# ACT Math : Operations and Fractions

## Example Questions

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### Example Question #1 : Operations And Fractions

What value of  makes the equation  true?

Explanation:

We can simply cross multiply to obtain  and divide by 8 to solve for .

### Example Question #2 : Operations And Fractions

Simplfiy the following expression;

Explanation:

Multiply the numerators  2 x 6 x 4 = 48. Then multiply the denominators 3 x 8 x 12 = 288.  The answer is 48/288. To simplify, divide both numerator and denominator by 48 to get 1/6.

### Example Question #3 : Operations And Fractions

Evaluate –3–2 * 2–3.

Explanation:

Because the exponents are negative, we can convert –3–2  to 1/9 and 2–3 to 1/8. We then multiply straight across the top and the bottom, giving you 1/72.

### Example Question #4 : Operations And Fractions

Simplify the following into one fraction

Explanation:

To multiply fractions you multiply the entire numerator and the entire denominator together. However, before we do that we can cancel anything from the denominator with anything in the numerator.

Six cancels with 12

5 cancels with 25

multiply it all out and get

### Example Question #5 : Operations And Fractions

Explanation:

Cross multiply or multiply using the reciprocal of the second fraction.

### Example Question #6 : Operations And Fractions

Simplify the following expression:

Explanation:

### Example Question #7 : Operations And Fractions

Evaluate the following:

Explanation:

Start by converting 71/to 22/3, and 6 2/to 20/3. We then multiply 22/3 by the reciprocal of 20/3, 3/20, and you get 66/60. This simplifies to 11/10.

### Example Question #8 : Operations And Fractions

Solve.

Explanation:

Remember, to divide a number by a fraction, multiply the number by the reciprocal of the fraction. In this case,

### Example Question #9 : Operations And Fractions

Solve for x where

Explanation:

To solve this, subtract 1 1/2 from both sides. Convert to common denominators.

4 1/3 – 1 1/2 = 4 2/6 – 1 3/6.

In order to subtract, you'll want to "borrow" from the 4 2/6. Rewrite 4 2/6 as 3 8/6 and then subtract 1 3/6 from this. Your solution is 2 5/6. Most calculators will also do these calculations for you.

Solve for :

Explanation: