Lesson 8.9 Multiplying Fractions
(4.M.NF.B.04)
Lesson Objective: The students will multiply fractions and whole numbers. Video Lesson: Multiplying fractions by whole numbers
When multiplying fractions by a whole number, we can use the same type of
techniques we started out doing when when multiplied just whole numbers.
When presented with a problem like ¾ * 4 we can use repeated addition to
come up with our answer.
¾ * 4 = ¾ + ¾ + ¾ + ¾= 12/4
When we are finished adding this up we get an improper fraction. It is
important to make our improper fraction a mixed number in simplest form. We
can do this through decomposition or division.
12/4 = 4/4 + 4/4 + 4/4 = 3
12 divided by 4 = 3
When adding multiple fractions like above we realize that the denominator does
not change. That is because it tells us how many make one whole. Just like in
repeated addition, it will work for most numbers, but multiplying can be faster.
We can do this by giving the four a denominator of 1 and multiplying the
numerators and denominators by each other.
¾ * 4/1 = 12/4 = 3
Try one below. Draw a picture to prove what you have.
⅔*3=
Let’s take a look at how it would fit on a number line. Let’s place ½ *4 on the
number line. Start out by drawing one half and then add three more one halfs
to the number line. Remember that every time you get to two halfs you have a
whole.
Before you get started on your homework, show me you can multiple the
following two problems. Make sure to put them in simplest form.
⅖*7
⅜*6
1. Draw pictures to show ⅘ * 3
2. Use a number line to show ⅔ * 5
3. ⅚ * 4 =
a. 1/9 * 7 =
Lesson 8.10 Multiplying Fractions in
Word Problems (4.M.NF.B.04)
Lesson Objective: The students will solve story problems with fractions. . Video Lesson: story problems We can look at multiplying fractions in two ways. When we have the problem
Johnny ate ¼ of 5 cakes we can solve that problem, ¼ times 5, and take it as ¼
added 5 times. Our answer is then 5/4 or 1 and ¼. The commutative property
of multiplication says we can multiply either way. So we could look at the
problem as ¼ of five. Here we would break each cake into fourths. Let’s do that
below:
Now when we take ¼ of each cake we will have a total of 5/4 or 1 and ¼, which
is the same as above.
So regardless if you walk ⅓ of 9 miles or 9 times at ⅓ of a mile, you will have
walked the same distance.
Let’s break down a story problem to see what we need to do:
Haylee used ⅓ of a container of lemonade for her stand on Monday. She used
4 times that on Tuesday. How many containers of lemonade did she use on
Tuesday? Prove this using words or pictures.
We need to take _______ and multiply it by _____ (remember to change the
whole number into a fraction).
Our answer is _____________________
I can show that by drawing _____ containers. I need to break apart the
containers into __________ pieces. (do that below)
Keys to your Homework:
John ran ¾ of a mile on Monday. He ran 3 times as much on Tuesday. How
much did he run on Tuesday?
1. There was 25 strawberries. Cameron ate ⅖ of them. How many strawberries did she
eat? Justify your answer using a picture or words.
2. Casey spent 7 dollars on Monday. He spent ⅘ as much on Tuesday. How much did he
spend on Tuesday? Justify your answer using a picture or words.
3. Katie used ⅓ of a sheet of construction paper Wednesday for an art project. She used
5 times as many sheets on Thursday. How many sheets did she use? Justify your
answer using pictures or words.