https://file.aiquickdraw.com/mathbot/file/17264336901206qlczq3u.jpg

The text in the image reads:

"Three quarters of a number added to two and a half of that number gives 13. Find the missing number."

We can translate this into a mathematical equation. Let's call the unknown number \( x \).

- Three quarters of the number is \( \frac{3}{4}x \).
- Two and a half of the number is \( \frac{5}{2}x \).
- Together, they sum to 13.

So the equation is:

\[
\frac{3}{4}x + \frac{5}{2}x = 13
\]

To solve this, let's first find a common denominator for the fractions (the least common denominator between 4 and 2 is 4). Therefore:

\[
\frac{3}{4}x + \frac{10}{4}x = 13
\]

Now, combine the fractions:

\[
\frac{3x + 10x}{4} = 13
\]

Simplify the numerator:

\[
\frac{13x}{4} = 13
\]

Now, solve for \( x \) by multiplying both sides by 4:

\[
13x = 52
\]

Finally, divide both sides by 13:

\[
x = 4
\]

Thus, the missing number is \( x = 4 \).

Would you like more details or have any further questions? 

Here are five related questions you might want to explore:
1. How would you solve this equation if the fractions were more complex?
2. What if the equation involved subtraction instead of addition?
3. Can you solve a similar problem where three different fractions are involved?
4. How can we check if the solution is correct?
5. How would the equation change if the sum were a different number, say 20?

**Tip:** When solving equations with fractions, finding a common denominator is key to simplifying the problem effectively.

Three quarters of a number added to two and a half of that number gives 13. Find the missing number.

Learn how to solve an algebraic equation involving fractions where three quarters of a number and two and a half times the same number sum to 13. This tutorial includes step-by-step instructions, formulas, and key algebra concepts, suitable for middle school students in Grades 6-8.

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