Have you ever tried to estimate a product or a quotient? Take a look at this dilemma with fractions and mixed numbers.

\begin{align*}4 \frac{1}{12} \times 12 \frac{3}{2}\end{align*}

To figure this out, you need to know how to estimate a product. You will know how to do this by the end of the Concept.

### Guidance

** 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 \begin{align*}\frac{1}{2}\end{align*}

**Estimate the product: \begin{align*}8 \frac{4}{11} \times 7\frac{11}{12}\end{align*} 8411×71112**

Round the first number.

Since \begin{align*}\frac{4}{11}\end{align*}

Round the second number.

Since \begin{align*}\frac{11}{12}\end{align*}

Now multiply to find the estimated product.

\begin{align*}8\times8=64\end{align*}

**A reasonable estimate is 64.**

Here is another one.

**Estimate the quotient: \begin{align*}22\frac{3}{10}\div 6\frac{9}{13}\end{align*} 22310÷6913**

Round the first number.

Since \begin{align*}\frac{3}{10}\end{align*}

Round the second number.

Since \begin{align*}\frac{9}{13}\end{align*}

Now divide to find the estimated product. Since 22 is not divisible by 7, round it down to 21 to make compatible numbers that are easier to divide.

\begin{align*}21\div 7=3\end{align*}

**A good estimate for the quotient is 3.**

**Notice that you have to use some common sense and thinking to figure out that you had to round 22 down to 21 to find a good estimate.**

Estimate each product or quotient.

#### Example A

\begin{align*}6 \frac{1}{2} \times 4 \frac{1}{8}\end{align*}

**Solution: \begin{align*}7 \times 4 = 28\end{align*} 7×4=28**

#### Example B

\begin{align*}11 \frac{3}{4} \div 2 \frac{1}{10}\end{align*}

**Solution: \begin{align*}12 \div 2 = 6\end{align*} 12÷2=6**

#### Example C

\begin{align*}\frac{3}{4} \times \frac{8}{9}\end{align*}

**Solution: \begin{align*}1 \times 1 = 1\end{align*} 1×1=1**

Now let's go back to the dilemma from the beginning of the Concept.

\begin{align*}4 \frac{1}{12} \times 12 \frac{3}{12}\end{align*}

First, round each value.

\begin{align*}4 \frac{1}{12}\end{align*}

\begin{align*}12 \frac{3}{12}\end{align*}

Now we can write a new problem.

\begin{align*}4 \times 12 = 48\end{align*}

**Our reasonable estimate is \begin{align*}48\end{align*} 48.**

### Vocabulary

- Greatest Common Factor
- a number that will divide evenly into both the numerator and the denominator of a fraction.

- Product
- the answer in a multiplication problem.

- Quotient
- the answer in a division problem.

- Fraction
- a part of a whole

- Mixed Number
- a number with a whole number and a fraction.

- Improper Fraction
- a number that is greater than a whole with a larger top number and a smaller bottom number.

- Estimation
- a reasonable answer

### Guided Practice

Here is one for you to try on your own.

Estimate the following quotient.

\begin{align*}14 \frac{11}{12} \div 2 \frac{7}{8}\end{align*}

**Solution**

Begin by rounding each value. Here is the new equation.

\begin{align*}15 \div 3 = x\end{align*}

Now solve for \begin{align*}x\end{align*}.

\begin{align*}x = 5\end{align*}

**This is our estimate.**

### Video Review

### Practice

Directions: Estimate each product or quotient.

1. \begin{align*}\frac{7}{8} \times \frac{7}{8}\end{align*}

2. \begin{align*}3 \frac{1}{2} \times \frac{3}{4}\end{align*}

3. \begin{align*}6 \frac{2}{3} \times \frac{4}{5}\end{align*}

4. \begin{align*}8 \frac{1}{12} \times 3 \frac{1}{8}\end{align*}

5. \begin{align*}9 \frac{4}{5} \times 6 \frac{1}{9}\end{align*}

6. \begin{align*}12 \frac{1}{3} \times 4 \frac{5}{6}\end{align*}

7. \begin{align*}6 \frac{4}{7} \times 3 \frac{3}{8}\end{align*}

8. \begin{align*}12 \frac{1}{8} \div 3 \frac{1}{3}\end{align*}

9. \begin{align*}24 \frac{2}{10} \div 3 \frac{1}{3}\end{align*}

10. \begin{align*}28 \frac{1}{9} \div 7 \frac{1}{10}\end{align*}

11. \begin{align*}9 \frac{2}{3} \div 1 \frac{4}{5}\end{align*}

12. \begin{align*}14 \frac{1}{2} \div 3 \frac{1}{10}\end{align*}

13. \begin{align*}9 \frac{3}{10} \div 3 \frac{1}{9}\end{align*}

14. \begin{align*}16 \frac{4}{15} \div 2 \frac{1}{5}\end{align*}

15. \begin{align*}30 \frac{4}{12} \div 3 \frac{6}{18}\end{align*}