Question

Unit test Problem Becky tried to evaluate an expression step by step. \quad\begin{aligned} &\dfrac{4}{5} +7 -\dfrac{5}{4}\\\\ \\ =&\dfrac{4}{5} -\dfrac{5}{4}+7&\green{\text{Step } 1} \\\\ \\ \\ =&0+7&\blue{\text{Step } 2}\\\\ \\ \\ =&7&\purple{\text{Step } 3} \\\\ \\ \\ \end{aligned} = = = ​ 5 4 ​ +7− 4 5 ​ 5 4 ​ − 4 5 ​ +7 0+7 7 ​ Step 1 Step 2 Step 3 ​ Find Becky's mistake.

Answer 1

step 2 is wrong

Explanation:

Answer 2

Becky's mistake was that she said
`(4)/(5) - (5)/(4) = 0`, while it's actually equal to
`-(9)/(4)`.

Explanation:

`\quad\begin{aligned} &(4)/(5) +7 -(5)/(4)\\\\ \\ =&(4)/(5) -(5)/(4)+7&\green{\text{Step } 1} \\\\ \\ \\ =&0+7&\blue{\text{Step } 2}\\\\ \\ \\ =&7&\purple{\text{Step } 3} \\\\ \\ \\ \end{aligned}`

Step 1 looks fine as she just rearranged the equation, keeping the negatives and positives right.

Step 2 is where she said that
`(4)/(5) - (5)/(4) = 0`. This would only be true if we were multiplying one of the numbers by 0. So Step 2 was wrong.

Step 3 is right, as 0+7 = 7.

Hope this helped!