https://r2.erweima.ai/mathbot/image/17258865293705zb7chk6.jpg

The equation given in the image is:

\[
\frac{9}{4}x - \frac{1}{8} = \frac{5}{8}
\]

**(a) To find the smallest positive number by which both sides of the equation can be multiplied to clear fractions:**

1. Identify the denominators in the equation: 4 and 8.
2. Find the Least Common Multiple (LCM) of these denominators.

The LCM of 4 and 8 is 8, as 8 is the smallest number that both 4 and 8 divide into evenly.

Therefore, the smallest positive number by which both sides of the equation can be multiplied to clear fractions is:

\[
\boxed{8}
\]

Would you like further assistance or have any questions? 

### Related Questions:
1. How do you solve the equation after clearing fractions?
2. What is the LCM of other pairs of numbers, like 3 and 9?
3. How do you clear fractions in more complex equations?
4. Can the LCM method be used in equations with variables in the denominator?
5. How does multiplying by the LCM simplify solving equations?

**Tip:** Multiplying both sides of an equation by the LCM of all denominators is a quick way to eliminate fractions and simplify calculations.

For the equation 9/4x - 1/8 = 5/8, give the smallest positive number by which both sides of the equation can be multiplied to clear fractions.

Discover how to solve algebraic equations by finding the Least Common Multiple (LCM) to clear fractions, using the example of 9/4x - 1/8 = 5/8. This method simplifies calculations and provides a straightforward path to solve for x. Ideal for middle school to high school students.

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