ACT Math : Arithmetic

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #31 : Proportion / Ratio / Rate

Max drives his car at a constant rate of 25 miles per hour. At this rate, many minutes will it take him to drive 15 miles?

Possible Answers:

36

32

28

20

40

Correct answer:

36

Explanation:

We know that it takes Max an hour to drive 25 miles. We also know that there are 60 minutes in an hour. Using this information we can create the following ratio:

We are trying to calculate the the amount of time it will take to drive 15 miles. Let's create a proportion and use a variable for the unknown time.

Cross-multiply and solve for the time.

 

Example Question #551 : Arithmetic

A pie is made up of   crust,  apples, and  sugar, and the rest is jelly. What is the ratio of crust to jelly?

Possible Answers:

Correct answer:

Explanation:

A pie is made up of   crust,  apples,  sugar, and the rest is jelly. What is the ratio of crust to jelly?

To compute this ratio, you must first ascertain how much of the pie is jelly. This is:

Begin by using the common denominator :

So, the ratio of crust to jelly is:

This can be written as the fraction:

, or 

Example Question #52 : Proportion / Ratio / Rate

In a solution,  of the fluid is water,  is wine, and  is lemon juice. What is the ratio of lemon juice to water?

Possible Answers:

Correct answer:

Explanation:

This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:

Remember, to divide fractions, you multiply by the reciprocal:

This is the same as saying: 

Example Question #46 : Proportion / Ratio / Rate

If  and , what is the ratio of  to ?

Possible Answers:

Correct answer:

Explanation:

To find a ratio like this, you simply need to make the fraction that represents the division of the two values by each other. Therefore, we have:

Recall that division of fractions requires you to multiply by the reciprocal:

which is the same as:

This is the same as the ratio:

Example Question #1 : How To Express A Fraction As A Ratio

When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?

Possible Answers:

1:200

199:1

1:199

200:1

Correct answer:

1:199

Explanation:

One remote is defective for every 199 non-defective remotes.

Example Question #91 : Number Concepts And Operations

On a desk, there are  papers for every  paper clips and  papers for every  greeting card. What is the ratio of paper clips to total items on the desk?

Possible Answers:

Correct answer:

Explanation:

Begin by making your life easier: presume that there are  papers on the desk. Immediately, we know that there are  paper clips. Now, if there are  papers, you know that there also must be  greeting cards. Technically you figure this out by using the ratio:

By cross-multiplying you get:

Solving for , you clearly get .

(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)

Now, this means that our desk has on it:

 papers

 paper clips

 greeting cards

Therefore, you have  total items.  Based on this, your ratio of paper clips to total items is:

, which is the same as .

Example Question #92 : Number Concepts And Operations

In a classroom of  students, each student takes a language class (and only one—nobody studies two languages).  take Latin,  take Greek,  take Anglo-Saxon, and the rest take Old Norse. What is the ratio of students taking Old Norse to students taking Greek?

Possible Answers:

Correct answer:

Explanation:

To begin, you need to calculate how many students are taking Old Norse. This is:

Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:

Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of :

This is the same as .

Example Question #81 : Fractions

In a garden, there are  pansies,  lilies,  roses, and  petunias. What is the ratio of petunias to the total number of flowers in the garden?

Possible Answers:

Correct answer:

Explanation:

To begin, you need to do a simple addition to find the total number of flowers in the garden:

Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by . This is:

Next, reduce the fraction by dividing out the common  from the numerator and the denominator:

This is the same as .

Example Question #1 : How To Find Proportion

Max will be age X in 5 years. How old was he 4 years ago?

 

Possible Answers:

X – 5

X – 4

X – 9

X +5

Correct answer:

X – 9

Explanation:

Max will be X in 5 years. So today he is X -5 and 4 years ago he was (X-5)  - 4, that is X – 9.  It always helps to put numbers into the equations. Example: Max will be 12 in 5 years. How old was he 4 years ago? So today Max is 12 – 5 = 7.  Therefore, four years ago he was 7 -4 =3. Which is 12-5-4 =12-9 = 3

 

Example Question #2 : How To Find Proportion

If a pizza pie that has 16 slices and costs $12.00 is to be shared among 8 friends, how much should each person contribute?

 

Possible Answers:

$0.75

$2

$1.50

$1.75

Correct answer:

$1.50

Explanation:

It is $12 divided by 8 which is $1.50. The number of slices in the pizza pie is not relevant in this question.

 

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