The expression in the image is:

$7 \frac{1}{2} \div 5 + \frac{3}{4} \times 8 - \frac{1}{8}$

To solve this, we can break it down into steps.

Step 1: Convert Mixed Numbers to Improper Fractions

The term $7 \frac{1}{2}$ can be written as: $7 \frac{1}{2} = \frac{15}{2}$

Step 2: Divide $\frac{15}{2}$ by 5

Dividing by 5 is the same as multiplying by $\frac{1}{5}$: $\frac{15}{2} \div 5 = \frac{15}{2} \times \frac{1}{5} = \frac{15}{10} = \frac{3}{2}$

Step 3: Multiply $\frac{3}{4}$ by 8

$\frac{3}{4} \times 8 = \frac{3 \times 8}{4} = \frac{24}{4} = 6$

Step 4: Evaluate the Final Expression

Now substitute back into the original expression: $\frac{3}{2} + 6 - \frac{1}{8}$

Step 5: Find a Common Denominator and Simplify

The common denominator for $\frac{3}{2}$, $6$, and $\frac{1}{8}$ is 8. Rewrite each term with this denominator:

• $\frac{3}{2} = \frac{12}{8}$
• $6 = \frac{48}{8}$
• $\frac{1}{8}$ stays as it is.

Now the expression is: $\frac{12}{8} + \frac{48}{8} - \frac{1}{8} = \frac{59}{8}$

Final Answer

$\frac{59}{8} \text{ or } 7 \frac{3}{8}$

Would you like further details or have any questions?

Here are five related questions for practice:

1. How would you simplify $5 \frac{1}{3} \div 3$?
2. What is $8 \frac{2}{5} \times 4$?
3. How do you convert a mixed number into an improper fraction?
4. How do you handle fractions in addition or subtraction?
5. How would you solve $\frac{7}{3} + 5 - \frac{2}{3}$?

Tip: When dividing by a whole number, convert it to a fraction (like 5 becomes $\frac{1}{5}$) and multiply instead.