Arithmetic - ACT Math
Card 0 of 6453
On a real number line, what is the midpoint of –4 and 18?
On a real number line, what is the midpoint of –4 and 18?
The integer halfway between –4 and 18 is 7. The number 7 is 11 greater than –4 and 11 less than 18. Another way to determine this would be to find the average of the two numbers: (–4 + 18)/2 = 14/2 = 7.
The integer halfway between –4 and 18 is 7. The number 7 is 11 greater than –4 and 11 less than 18. Another way to determine this would be to find the average of the two numbers: (–4 + 18)/2 = 14/2 = 7.
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What is the difference between the LCM and GCF for the following set of numbers: 3, 12, and 30?
What is the difference between the LCM and GCF for the following set of numbers: 3, 12, and 30?
LCM = least common multiple = 2 x 2 x 3 x 5 = 60
GCF = greatest common factor = 3
Prime factor each number
3 = 3 x 1
12 = 3 x 4 = 3 x 2 x 2
30 = 5 x 6 = 5 x 2 x 3
LCM – GCF = 60 – 3 = 57
LCM = least common multiple = 2 x 2 x 3 x 5 = 60
GCF = greatest common factor = 3
Prime factor each number
3 = 3 x 1
12 = 3 x 4 = 3 x 2 x 2
30 = 5 x 6 = 5 x 2 x 3
LCM – GCF = 60 – 3 = 57
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Find the lowest common denominator of these four fractions:
Find the lowest common denominator of these four fractions:
All of the denominators must be able to divide into the same number. First, see if the three smaller numbers (3, 4, 12) divide into the largest number (15)—NO. Then check the multiples of the largest number to see if the lower numbers divide into it:
15 * 2 = 30 (NO)
15 * 3 = 45 (NO)
15 * 4 = 60 (YES!)
All of the denominators must be able to divide into the same number. First, see if the three smaller numbers (3, 4, 12) divide into the largest number (15)—NO. Then check the multiples of the largest number to see if the lower numbers divide into it:
15 * 2 = 30 (NO)
15 * 3 = 45 (NO)
15 * 4 = 60 (YES!)
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Michael Phelps’ workout program consists of Aerobics, Bench Presses, and Cycling. Aerobics and Bench Presses take a total of 24 minutes, Bench Press and Cycling take a total of 40 minutes, and the entire workout takes a total of 56 minutes. How many minutes are required for the Bench Press portion of his workout?
Michael Phelps’ workout program consists of Aerobics, Bench Presses, and Cycling. Aerobics and Bench Presses take a total of 24 minutes, Bench Press and Cycling take a total of 40 minutes, and the entire workout takes a total of 56 minutes. How many minutes are required for the Bench Press portion of his workout?
To find your answer, we would use substitution within a system of equations. If (A+B) +C = 56, we can replace (A+B )= 24 to get (24) + C = 56, Thus making C = 32. Then we can replace C with 32 in the equation B+C = 40, thus making B + (32) = 40 to get an answer of 8.
To find your answer, we would use substitution within a system of equations. If (A+B) +C = 56, we can replace (A+B )= 24 to get (24) + C = 56, Thus making C = 32. Then we can replace C with 32 in the equation B+C = 40, thus making B + (32) = 40 to get an answer of 8.
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0.3 < 1/3
4 > √17
1/2 < 1/8
–|–6| = 6
Which of the above statements is true?
0.3 < 1/3
4 > √17
1/2 < 1/8
–|–6| = 6
Which of the above statements is true?
The best approach to this equation is to evaluate each of the equations and inequalities. The absolute value of –6 is 6, but the opposite of that value indicated by the “–“ is –6, which does not equal 6.
1/2 is 0.5, while 1/8 is 0.125 so 0.5 > 0.125.
√17 has to be slightly more than the √16, which equals 4, so“>” should be “<”.
Finally, the fraction 1/3 has repeating 3s which makes it larger than 3/10 so it is true.
The best approach to this equation is to evaluate each of the equations and inequalities. The absolute value of –6 is 6, but the opposite of that value indicated by the “–“ is –6, which does not equal 6.
1/2 is 0.5, while 1/8 is 0.125 so 0.5 > 0.125.
√17 has to be slightly more than the √16, which equals 4, so“>” should be “<”.
Finally, the fraction 1/3 has repeating 3s which makes it larger than 3/10 so it is true.
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Which of the following numbers is between 1/5 and 1/6?
Which of the following numbers is between 1/5 and 1/6?
Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.
Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.
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Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?
Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?
Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.
Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.
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An acid-water solution is made in which 65% of the solution is water by volume. How many liters of acid are there in 50 liters of the solution?
An acid-water solution is made in which 65% of the solution is water by volume. How many liters of acid are there in 50 liters of the solution?
35% of the solution is acid, therefore 0.35 * 50 = 17.5.
35% of the solution is acid, therefore 0.35 * 50 = 17.5.
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Which number below is farthest from –3 on a number line?
Which number below is farthest from –3 on a number line?
The answer here relies on knowledge of how numbers are arranged on a number line. We are looking for the number furthest from –3. The number furthest from –3 can lie either to the left of –3 which would be negative numbers that are more negative, or further from 0 than –3. The number furthest from –3 could also lie to its right on the number line, these numbers include all negative numbers between –3 and 0,0, and all positive numbers. The number that satisifes these conditions and is the furthest from –3 on the number line is –8
The answer here relies on knowledge of how numbers are arranged on a number line. We are looking for the number furthest from –3. The number furthest from –3 can lie either to the left of –3 which would be negative numbers that are more negative, or further from 0 than –3. The number furthest from –3 could also lie to its right on the number line, these numbers include all negative numbers between –3 and 0,0, and all positive numbers. The number that satisifes these conditions and is the furthest from –3 on the number line is –8
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On a number line, what is the distance between –6 and 7?
On a number line, what is the distance between –6 and 7?
To find distance between two points, take the second and subtract the first.
So 7–(–6) = 7 + 6 = 13
To find distance between two points, take the second and subtract the first.
So 7–(–6) = 7 + 6 = 13
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The number 9 is the second smallest integer with 3 factors, 1, 3, and 9. What is the sum of the factors of the smallest integer with only 3 factors?
The number 9 is the second smallest integer with 3 factors, 1, 3, and 9. What is the sum of the factors of the smallest integer with only 3 factors?
Here we must do two things. First we must find the smallest integer with 3 factors, then we must add those factors so that we can obtain our answer.
Looking at numbers less than 9 with only 3 factors, the only possibility is the number 4, whose factors are 1, 2, and 4.
The sum of these factors is 1 + 2 + 4 = 7
Here we must do two things. First we must find the smallest integer with 3 factors, then we must add those factors so that we can obtain our answer.
Looking at numbers less than 9 with only 3 factors, the only possibility is the number 4, whose factors are 1, 2, and 4.
The sum of these factors is 1 + 2 + 4 = 7
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What are the factors of the number 12?
What are the factors of the number 12?
The factors of a number are all the numbers that can be multiplied by an integer to get that number.
The factors of a number are all the numbers that can be multiplied by an integer to get that number.
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If a and b are both factors of 64, which of the following could be a * b?
If a and b are both factors of 64, which of the following could be a * b?
The factors of 64 are: 1,2,4,8,16,32,64. Therefore, 128 could be the product of 16 and 8.
The factors of 64 are: 1,2,4,8,16,32,64. Therefore, 128 could be the product of 16 and 8.
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Which of the following is not a factor of 52?
Which of the following is not a factor of 52?
Listing all the factors of 52: 1,2,4,13,26,52.
3 is not one of the factors.
Listing all the factors of 52: 1,2,4,13,26,52.
3 is not one of the factors.
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There is a set of numbers. The mean of this set of numbers is equal to the median. If four of the numbers are 10, 15, 15, and 17, what is the fifth number?
There is a set of numbers. The mean of this set of numbers is equal to the median. If four of the numbers are 10, 15, 15, and 17, what is the fifth number?
Since the set contains two 15s, along with 10 and 17, the median can only be 15, no matter what the fifth number is. So now we know that the mean is equal to 15, since it is equal to the median. Now an equation can be set up to solve this problem. 15 = (10 + 15 + 15 + 17 + x)/5. Solving for x we get an answer of 18.
Since the set contains two 15s, along with 10 and 17, the median can only be 15, no matter what the fifth number is. So now we know that the mean is equal to 15, since it is equal to the median. Now an equation can be set up to solve this problem. 15 = (10 + 15 + 15 + 17 + x)/5. Solving for x we get an answer of 18.
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Solve the following equation:
(9 + 1) * (42 + 2) * (72 + 1) / 2 = ?
Solve the following equation:
(9 + 1) * (42 + 2) * (72 + 1) / 2 = ?
Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"
"Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction".
(9 + 1) * (42 + 2) * (72 + 1) / 2 =
(10) * (16 + 2) * (49 + 1) / 2 =
(10) * (18) * (50) / 2 =
9000/2 = 4500
Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"
"Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction".
(9 + 1) * (42 + 2) * (72 + 1) / 2 =
(10) * (16 + 2) * (49 + 1) / 2 =
(10) * (18) * (50) / 2 =
9000/2 = 4500
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How many irrational numbers are there between 3 and 7?
How many irrational numbers are there between 3 and 7?
There is an infinite amount of irrational numbers between any two "real" (whole) numbers. 3 and 7 are both real numbers
There is an infinite amount of irrational numbers between any two "real" (whole) numbers. 3 and 7 are both real numbers
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On an airline flight of 250 people there is a choice of pasta, salad, or pizza for dinner. If 113 passengers choose pasta and 30% choose salad, how many passengers choose pizza?
On an airline flight of 250 people there is a choice of pasta, salad, or pizza for dinner. If 113 passengers choose pasta and 30% choose salad, how many passengers choose pizza?
30% of 250 is 75. Therefore, 250 – 75 – 113 = 62
30% of 250 is 75. Therefore, 250 – 75 – 113 = 62
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At a store, a t-shirt costs 
. If Shane bought 
t-shirts and shoes from the store for 
, how much were the shoes?
At a store, a t-shirt costs
If one shirt costs 
, then two shirts must cost 
. The difference of the total and this number is the cost of the the shoes.
If one shirt costs
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is equivalent to which of the following?
To answer this question, we must remember how to distribute a negative when we are subtracting an entire expression.
To distribute a negative, you change the sign of everything within the expression being subtracted from positive to negative or negative to positive. You then add the resulting expression. So, for this data:
We can then add the like expressions normally (combine 
with 
, 
with 
, and 
with 
). Therefore, for this data:
Therefore, our answer is 
.
To answer this question, we must remember how to distribute a negative when we are subtracting an entire expression.
To distribute a negative, you change the sign of everything within the expression being subtracted from positive to negative or negative to positive. You then add the resulting expression. So, for this data:
We can then add the like expressions normally (combine
Therefore, our answer is
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