# TACHS Math : Fractions

## Example Questions

### Example Question #1 : Fractions

What is the value of ?

Explanation:

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 #2 : Fractions

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?

Explanation:

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 #3 : Fractions

What is the product of  and ?

Explanation:

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 #4 : Fractions

What is the difference between  and ?

Explanation:

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 #5 : Fractions

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