Question

2. Perform the indicated operation. Express your answer in simplest form. Show any necessary work. Then answer the question. (a) -2.48/12.4 (b) -12.5/-0.025 (c) Imagine your friend uses long division to determine the quotients, and is confused by how quickly you were able to determine the correct answer without performing long division. Explain how you were able to determine the quotients without performing long division.

Answer 1

Part a

we have the expression

`(-2.48)/(12.4)`

Multiply the fraction by 100/100 to remove decimal numbers

`(-2.48)/(12.4)\cdot(100)/(100)=-(248)/(1,240)`

Simplify the fraction

`-(248)/(1,240)=-(1)/(5)`

Part b

we have the expression

`(-12.5)/(-0.025)`

Multiply the expression by 1,000/1,000 to remove decimal numbers

so

`(-12.5)/(-0.025)\cdot(1000)/(1000)=(12,500)/(25)`

Simplify

`(12,500)/(25)=(500)/(1)=500`

Part c

to determine the quotients without performing long division

step 1

Convert the decimal numbers of the quotient to integer numbers, multiplying the numerator and denominator by a fraction of the form 10/10, 100/100,1000/1000, etc

step 2

Simplify the fraction in the simplest form