### All TACHS Math Resources

## Example Questions

### Example Question #1 : Math

Subtract.

**Possible Answers:**

**Correct answer:**

In order to solve this problem we must subtract the second number from the first number.

### Example Question #1 : Tachs: Math And Ability

Square 0.44.

**Possible Answers:**

**Correct answer:**

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.

### Example Question #1 : Decimals

Tiffany earns each week. If Mark earns less than Tiffany, what is the sum of their salaries each week?

**Possible Answers:**

**Correct answer:**

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 #1 : Decimals

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 ?

**Possible Answers:**

Cannot be determined

**Correct answer:**

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 #4 : Decimals

Add.

**Possible Answers:**

**Correct answer:**

In order to solve this problem we need to line up the decimal places and add.

### Example Question #1 : Operations

What is the value of ?

**Possible Answers:**

**Correct answer:**

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 #1 : Operations

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?

**Possible Answers:**

**Correct answer:**

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 #1 : Fractions

What is the product of and ?

**Possible Answers:**

**Correct answer:**

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 #1 : Fractions

What is the difference between and ?

**Possible Answers:**

**Correct 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 by to get .

Now, subtract.

Make sure to simplify the answer.

### Example Question #2 : Operations

Paul can type words per minute. If Josie can type faster than Paul can, how many words can Josie type in minutes?

**Possible Answers:**

Cannot be determined

**Correct answer:**

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.