ACT Math : How to simplify an expression

Study concepts, example questions & explanations for ACT Math

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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?

Possible Answers:

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

Correct answer:

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:

Total Cost = $2.50 * (# Oranges) +  $1.50 * (# Apples) +  $0.50 * (# Apples)

Example Question #1 : How To Simplify Expressions

Simplify the following expression:

 \dpi{100} \small 2(4x-3x)-6t+5x

Possible Answers:

\dpi{100} \small 6t-7x

\dpi{100} \small 14x - 11xt

\dpi{100} \small 7x-6t

\dpi{100} \small 1x-6t+5

\dpi{100} \small 6x+11x

Correct answer:

\dpi{100} \small 7x-6t

Explanation:

\dpi{100} \small 2(4x-3x)-6t+5x

First distribute the 2:    \dpi{100} \small 8x-6x-6t+5x

Combine the like terms:      \dpi{100} \small 7x-6t

Example Question #11 : How To Simplify An Expression

f pigeons land on a telephone wire. Then, g+2 pigeons fly away. Find an expression for the number of pigeons remaining.

Possible Answers:

2(f - g)

2(f + g)

f + g + 2

f - g - 2

f - g + 2

Correct answer:

f - g - 2

Explanation:

There are f - g - 2 pigeons remaining on the wire. We start with f pigeons, then subtract (g + 2) pigeons. f - (g + 2) = f - g - 2.

Example Question #1 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Erin is making thirty shirts for her upcoming family reunion. At the reunion she is selling each shirt for $18 apiece. If each shirt cost her $10 apiece to make, how much profit does she make if she only sells 25 shirts at the reunion?

Possible Answers:

Correct answer:

Explanation:

This problem involves two seperate multiplication problems. Erin will make $450 at the reunion but supplies cost her $300 to make the shirts. So her profit is $150.

Example Question #11 : Simplifying Expressions

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

Possible Answers:

x2

x3

x2

x8

Correct answer:

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 \small \frac{2(x^{3}y^{4})+2(x^{2}y^{2})}{(4x^{2})(4y^{2})} in simplified form?

Possible Answers:

\small \frac{xy^{2}}{4}

\small \frac{2xy^{2}+2}{16}

\small \frac{x^{3}y^{4}+x^{2}y^{2}}{4x^{2}y^{2}}

\small \frac{xy^{2}+1}{8}

\small \frac{x^{2}y^{2}+1}{4}

Correct answer:

\small \frac{xy^{2}+1}{8}

Explanation:

Reduce by first dividing all terms by 2:  \small \frac{(x^{3}y^{4})+(x^{2}y^{2})}{8x^{2}y^{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: \small \frac{xy^{2}+1}{8}

Example Question #11 : Simplifying Expressions

Simplify the expression:

Possible Answers:

x

2x

x+ 2x + 1

x + 1

2x + 1

Correct answer:

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

 

Possible Answers:

None of the other answers

Correct answer:

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?

Possible Answers:

Correct answer:

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)?

Possible Answers:

27

8

20

15

12

Correct answer:

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

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