simplify each expression  5- 3/4 - (- 8/9)

Let's simplify the expression:

\[
5 - \frac{3}{4} - \left( - \frac{8}{9} \right)
\]

### Step 1: Eliminate the double negative
The expression \( - (-\frac{8}{9}) \) becomes \( + \frac{8}{9} \), so the new expression is:

\[
5 - \frac{3}{4} + \frac{8}{9}
\]

### Step 2: Convert 5 to a fraction
Rewrite 5 as a fraction with a denominator that matches the others. The least common denominator between 4 and 9 is 36, so rewrite 5 as:

\[
5 = \frac{180}{36}
\]

Now the expression is:

\[
\frac{180}{36} - \frac{3}{4} + \frac{8}{9}
\]

### Step 3: Convert the fractions to have the same denominator
- \(\frac{3}{4}\) can be written as \(\frac{27}{36}\) (since \(4 \times 9 = 36\))
- \(\frac{8}{9}\) can be written as \(\frac{32}{36}\) (since \(9 \times 4 = 36\))

Now the expression is:

\[
\frac{180}{36} - \frac{27}{36} + \frac{32}{36}
\]

### Step 4: Combine the fractions
Now, combine all the fractions over the common denominator:

\[
\frac{180 - 27 + 32}{36} = \frac{185}{36}
\]

Thus, the simplified form of the expression is:

\[
\frac{185}{36}
\]

This fraction is already in its simplest form.

Would you like any further explanation or details?

Here are five questions to expand your understanding:
1. How do you find the least common denominator of multiple fractions?
2. What happens when you subtract a negative number?
3. How do you simplify fractions after performing operations on them?
4. Can the result \(\frac{185}{36}\) be written as a mixed number?
5. How would you solve this if the numbers were decimals instead of fractions?

**Tip:** When combining fractions, always find a common denominator to make addition and subtraction easier.

simplify each expression 5 - 3/4 - (-8/9)

Learn how to simplify the expression 5 - 3/4 - (-8/9) with detailed step-by-step instructions. This math problem covers key concepts like adding and subtracting fractions and handling double negatives. Ideal for students in Grades 6-8.

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