Arithmetic

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ACT Math › Arithmetic

Questions 1 - 10
1

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.

2

Find the sum of the following:

Explanation

To get the decimal from a fraction, divide the numerator by the denominator

3

Restaurant

The menu above is from Lena’s Italian Kitchen. If you are going there for dinner, how many different combinations of a meal and a salad are there?

20

5

10

15

25

Explanation

Combinations = # first option * # second option

= # meals * # salads

= 5 * 4 = 20

4

A bowl contains marbles that are either red or green. The probability of selecting a red marble at random from the bowl is

Which of the following expressions represents the total number of red marbles in the bowl?

Explanation

It’s best to start with a fraction that is a part over 100. For this problem, we are looking for a fraction that shows . If you go through the choices available, . Therefore, if you plug in any value for “X” in this fraction, you will know the total number of marbles in the bowl. Here is an example:

If there are 4 marbles in the bowl, you’d expect 1 to be red. If we use this equation, we get

5

Solve:

Explanation

This problem can be solved using common factors.

Rewrite using factors.

6

At the beginning of a race, a person's speed is miles per hour. One hour into the race, a person increases his speed by . A half an hour later, he increases again by another . If he finishes this race in two hours, what is the average speed for the entire race? Round to the nearest hundredth of a mile per hour.

Explanation

Recall that in general

Now, let's gather our three rates:

Rate 1:

Rate 2:

Rate 3:

Now, we know that the time is a total of hours. Based on our data, we can write:

This is miles per hour, which rounds to .

7

Danielle has two jobs. Her retail job pays her $8.50 per hour and she works 20 hours per week in that job. Her office job pays her $12 per hour and she works 15 hours per week in the office. If she starts working an extra 10 hours a week at her office job, what is her percentage increase in total weekly pay? Round to one decimal point.

34.3%

33.4%

22.9%

25.7%

40.0%

Explanation

Pay = Hours worked x Rate per hour

Retail job = 20 x $8.50 = $170.00

Office job = 15 x $12.00 = $180.00

Current weekly pay = $170.00 + $180.00 = $350.00

Additional Office job hours = 10 x $12.00 = $120.00

Percentage Increase = $120 / $350 = .343 (rounded) --> 34.3%

8

A car averages 29 miles per gallon. If gas costs $3.75 per gallon how much money would need to be spent on gas to travel 1464.5 miles?

$189.38

$5491.88

$108.75

$50.5

None of the other answers

Explanation

The question is asking for the amount of money that would need to be spent on gas. Using the value given for the miles per gallon of the car and the amount of miles traveled it is possible to determine the gallons of fuel that will be required. This will be set up as 1464.5 miles travelled divided by the 29 miles per gallon that the car gets. This leaves us with 50.5 gallons of fuel used. From this point we can multiply the amount of fuel used, 50.5 gallons, by the price of fuel per gallon, $3.75, to obtain the amount of money that will spent on fuel, $189.38.

9

Evaluate:

–1 + 2 * –3

–3

5

–7

7

3

Explanation

First you perform multiplication 2 * –3 = –6

Then you add –1 which gives you -7.

10

A sliced cake can be equally split among 4, 5, or 6 people, with each person receiving the same number of slices. Which of the following answers represents a possible number of slices that the cake could have?

24

30

56

116

120

Explanation

If you divide the answer choices by 4, 5, and 6, 120 is the only choice that divides evenly by all three numbers.

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