Dividing Fractions - Big Ideas Learning
嚜激nglish
Spanish
2.5
Dividing Fractions
How do you divide by a fraction?
1
ACTIVITY: Dividing by a Fraction
Work with a partner.
8 ‾ 16
〞
b. Describe the pattern of the red numbers.
Use the pattern to complete the table.
8‾8
1
8‾4
2
8‾2
4
8‾1
8
1
2
c. The division 8 ‾ 〞 can be read as ※How many halves
are in 8?§ Use the completed table to answer this
question. Then draw a model that shows your answer.
d. Use the pattern in the table to complete the following.
1
2
8 ‾ 〞 = 16 = 8 ℅ 〞
2
1
1
2
8‾〞
1
Invert 〞 and multiply.
2
1
4
8‾〞
1
8 ‾ 〞 = 32 =
4
1
8
8‾〞
1
8
8 ‾ 〞 = 64 =
2
ACTIVITY: Dividing by a Fraction
Work with a partner.
2
3
a. Draw a model for 3 ‾ 〞. Use the model to answer the question
※How many two-thirds are in 3?§
1
1
b. Complete the table in two ways.
First use the model. Then use the
※invert and multiply§ rule that
you found in Activity 1. Compare
your answers.
1
2
3
3‾〞
2
3
6‾〞
2
3
9‾〞
2
3
12 ‾ 〞
70
Chapter 2
1
2
a. Describe the pattern of the blue numbers.
Multiplying and Dividing Fractions
English
Spanish
3
ACTIVITY: Dividing by a Fraction
Work with a partner. Write the division problem and answer it using a model.
a. How many halves are in five halves?
1
1
1
2
b. How many sixths are in three halves?
1
2
1
2
1
2
c. How many three-fourths are in 3?
1
1
1
d. How many four-fifths are in 8?
1
1
1
1
1
1
1
1
1
1
e. How many three-tenths are in 6?
1
f.
1
1
1
How many halves are in a fourth?
1
4
1
4
1
4
1
4
4. IN YOUR OWN WORDS How do you divide by a fraction? Give an example.
Use what you learned about dividing fractions to complete
Exercises 11每18 on page 75.
Section 2.5
Dividing Fractions
71
English
2.5
Spanish
Lesson
Lesson Tutorials
Two numbers whose product is 1 are reciprocals. To write a reciprocal
of a number, write the number as a fraction. Then invert the fraction.
Key Vocabulary
reciprocals, p. 72
Invert
When y
you invert a g
glass,,
EXAMPLE
Study Tip
When any number is
multiplied by 0, the
product is 0. So, the
number 0 does not
have a reciprocal.
y
you turn it over.
Writing Reciprocals
1
Original Number
Fraction
Reciprocal
Check
a.
〞
3
5
〞
3
5
〞
5
3
〞℅〞=1
3
5
5
3
b.
〞
9
5
〞
9
5
〞
5
9
〞℅〞=1
9
5
5
9
c.
2
〞
2
1
〞
1
2
〞℅〞=1
2
1
1
2
Write the reciprocal of the number.
Exercises 7每10
3
4
1. 〞
7
2
3. 〞
2. 5
4
9
4. 〞
Dividing Fractions
Words
To divide a number by a fraction, multiply the number by the
reciprocal of the fraction.
Numbers
Algebra
72
Chapter 2
1
5
3
4
1
5
4
3
〞‾ 〞= 〞℅ 〞
a
b
c
d
a
b
d
c
〞 ‾ 〞 = 〞 ℅ 〞, where b, c, and d ≧ 0
Multiplying and Dividing Fractions
English
Spanish
EXAMPLE
2
Dividing a Fraction by a Fraction
1
6
2
3
Find 〞 ‾ 〞.
1
6
2
3
1
6
3
2
2
3
〞‾〞=〞℅〞
1℅3
=〞
6℅2
3
2
Multiply by the reciprocal of 〞, which is 〞.
1
Multiply fractions. Divide out the common factor 3.
2
1
4
=〞
EXAMPLE
3
Simplify.
Dividing a Whole Number by a Fraction
3
A piece of wood is 3 feet long. How many 〞 -foot pieces can be cut from
4
the piece of wood?
3
4
Method 1: Draw a diagram. Mark each foot on the diagram. Then divide
1
4
each foot into 〞 -foot sections.
3
4
Count the number of 〞 -foot pieces of wood. There are four.
1 ft
3
4
3
4
So, four 〞 -foot pieces can be cut from the piece of wood.
3
4
3
4
Method 2: Divide 3 by 〞 to find the number of 〞 -foot pieces.
2 ft
3
4
4
3
Multiply by the reciprocal of 〞, which is 〞.
3℅4
3
Multiply. Divide out the common factor 3.
3
4
3‾〞=3℅〞
3
4
1
=〞
4
3
1
=4
3
4
Simplify.
3
4
So, four 〞 -foot pieces can be cut from the piece of wood.
3 ft
Divide. Write the answer in simplest form.
Exercises 11每26
2
7
1
3
1
2
5. 〞 ‾ 〞
1
8
6. 〞 ‾ 〞
3
8
1
4
7. 〞 ‾ 〞
2
5
3
10
8. 〞 ‾ 〞
1
2
9. How many 〞-foot pieces can be cut from a 7-foot piece of wood?
Section 2.5
Dividing Fractions
73
English
Spanish
EXAMPLE
4
Evaluating an Algebraic Expression
4
5
Evaluate a ‾ b when a = 〞 and b = 2.
4
5
4
5
a‾b=〞‾2
4
5
Substitute 〞 for a and 2 for b.
1
2
1
2
=〞℅〞
2
4℅1
5℅2
Multiply by the reciprocal of 2, which is 〞.
=〞
Multiply fractions. Divide out the common factor 2.
1
2
5
=〞
Simplify.
Evaluate the expression x ‾ y for the given values of x and y.
Exercises 32每35
1
2
11. x = 〞, y = 10
2
3
5
8
13. x = 4, y = 〞
10. x = 〞, y = 3
1
3
12. x = 〞, y = 4
EXAMPLE
5
Using Order of Operations
3
8
5
6
Evaluate 〞 + 〞 ‾ 5.
3
8
5
6
3
8
5
6
1
5
1
5
〞+〞‾5=〞+〞℅〞
Multiply by the reciprocal of 5, which is 〞.
1
3 5℅1
=〞+〞
8 6℅5
5
6
1
3 1
=〞+〞
8 6
9
24
1
5
Multiply 〞 and 〞. Divide out the common factor 5.
Simplify.
4
24
=〞+〞
Rewrite fractions using the LCD 24.
13
24
=〞
Add.
Evaluate the expression.
Exercises 47每 55
74
Chapter 2
4
5
2
5
14. 〞 + 〞 ‾ 4
15.
Multiplying and Dividing Fractions
3
8
3
4
1
6
〞‾〞?〞
16.
8
9
〞‾2‾8
................
................
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