Nisi and Jamie ordered pizza for lunch. They ate fraction of the 24 slices did he eat?

of the pizza which was cut into 24 slices. How many slices did they eat altogether? If Ethan woke up in the morning and ate half of the remaining pizza, whatIn this concept, you will learn to estimate products and quotients of fractions and mixed numbers.

### Estimating Products and Quotients of Fractions

Estimation is a useful strategy to use to check that your computation is reasonable. It is also a way to find an approximate answer to a solution.

To estimate products and quotients of mixed numbers, round the fractions to the nearest whole number. If the fraction is less than round down and if it is more than round up.

Let's look at an example.

Estimate the product:

First, since

is less than rounds down to 8.Next, since

is greater than , rounds up to 8.Then, multiply to find the estimated product.

The answer is 64.

Here is another example.

Estimate the quotient:

First, since

is less than , rounds down to 22.Next, since

is greater than , rounds up to 7.Then, divide to find the estimated product.

The answer is approximately 3.

### Examples

#### Example 1

Earlier, you were given a problem about Nisi and Jamie and their pizza.

Of the 24 slices, they had eaten

of the pizza.Therefore, multiply

First, set up the expression to multiply:

Next, multiply the numerator and the denominators.

Then, simplify.

Therefore, Nisi and Jamie ate 16 of the 24 slices.

Now, since they ate 16 of the 24 slices, there were 8 of the 24 slices left. How many did Ethan eat when he got up?

First, remember that Ethan ate

of the remaining pizza.Next, set up the expression to solve.

Then solve and simplify.

So, Ethan ate

#### Example 2

Estimate the following quotient.

First, since

is greater than , rounds up to 15.Next, since

Then, divide to find the estimated product.

The answer is approximately 5.

#### Example 3

First, since the fraction is

, rounds up to 7.Next, since

is less than , rounds down to 4.Then, multiply to find the estimated product.

The answer is 28.

#### Example 4

First, since

is greater than rounds up to 12.Next, since

is less than rounds down to 2.Then, divide to find the estimated product.

The answer is approximately 6.

#### Example 5

First, since

is greater than rounds up to 1.Next, since

is greater than rounds up to 1.Then, multiply to find the estimated product.

The answer is 1.

### Review

Estimate each product or quotient.

78×78=−−−−− 8112×318=−−−−− 1412÷3110=−−−−−