the correct boxes to complete the pairs.

Match each division problem to its quotient.

Answer 1

Part 1)
`-1.25` ------->
`2.75/(-2.2)`

Part 2)
`-4(1)/(3)` -------->
`(-2(3)/(5)) / ((3)/(5))`

Part 3)
`(2)/(3)` ------>
`(-(10)/(17)) / (-(15)/(17))`

Part 4)
`3` ------>
`(2(1)/(4)) / ((3)/(4))`

Explanation:

Part 1) we have

`2.75/(-2.2)`

To calculate the division problem convert the decimal number to fraction number

`2.75=275/100\\ -2.2=-22/10`

so

`(275/100)/(-22/10)`

Remember that

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

`(275/100)/(-22/10)=(275/100)*(-10/22)=-(275*10)/(22*100)=-(275)/(220)`

Simplify

Divide by 22 both numerator and denominator

`-(275)/(220)=-125/100=-1.25`

Part 2) we have

`(-2(3)/(5)) / ((3)/(5))`

To calculate the division problem convert the mixed number to an improper fraction

`(-2(3)/(5))=-(2*5+3)/(5)=-(13)/(5)`

so

`(-(13)/(5)) / ((3)/(5))`

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

`(-(13)/(5)) / ((3)/(5))=(-(13)/(5))*((5)/(3))=-(13*5)/(5*3)=-(13)/(3)`

Convert to mixed number

`-(13)/(3)=-((12)/(3)+(1)/(3))=-4(1)/(3)`

Part 3) we have

`(-(10)/(17)) / (-(15)/(17))`

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

`(-(10)/(17)) / (-(15)/(17))=(-(10)/(17))*(-(17)/(15))=(10*17)/(17*15)=(10)/(15)`

Simplify

Divide by 5 both numerator and denominator

`(10)/(15)=(2)/(3)`

Part 4) we have

`(2(1)/(4)) / ((3)/(4))`

To calculate the division problem convert the mixed number to an improper fraction

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

so

`((9)/(4)) / ((3)/(4))`

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction

`((9)/(4)) / ((3)/(4))=((9)/(4))*((4)/(3))=(9*4)/(4*3)=(9)/(3)=3`