Question
Slackmojis -... Play Consolat... Splendora ISD Zearn Roblox Start Page M3|L14 Rearrange and Solve Sign out Add the fifths, then the sevenths. \[ \begin{aligned} & \frac{4}{5}+\frac{2}{7}+1 \frac{1}{5}+\frac{5}{7} \\ = & \left(\frac{4}{5}+1 \frac{1}{5}\right)+\left(\frac{2}{7}+\frac{5}{7}\right) \\ = & \square+\square \end{aligned} \] (1) 2 3 4 5 6 7 8 9 0 Enter
Ask by Campos Fitzgerald. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\boxed{3}
\]
Solution
To solve the problem, we will follow the steps outlined in the equation. We need to add the fractions and the mixed number step by step.
1. **Convert the mixed number to an improper fraction:**
\[
1 \frac{1}{5} = \frac{5 \cdot 1 + 1}{5} = \frac{6}{5}
\]
2. **Rewrite the equation with the improper fraction:**
\[
\frac{4}{5} + \frac{2}{7} + \frac{6}{5} + \frac{5}{7}
\]
3. **Group the fractions as indicated:**
\[
\left(\frac{4}{5} + \frac{6}{5}\right) + \left(\frac{2}{7} + \frac{5}{7}\right)
\]
4. **Calculate the first group:**
\[
\frac{4}{5} + \frac{6}{5} = \frac{4 + 6}{5} = \frac{10}{5} = 2
\]
5. **Calculate the second group:**
\[
\frac{2}{7} + \frac{5}{7} = \frac{2 + 5}{7} = \frac{7}{7} = 1
\]
6. **Combine the results:**
\[
2 + 1 = 3
\]
Now we can fill in the squares in the original equation:
\[
\begin{aligned}
& \frac{4}{5}+\frac{2}{7}+1 \frac{1}{5}+\frac{5}{7} \\
= & \left(\frac{4}{5}+1 \frac{1}{5}\right)+\left(\frac{2}{7}+\frac{5}{7}\right) \\
= & 2 + 1
\end{aligned}
\]
Thus, the final answer is:
\[
\boxed{3}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To tackle the expression, let's first convert the mixed number into an improper fraction. One and one-fifth can be rewritten as \( \frac{6}{5} \). Now our equation looks like this: \[ \frac{4}{5} + \frac{6}{5} + \frac{2}{7} + \frac{5}{7} \] Now, we can combine the fifths and the sevenths separately. The fifths add up to \( \frac{10}{5} = 2 \), and the sevenths combine to \( \frac{7}{7} = 1 \). So, our final result is: \[ \square + \square = 2 + 1 \] That gives us a total of **3**! I hope that was as satisfying as combining LEGO bricks to create something awesome! Now you can put that knowledge to use in your next math challenge!
