Question

An expression is shown

5/6 m + 12 - 2/3 m-6

a student wrote the steps she used to determine an expression equivalent to the expression shown.

step 1: 5/6 m+12-2/3 m-6

step 2: 5/6 m-2/3 m + 12-6

step 3:(5/6) (- 2/3) m +12-6

step 4: - 10/18 m +6

in which step did the student make her first error?

explain your response

write the correct expression for this step

explain your response

Answer 1

Explanation:

`(5)/(6)m+12-(2)/(3)-6`

*Note that
`-(2)/(3)` is equivalent to
`-(4)/(6)`*

`Step\ 1\ (5)/(6)m+12-(2)/(3)m-6 \\\\`

`Step\ 2\ (5)/(6)m-(2)/(3)m+12-6 \\\\`

`Step\ 3\ ((5)/(6))(-(2)/(3))m+12-6 \\\\` <== this is where the mistake was made.

`Step\ 4\ -(10)/(6)m+6`

Questions:

1. In which step did the student make her first error?

Explanation: The students made her first error in Step 3 because she multiplied the fractions, instead of subtracting them.

2. Write the correct expression for this step

The correct expression for Step 3:

`Step\ 2\ (5)/(6)m-(2)/(3)m+12-6\\\\`

`(5)/(6)m-(4)/(6)m+12-6\\\\`

`(1)/(6)m+12-6\\`

`(1)/(6)m+6`

Explanation: First, I converted
`-(2)/(3)` to
`-(4)/(6)`. Then subtracted the fraction. After, I subtracted the number (integers).

Hope this helps!