All TACHS Math Resources
Example Questions
Example Question #2 : Decimals
Tiffany earns each week. If Mark earns less than Tiffany, what is the sum of their salaries each week?
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.
Example Question #11 : Math
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 ?
Cannot be determined
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.
Example Question #3 : Operations
Add.
In order to solve this problem we need to line up the decimal places and add.
Example Question #1 : Fractions
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,
Example Question #11 : Tachs: Math And Ability
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?
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.
Example Question #12 : Math
What is the product of and ?
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.
Example Question #3 : Fractions
What is the difference between and ?
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.
Example Question #13 : Math
Paul can type words per minute. If Josie can type faster than Paul can, how many words can Josie type in minutes?
Cannot be determined
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.
Example Question #1 : Mixed Numbers
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.
Example Question #13 : Math
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: