### All TACHS Math Resources

## Example Questions

### 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 #2 : Operations

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 : Operations

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 #1 : 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.

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