Math - TACHS Math
Card 1 of 192
Solve:
Solve:
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The lines on either side of the negative integer represent that we need to find its absolute value. The absolute value of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line. This number is a distance from zero and will not be negative. All absolute values are positive.
Therefore, the absolute value—or distance from zero—is the following:
The lines on either side of the negative integer represent that we need to find its absolute value. The absolute value of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line. This number is a distance from zero and will not be negative. All absolute values are positive.
Therefore, the absolute value—or distance from zero—is the following:
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Which of the following is equivalent to 
?
Which of the following is equivalent to
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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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What is the greatest common factor of 
and 
?
What is the greatest common factor of
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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 least common multiple of 
and 
?
What is the least common multiple of
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Start by listing out multiples of 
:
Next, list out multiples of 
:
Now, find the smallest number that is found in both lists. In this case, the least common multiple must be 
.
Start by listing out multiples of
Next, list out multiples of
Now, find the smallest number that is found in both lists. In this case, the least common multiple must be
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Give the next number in the sequence:
Give the next number in the sequence:
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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:
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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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Which of the following is equal to six thousand seven ten-thousandths?
Which of the following is equal to six thousand seven ten-thousandths?
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"Six thousand seven ten-thousandths" in fraction form is 
. To write this in decimal form, put the "7" in the ten-thousandths place, which is the fourth place after the decimal point. This number is "0.6007."
"Six thousand seven ten-thousandths" in fraction form is
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Examine the decimal
What is the place value of the position occupied by the "6"?
Examine the decimal
What is the place value of the position occupied by the "6"?
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After the decimal point, the place values of the digits are, in order:
...
The "6" is in the fourth place after the decimal point, so its place value is one ten-thousandth.
After the decimal point, the place values of the digits are, in order:
The "6" is in the fourth place after the decimal point, so its place value is one ten-thousandth.
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Add.
Add.
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In order to solve this problem we need to line up the decimal places and add.
In order to solve this problem we need to line up the decimal places and add.
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Square 0.44.
Square 0.44.
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To square a number means to multiply it by itself, so we seek to compute
To multiply two decimal fractions, first multiply, ignoring the decimal points:
Move the (implied) decimal point the number of spaces right equal to the total number of digits right of the decimal points in the factors; this can be seen to be four:
The square of 0.44 is 0.1936.
To square a number means to multiply it by itself, so we seek to compute
To multiply two decimal fractions, first multiply, ignoring the decimal points:
Move the (implied) decimal point the number of spaces right equal to the total number of digits right of the decimal points in the factors; this can be seen to be four:
The square of 0.44 is 0.1936.
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Tiffany earns 
each week. If Mark earns 
less than Tiffany, what is the sum of their salaries each week?
Tiffany earns
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Start by finding out how much Mark makes. Since he makes 
less than Tiffany, we can write the following to find Mark's weekly salary:
Mark must make 
each week. Now, add together their salaries to find the sum.
Start by finding out how much Mark makes. Since he makes
Mark must make
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Rachel earns 
an hour as an assistant in a science lab. How many 
hour work weeks will she need to work in order to pay for a car that costs 
?
Rachel earns
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Start by figuring out how much Rachel can earn in each week by multiplying her hourly rate by the number of hours worked each week.
Now, divide the amount she needs to earn by the amount earned each week to find how many weeks she will need to work to earn that amount.
Rachel must work for 
weeks in order to earn enough for the car.
Start by figuring out how much Rachel can earn in each week by multiplying her hourly rate by the number of hours worked each week.
Now, divide the amount she needs to earn by the amount earned each week to find how many weeks she will need to work to earn that amount.
Rachel must work for
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What is the value of 
?
What is the value of
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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
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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
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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
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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
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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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Subtract.
Subtract.
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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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Which of the following is the most reduced form of 
?
Which of the following is the most reduced form of
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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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Evaluate:
Evaluate:
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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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