All ACT Math Resources
Example Questions
Example Question #15 :How To Find Rate
A climber scrambles overyards of rocks inminutes and then returns across the rocks. If his total rate wasyards per minute, how long did it take him to return back?
Begin by setting up the standard equation
However, for our data, we know the distance and the rate only. We do not know the time that it took for the person's return. It is, whereis the return time. Thus, we can write:
Solving for, we get:
, which rounds tominutes.
Example Question #16 :How To Find Rate
有限公司lumbus is locatedaway from Cincinnati. You drive atfor the first. Then, you hit traffic, and drive the remaining portion of the way at only. How many minutes did it take you to reach your destination?
Here, we need to do some unit conversions, knowing that there arein an. We have two different rates, which result in two different equations, which we need to add to get a total time.
.
Example Question #81 :Fractions
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?
20
32
28
40
36
36
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 #3 :How To Find The Ratio Of A Fraction
A pie is made up ofcrust,apples, andsugar, and the rest is jelly. What is the ratio of crust to jelly?
A pie is made up ofcrust,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:
这可以be written as the fraction:
, or
Example Question #41 :Proportion / Ratio / Rate
In a solution,of the fluid is water,is wine, andis lemon juice. What is the ratio of lemon juice to water?
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 #551 :Arithmetic
Ifand, what is the ratio ofto?
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?
1:200
199:1
200:1
1:199
1:199
One remote is defective for every 199 non-defective remotes.
Example Question #1 :How To Express A Fraction As A Ratio
On a desk, there are论文每paper clips and论文每greeting card. What is the ratio of paper clips to total items on the desk?
Begin by making your life easier: presume that there arepapers on the desk. Immediately, we know that there arepaper clips. Now, if there arepapers, you know that there also must begreeting 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 havetotal items. Based on this, your ratio of paper clips to total items is:
, which is the same as.
Example Question #1 :How To Express A Fraction As A Ratio
In a classroom ofstudents, 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?
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 #51 :Proportion / Ratio / Rate
在一个花园,有pansies,lilies,roses, andpetunias. What is the ratio of petunias to the total number of flowers in the garden?
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 commonfrom the numerator and the denominator:
This is the same as.
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