Download How do we use fraction bars to find a fraction of a fraction? Finding a

Lesson
2 Finding a Fraction of a Fraction
Problem Solving:
Measuring With a Metric Ruler
Finding a Fraction of a Fraction
How do we use fraction bars to find a fraction
of a fraction?
In the last lesson, we looked at the multiplication of whole numbers by
1
fractions. When we multiply 1
2 · 2, we find 2 of 2.
2
When we multiply 2
3 · 3, we find 3 of 3.
Now let’s multiply a fraction by another fraction.
4
1
4
When we multiply 1
2 · 5, we find 2 of 5 .
Let’s complete this problem using fraction bars.
1 4
2·5
This fraction bar shows 4
5.
Now we focus on just the shaded part and we take half of this.
1
There are four total shaded parts. If we take 2
of the shaded parts, we have 2 parts.
We know that the 2 parts are fifths, so the answer to the problem is
1 4 2
2·5=5
The answer is smaller than the starting number, 4
5 . It’s smaller because
4
4
we are only finding a part of the fraction 5 . We are taking 1
2 of 5 .
90 Unit 2 • Lesson 2
Lesson 2
Using fraction bars helps us see what it means to multiply fractions.
Let’s use fraction bars to solve another problem.
Example 1
Find 15 · 5
8 using fraction bars.
1 5
5·8
5
We can think of this as 1
5 of 8 .
First, we draw the fraction bar for 5
8 . This fraction bar has 8 total parts
and 5 shaded parts.
Let's focus on the shaded part. We can find 1
5 of it because there are 5
1
parts shaded and 5 is 1 part.
1
There are 5 total shaded parts. If we take 5 of the shaded
parts, we have 1 part.
Each part is an eighth, so the answer to the problem is 1
8.
1
Again, the answer is smaller than both 5
8 and 5 . We are finding a
1
5
fractional part of 5
8 . We are finding 5 of 8 .
Apply Skills
Turn to Interactive Text,
page 50.
When we multiply
using fractions, we
are taking a portion of
another fraction, and
that is why the answer
or product is often a
smaller number.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 2 • Lesson 2 91
Lesson 2
Problem Solving: Measuring With a Metric Ruler
Vocabulary
How do we use a metric ruler?
metric ruler
millimeters
centimeters
When we measure small objects with a metric ruler , we use units
called millimeters and centimeters . Here is an example of a metric
ruler that shows these units.
The metric ruler looks like this:
cm 1
2
3
4
5
6
7
8
9
10
11
The smallest units on the metric ruler are millimeters.
cm 1
3
Ten millimeters make up 1 centimeter. On a metric ruler, the
centimeters are numbered.
There are 5 millimeters in 1
2 centimeter.
cm 1
Problem-Solving Activity
Turn to Interactive Text,
page 51.
92 Unit 2 • Lesson 2
3
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
12
Lesson 2
Homework
Activity 1
Use the fraction bar to help you solve the problems.
1.
1
2
· 46 2
6
1
3
1
2. 3 · 6 6
1
2
1
2
3. 2 · 6 6
Activity 2
Use the fraction bar to help you solve the problems.
1.
1
2
· 24 1
4
1
3
1
2. 3 · 4 4
3. 2 · 4 4
Activity 3
Draw the points, line segments, rays, and lines. Follow the instructions for
labeling.
1. Draw a ray. Label it AB.
2. Draw a line segment. Label it CD.
3. Draw a point. Label it X.
4. Draw a line. Label it EF.
5. Draw a line segment. Label it MN.
Activity 4 • Distributed Practice
Solve.
1.
253
+ 28
281
2.
125
 11
114
3.
173
 88
85
4.
17
3
51
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Unit 2 • Lesson 2 93