Question

Elena divided a decimal by a whole number. 84.36 ÷ 12 = ? Part A: Explain each step needed to divide 84.3y by 12. Part B: What is the correct qoutient?

Answer 1

Part A.
`(84.3y)/(12) = 7 +(0.1\cdot y)/(4)`

Part B. The correct quotient is (3 × 4)

Explanation:

Part A.

To divide 84.36 by 12 we look for the Highest Common Factor of the whole number and the decimal portions of the numerator and the denominator individually as follows;

`(84.36)/(12) = (84+0.3636)/(12) = (2 * 2 * 3 * 7+0.01* 12* 3)/(12) = (12 * 7+0.03* 12)/(12)`

Therefore, dividing 84.36 by 12 gives
`(12 * 7+0.03* 12)/(12) = 7+0.03` = 7.03

When dividing 84.3·y by 12, therefore, we have;

`(12 * 7+0.3* y)/(12) = 7 +(0.1\cdot y)/(4)`

Part B.

The correct quotient should have factors of the numerator

Therefore the divisor 12 should be represented as follows

`(12 * 7+0.3* y)/(12) =(12 * 7+0.3* y)/(3 * 4)`

The correct quotient therefore = (3 × 4)