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Multiplication of Whole Numbers by Fractions

Fraction multiplier, whole number multiplicand

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Multiplication of Whole Numbers by Fractions

Remember Julie and the rainforest dilemma from the Multiply Fractions by Whole Numbers Concept? Well, in that problem Julie began by looking at the fraction of rainfall.Then she multiplied that fraction by the number of days.

What if we worked the other way around?

We could do it that way too. We could start with the number of days in the week and multiply the number of days, a whole number, by the fraction of rainfall.

To do this, you will need to know how to multiply whole numbers with fractions. This Concept will teach you how to do this.

Guidance

Previously we worked multiplying fractions by whole numbers, now we can also reverse the order too and multiply whole numbers by fractions.

9×13\begin{align*}9 \times \frac{1}{3}\end{align*}

To work through this problem we do the same thing that we did when the numbers were reversed. We can turn 9 into a fraction over one and multiply across.

91×13=93\begin{align*}\frac{9}{1} \times \frac{1}{3} = \frac{9}{3}\end{align*}

Here we have an improper fraction. We can turn this into a mixed number, or in this case a whole number. Nine divided by three is three.

Example A

6×13=\begin{align*}6 \times \frac{1}{3} = \underline{\;\;\;\;\;\;\;}\end{align*}

Solution:2\begin{align*}2\end{align*}

Example B

8×12=\begin{align*}8 \times \frac{1}{2} = \underline{\;\;\;\;\;\;\;}\end{align*}

Solution:4\begin{align*}4\end{align*}

Example C

10×12=\begin{align*}10 \times \frac{1}{2} = \underline{\;\;\;\;\;\;\;}\end{align*}

Solution:5\begin{align*}5\end{align*}

Now let's think about the rainforest problem.

Today, Julie is working on the part of the project that has to do with rainfall. The rainforest gets an average of 18′′\begin{align*}\frac{1}{8}''\end{align*} of rain each day. Some days there isn’t any rain, but most days there is some. The 18′′\begin{align*}\frac{1}{8}''\end{align*} average seems to make the most sense.

Imagine that Julie wants to figure out how much rainfall there will be in 30 days. This is the whole number that she will multiply with the amount of rainfall in one day.

We can multiply 30 times 18′′\begin{align*}\frac{1}{8}''\end{align*} to get the total inches of rain.

30×18=\begin{align*}30 \times \frac{1}{8} = \underline{\;\;\;\;\;\;\;}\end{align*}

Now we multiply just as we would any whole number and fraction.

308=368=334\begin{align*} \frac{30}{8} = 3 \frac{6}{8} = 3 \frac{3}{4}\end{align*}

This is our answer in simplest form.

Vocabulary

Multiplication
“of”
means multiply in a word problem
Product
the answer to a multiplication problem
Estimate
to find a reasonable answer that is not exact but is close to the actual answer.

Guided Practice

Here is one for you to try on your own.

6×23=\begin{align*}6 \times \frac{2}{3} = \underline{\;\;\;\;\;\;\;}\end{align*}

Here we multiply the whole number and the fraction.

123=4\begin{align*} \frac{12}{3} = 4\end{align*}

This is our answer in simplest form.

Practice

Directions: Multiply the following fractions and whole numbers. Be sure that your answer is in simplest form.

1. 9×23=\begin{align*}9 \times \frac{2}{3} = \underline{\;\;\;\;\;\;\;}\end{align*}

2. 6×23=\begin{align*}6 \times \frac{2}{3} = \underline{\;\;\;\;\;\;\;}\end{align*}

3. 5×25=\begin{align*}5 \times \frac{2}{5} = \underline{\;\;\;\;\;\;\;}\end{align*}

4. 12×9=\begin{align*}\frac{1}{2} \times 9 = \underline{\;\;\;\;\;\;\;}\end{align*}

5. 27×9=\begin{align*}\frac{2}{7} \times 9 = \underline{\;\;\;\;\;\;\;}\end{align*}

6. 13×7=\begin{align*}\frac{1}{3} \times 7 = \underline{\;\;\;\;\;\;\;}\end{align*}

7. 34×10=\begin{align*}\frac{3}{4} \times 10 = \underline{\;\;\;\;\;\;\;}\end{align*}

8. 34×12=\begin{align*}\frac{3}{4} \times 12 = \underline{\;\;\;\;\;\;\;}\end{align*}

9. 35×10=\begin{align*}\frac{3}{5} \times 10 = \underline{\;\;\;\;\;\;\;}\end{align*}

10. 19×36=\begin{align*}\frac{1}{9} \times 36 = \underline{\;\;\;\;\;\;\;}\end{align*}

11. 19×63=\begin{align*}\frac{1}{9} \times 63 = \underline{\;\;\;\;\;\;\;}\end{align*}

12. 12 of 14=\begin{align*}\frac{1}{2} \ of \ 14 = \underline{\;\;\;\;\;\;\;}\end{align*}

13. 12 of 24=\begin{align*}\frac{1}{2} \ of \ 24 = \underline{\;\;\;\;\;\;\;}\end{align*}

14. 14 of 44=\begin{align*}\frac{1}{4} \ of \ 44 = \underline{\;\;\;\;\;\;\;}\end{align*}

15. 15 of 35=\begin{align*}\frac{1}{5} \ of \ 35 = \underline{\;\;\;\;\;\;\;}\end{align*}

16. 18 of 40=\begin{align*}\frac{1}{8} \ of \ 40 = \underline{\;\;\;\;\;\;\;}\end{align*}

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Color Highlighted Text Notes

Vocabulary Language: English

Estimate

To estimate is to find an approximate answer that is reasonable or makes sense given the problem.

multiplication

Multiplication is a simplified form of repeated addition. Multiplication is used to determine the result of adding a term to itself a specified number of times.

Product

The product is the result after two amounts have been multiplied.