# ACT Math : How to simplify an expression

## Example Questions

### Example Question #81 : Expressions

Suzanne is at the grocery store. She has $5.00 to spend on produce. Oranges are$2.50 per pound, apples cost $1.50 per pound and bananas are$0.50 per pound. Which combination of fruit will fit her budget?

3 pounds of apples and 2 pounds of bananas

1.5 pounds of oranges and 4 pounds of bananas

1 pound of oranges, 1 pound of apples and 2 pounds of bananas

2 pounds of oranges and 1 pound of apples

1 pound of oranges, 1.5 pounds of apples and 1.5 pounds of bananas

1 pound of oranges, 1 pound of apples and 2 pounds of bananas

Explanation:

Make a simple algebra equation and test it against each combination:

### Example Question #11 : Simplifying Expressions

Which of the following is equivalent to (x)(x)(x)(x)(x2)?

x2

x3

x2

x8

x2

Explanation:

When multiplying powers of x, we add the exponents. The first four terms are equivalent to x4.

### Example Question #991 : Algebra

What is  in simplified form?

Explanation:

Reduce by first dividing all terms by 2:

Next divide the terms in the numerator by the two variables in the denominator.  Remember that dividing variables with exponents is really just subtraction of those exponents:

### Example Question #11 : Simplifying Expressions

Simplify the expression:

x

2x

x+ 2x + 1

x + 1

2x + 1

x + 1

Explanation:

Factor out a (2x) from the denominator, which cancels with (2x) from the numerator. Then factor the numerator, which becomes (+ 1)(+ 1), of which one of them cancels and you're left with (+ 1).

### Example Question #11 : How To Simplify An Expression

Find , given that

Explanation:

Create two equations to eliminate the absolute value function, one where the value inside the absolute value bars is assumed to be positive and another where it is assumed to be negative: 7x – 4 + 5 >  –1  and  -7x + 4 + 5 > –1.

The solutions for the equations, respectively, are  x > -2/7  and x < -10/7. (Remember to flip the inequality sign when multiplying or dividing by a negative number.)

### Example Question #1 : How To Do Distance Problems

Trevor took a road trip in his new VW Beetle. His car averages 32 miles per gallon. Gas costs \$4.19 per gallon on average for the whole trip. How much would it coust to drive 3,152 miles?

Explanation:

To find this answer just do total miles divided by miles per gallon in order to find how many gallons of gas it will take to get from point A to Point B. Then multiply that answer by the cost of gasoline per gallon to find total amount spent on gasoline.

### Example Question #1 : How To Simplify An Expression

a # b = (a * b) + a

What is 3 # (4 # 1)?

27

8

20

15

12

27

Explanation:

Work from the "inside" outward.  Therefore, first solve 4 # 1 by replacing a with 4 and b with 1:

4 # 1 = (4 * 1) + 4 = 4 + 4 = 8

That means: 3 # (4 # 1) = 3 # 8.  Solve this now:

3 # 8 = (3 * 8) + 3 = 24 + 3 = 27