Math - TACHS Math
Card 0 of 192
What is the probability of rolling a one on a fair die?
What is the probability of rolling a one on a fair die?
In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:
Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,
Now, let's convert this into a percentage:
In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:
Let's use a simple example: the rolling of a die. We want to know the probability of rolling a one. We know that the sample space is six because there are six sides or outcomes to the die. Also, we know that there is only a single side with a value of one; therefore,
Now, let's convert this into a percentage:
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Which of the following is the most reduced form of 
?
Which of the following is the most reduced form of
Start by converting 
into a fraction.
We multiply both numerator and denominator by 
to get rid of the decimal.
Now, convert 
into a mixed number.
Start by converting
We multiply both numerator and denominator by
Now, convert
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Subtract.
Subtract.
In order to solve this problem we must subtract the second number from the first number.
In order to solve this problem we must subtract the second number from the first number.
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What value of 
makes this a true statement?
What value of
Isolate the 
on the left side of the equation by performing the same steps on both sides. These steps should be the opposite of the operations performed on 
.
Multiplication precedes addition in the order of operations, so reverse the addition of 16 by subtracting 16 from both sides:
Now reverse multiplication by 2 by dividing by 2:
Isolate the
Multiplication precedes addition in the order of operations, so reverse the addition of 16 by subtracting 16 from both sides:
Now reverse multiplication by 2 by dividing by 2:
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Give the next number in the sequence:
Give the next number in the sequence:
To form the sequence, begin with the term 8. Each subsequent term is equal to 9 added to the previous term, as follows:
,
the missing term.
To form the sequence, begin with the term 8. Each subsequent term is equal to 9 added to the previous term, as follows:
the missing term.
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Solve for the missing variable in the following proportion:
Solve for the missing variable in the following proportion:
Proportions are ratios that are equal to one another. We can solve for the missing variable by using cross multiplication to develop an equation.
Simplify.
Divide both sides of the equation by 
.
Solve.
Proportions are ratios that are equal to one another. We can solve for the missing variable by using cross multiplication to develop an equation.
Simplify.
Divide both sides of the equation by
Solve.
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What is the greatest common factor of 
and 
?
What is the greatest common factor of
Start by listing out the factors of 
.
Next, list out the factors of 
.
Now, find the largest factor that the two numbers share. In this case, the greatest common factor is 
.
Start by listing out the factors of
Next, list out the factors of
Now, find the largest factor that the two numbers share. In this case, the greatest common factor is
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What is the value of 
?
What is the value of
Start with finding the value of 
.
In order to add fractions with different denominators, we will need to change one or both denominators first. Notice that 
is a factor of 
, which means we can multiply the numerator and the denominator of 
by 
to get 
.
Now, add the two fractions together as they have the same denominator.
Next, solve 
.
The least common multiple of 
and 
is 
.
Thus, 
Start with finding the value of
In order to add fractions with different denominators, we will need to change one or both denominators first. Notice that
Now, add the two fractions together as they have the same denominator.
Next, solve
The least common multiple of
Thus,
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Janice's car can travel 
miles on one gallon of gas. Her car can normally hold 
gallons of gas, but it is only 
full. How many miles can Janice travel before the tank is empty?
Janice's car can travel
Start by finding out how many gallons is currently in Janice's tank.
Since it is only 
full,
.
The tank only has 
gallons in it right now. Multiply this by the number of miles traveled per gallon to find how far Janice can travel before the tank is empty.
Start by finding out how many gallons is currently in Janice's tank.
Since it is only
The tank only has
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Paul can type 
words per minute. If Josie can type 
faster than Paul can, how many words can Josie type in 
minutes?
Paul can type
Start by finding out Josie's typing rate.
Since she types 
faster, we can find her rate with the following equation:
Since Josie types at 
words per minute, we can multiply by the total number of given minutes to find out how many words she can type in the given time frame.
Start by finding out Josie's typing rate.
Since she types
Since Josie types at
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What is the product of 
and 
?
What is the product of
Since the question asks for the product, you will need to multiply the two fractions. Recall that in multiplying two fractions, you will multiply the numerators together and then multiply the denominators together.
Next, reduce the fraction.
Since the question asks for the product, you will need to multiply the two fractions. Recall that in multiplying two fractions, you will multiply the numerators together and then multiply the denominators together.
Next, reduce the fraction.
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What is the difference between 
and 
?
What is the difference between
Since the question asks you to find the difference, you will need to subtract the two fractions:
Start by making both denominators the same. Multiply the numerator and denominator of 
by 
to get 
.
Now, subtract.
Make sure to simplify the answer.
Since the question asks you to find the difference, you will need to subtract the two fractions:
Start by making both denominators the same. Multiply the numerator and denominator of
Now, subtract.
Make sure to simplify the answer.
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Evaluate:
Evaluate:
In the order of operations, in the absence of grouping symbols, multiplication takes precedence over addition and subtraction. Multiply 15 by 8 first:
Addition and subtraction have equal precedence and are worked in left-to-right order. Subtract 120 and 12 next:
Now add:
In the order of operations, in the absence of grouping symbols, multiplication takes precedence over addition and subtraction. Multiply 15 by 8 first:
Addition and subtraction have equal precedence and are worked in left-to-right order. Subtract 120 and 12 next:
Now add:
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What is the value of 
?
What is the value of
Make sure you follow the order of operations (PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction—from the left to the right).
Start by simplifying what's found within the parentheses:
Next, simplify any multiplication and division.
Finally, simplify any addition and subtraction.
Make sure you follow the order of operations (PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction—from the left to the right).
Start by simplifying what's found within the parentheses:
Next, simplify any multiplication and division.
Finally, simplify any addition and subtraction.
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What is the value of 
?
What is the value of
Make sure to follow the order of operations.
Start by simplifying what is found in the parentheses.
Next, simplify any exponents.
Next, simplify any multiplication and division.
Finally, simplify any addition and subtraction.
Make sure to follow the order of operations.
Start by simplifying what is found in the parentheses.
Next, simplify any exponents.
Next, simplify any multiplication and division.
Finally, simplify any addition and subtraction.
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Which of the following is equivalent to 
?
Which of the following is equivalent to
Recall that when a number is raised to an exponent, that means we will need to multiply the number the number of times that is equal to the exponent.
Thus, with 
, this means we will need to multiply 
by itself four times:
Recall that when a number is raised to an exponent, that means we will need to multiply the number the number of times that is equal to the exponent.
Thus, with
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Give the median of the following six scores:
83, 87, 99, 90, 82, 84
Give the median of the following six scores:
83, 87, 99, 90, 82, 84
To find the median of a group of scores, first, arrange the scores from least to greatest:
There are an even number of scores, so the median is the mean of the two scores that fall in the middle, which are noted in red above. Add the scores and divide by two:
.
To find the median of a group of scores, first, arrange the scores from least to greatest:
There are an even number of scores, so the median is the mean of the two scores that fall in the middle, which are noted in red above. Add the scores and divide by two:
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Over the course of a grading period, Kim had a total of 
tests in her math class. She achieved scores of 
on her tests. What is the average of her test scores?
Over the course of a grading period, Kim had a total of
Recall how to find the average of a set of numbers:
Thus, we can write the following to solve for the average of Kim's test scores:
Kim has a 
as her test score average.
Recall how to find the average of a set of numbers:
Thus, we can write the following to solve for the average of Kim's test scores:
Kim has a
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Give the median of the following six scores:
83, 87, 99, 90, 82, 84
Give the median of the following six scores:
83, 87, 99, 90, 82, 84
To find the median of a group of scores, first, arrange the scores from least to greatest:
There are an even number of scores, so the median is the mean of the two scores that fall in the middle, which are noted in red above. Add the scores and divide by two:
.
To find the median of a group of scores, first, arrange the scores from least to greatest:
There are an even number of scores, so the median is the mean of the two scores that fall in the middle, which are noted in red above. Add the scores and divide by two:
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Over the course of a grading period, Kim had a total of tests in her math class. She achieved scores of on her tests. What is the average of her test scores?
Over the course of a grading period, Kim had a total of
Recall how to find the average of a set of numbers:
Thus, we can write the following to solve for the average of Kim's test scores:
Kim has a as her test score average.
Recall how to find the average of a set of numbers:
Thus, we can write the following to solve for the average of Kim's test scores:
Kim has a
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