Transcript Slide 1

3-4
Equivalent Fractions and Mixed Numbers
California
Standards
NS2.4 Determine the least common
multiple and the greatest common divisor of
whole numbers; use them to solve problems
with fractions (e.g. to find a common
denominator to add two fractions or to find the
reduced form of a fraction).
Also covered:
NS1.1
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Equivalent Fractions and Mixed Numbers
Vocabulary
equivalent fractions
Different expressions for the same nonzero number.
(fractions that are equal to each other).
improper fraction
A fraction in which the numerator is greater than
the denominator.
mixed number
A number that contains a whole number and a
fraction.
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3-4
Equivalent Fractions and Mixed Numbers
Different fractions can name the same number.
3
5
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=
6
10
=
15
25
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Equivalent Fractions and Mixed Numbers
In the diagram 3 = 6 = 15 . These are called
5 10 25
equivalent fractions because they are
different expressions for the same nonzero
number.
To create fractions equivalent to a given
fraction, multiply or divide the numerator and
denominator by the same nonzero number.
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Equivalent Fractions and Mixed Numbers
Example 1: Finding Equivalent Fractions
Find two fractions equivalent to 5
7.
5  2 = 10
72
14
Multiply the numerator and
denominator by 2.
53
73
Multiply the numerator and
denominator by 3.
= 15
21
Remember!
A fraction with the same numerator and
2
denominator, such as is equal to 1.
2
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Equivalent Fractions and Mixed Numbers
10 , and 15 are equivalent,
The fractions 5
,
21
7 14
but only 5 is in simplest form. A fraction is in
7
simplest form when the greatest common divisor
of its numerator and denominator is 1.
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Equivalent Fractions and Mixed Numbers
Example 2: Writing Fractions in Simplest Form
18
Write the fraction 24 in simplest form.
Find the GCD of 18 and 24.
18 = 2
•
3
•
3
24 = 2
•
2
•
2
The GCD is 6 = 2
•
3.
3
18 = 18 ÷ 6 = 3
24
24 ÷ 6
4
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•
Divide the numerator and
denominator by 6.
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Equivalent Fractions and Mixed Numbers
You can also simplify fractions by dividing by
common factors until the numerator and
denominator have no more common factors
except one.
To determine if two fractions are equivalent,
simplify the fractions.
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3-4
Equivalent Fractions and Mixed Numbers
Additional Example 3A: Determining Whether
Fractions are Equivalent
Determine whether the fractions in each pair
are equivalent.
4 and 28
6
42
4
Simplify both fractions
4÷2
2
6 = 6÷2= 3
and compare.
28 = 28 ÷ 14 = 2
42 ÷ 14 3
42
4 and 28 are equivalent because both are equal to 2 .
6
42
3
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Equivalent Fractions and Mixed Numbers
Example 3B: Determining Whether Fractions are
Equivalent
Determine whether the fractions in each pair
are equivalent.
6 and 20
10
25
Simplify both fractions and compare.
6 = 6÷2 = 3
10 ÷ 2
10
5
20 = 20 ÷ 5 = 4
25 ÷ 5
25
5
6 and 20 are not equivalent because their simplest
10
25
forms are not equal.
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Equivalent Fractions and Mixed Numbers
8 is an improper
5
fraction. Its
numerator is
greater than its
denominator.
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3
is a mixed
5
number. It
contains both a
whole number
and a fraction.
1
8 = 13
5
5
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Equivalent Fractions and Mixed Numbers
Example 4: Converting Between Improper Fractions and
Mixed Numbers
A. Write 13 as a mixed number.
5
First divide the numerator by the denominator.
13 = 2 3
5
5
Use the quotient and remainder to
write the mixed number.
B. Write 7 2
as an improper fraction.
3
First multiply the denominator and whole number,
and then add the numerator.
+
2 = 3  7 + 2 = 23 Use the result to
write the improper
3
3
3

fraction.
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Equivalent Fractions and Mixed Numbers
Check It Out! Example 1
Find two fractions equivalent to 6 .
12
6  2 = 12
12  2
24
Multiply the numerator and
denominator by 2.
6 ÷2
3
=
12 ÷ 2
6
Divide the numerator and
denominator by 2.
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Equivalent Fractions and Mixed Numbers
Check It Out! Example 2
15
Write the fraction 45 in simplest form.
Find the GCD of 15 and 45.
15 = 3
•
5
45 = 3
•
3
The GCD is 15 = 3
•
5.
5
15 = 15 ÷ 15 = 1
45 45 ÷ 15
3
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•
Divide the numerator and
denominator by 15.
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Equivalent Fractions and Mixed Numbers
Check It Out! Example 3A
Determine whether the fractions in each pair
are equivalent.
3 and 6
9
18
Simplify both fractions and compare.
3
3÷3
1
=
=
9
9÷3
3
6 = 6 ÷6 = 1
18 ÷ 6
18
3
3 and 6 are equivalent because both are equal to 1 .
9
18
3
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Equivalent Fractions and Mixed Numbers
Check It Out! Example 4
A. Write 15
6 as a mixed number.
First divide the numerator by the denominator.
15 = 2 3 = 2 1
2
6
6
Use the quotient and remainder
to write the mixed number.
B. Write 8 1
3 as an improper fraction.
First multiply the denominator and whole number,
and then add the numerator.
+
Use the result to
3

8
+
1
1
25
=
83 =
write the improper
3
3

fraction.
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