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

Answer:

Becky's mistake was that she said $\frac{4}{5} - \frac{5}{4} = 0$, while it's actually equal to $-\frac{9}{4}$.

Step-by-step explanation:

$\quad\begin{aligned} &\dfrac{4}{5} +7 -\dfrac{5}{4}\\\\ \\ =&\dfrac{4}{5} -\dfrac{5}{4}+7&\green{\text{Step } 1} \\\\ \\ \\ =&0+7&\blue{\text{Step } 2}\\\\ \\ \\ =&7&\purple{\text{Step } 3} \\\\ \\ \\ \end{aligned}$

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

Step 2 is where she said that  $\frac{4}{5} - \frac{5}{4} = 0$. 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!