Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Warm UpWarm Up
California StandardsCalifornia Standards
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Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Warm UpName a common factor for each pair.
1. 5 and 10 2. 9 and 12
3. 20 and 24 4. 10 and 14
5. 6 and 8 6. 8 and 15
5 3
4 2
2 1
Possible answers:
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Number Sense (NS2.4)Number Sense (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: Number Sense (NS1.1)Number Sense (NS1.1)
California Standards
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Vocabulary
equivalent fractionsimproper fractionmixed number
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Different fractions can name the same number.
35 = = 15
256
10
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
=
To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.
In the diagram = . These are called
equivalent fractions because they are different expressions for the same nonzero number.
5
310
6
25
15
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Find two fractions equivalent to .
Additional Example 1: Finding Equivalent Fractions
57
5 27 2 = 10
14Multiply the numerator and denominator by 2.
5 37 3 = 15
21Multiply the numerator and denominator by 3.
Remember!A fraction with the same numerator and
denominator, such as is equal to 1.2 2
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
5 7
The fractions , , and are equivalent,
but only is in simplest form. A fraction is in
simplest form when the greatest common divisor
of its numerator and denominator is 1.
57
1014
1521
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Check It Out! Example 1
Find two fractions equivalent to .
6 212 2 = 12
24Multiply the numerator and denominator by 2.
6 ÷ 212 ÷ 2
= 36
Divide the numerator and denominator by 2.
612
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Write the fraction in simplest form.
Additional Example 2: Writing Fractions in Simplest Form
1824
Find the GCD of 18 and 24.
The GCD is 6 = 2 • 3.
=1824
Divide the numerator and denominator by 6.
18 = 2 • 3 • 3
24 = 2 • 2 • 2 • 3
18 ÷ 624 ÷ 6 = 3
4
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Write the fraction in simplest form.
Check It Out! Example 2
1545
Find the GCD of 15 and 45.
The GCD is 15 = 3 • 5.
=1545
Divide the numerator and denominator by 15.
15 = 3 • 5
45 = 3 • 3 • 5
15 ÷ 1545 ÷ 15= 1
3
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
To determine if two fractions are equivalent, simplify the fractions.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Determine whether the fractions in each pair are equivalent.
Additional Example 3A: Determining Whether Fractions are Equivalent
and 46
2842
Simplify both fractions and compare.
46 = 4 ÷ 2
6 ÷ 2 = 23
2842
=28 ÷ 1442 ÷ 14 = 2
3
are equivalent because both are equal to . and 46
2842
23
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Additional Example 3B: Determining Whether Fractions are Equivalent
Determine whether the fractions in each pair are equivalent.
and 610
2025
Simplify both fractions and compare.
= 6 ÷ 210 ÷ 2 = 3
52025
= 20 ÷ 525 ÷ 5 = 4
5
610
are not equivalent because their simplest and 2025
610
forms are not equal.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Check It Out! Example 3A
Simplify both fractions and compare.
39 = 3 ÷ 3
9 ÷ 3 = 13
= 6 ÷ 618 ÷ 6 = 1
3
and 39
618
618
Determine whether the fractions in each pair are equivalent.
are equivalent because both are equal to . and 39
618
13
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Check It Out! Example 3B
and 412
948
Simplify both fractions and compare.
= 4 ÷ 412 ÷ 4 = 1
3
948
= 9 ÷ 348 ÷ 3 = 3
16
412
Determine whether the fractions in each pair are equivalent.
are not equivalent because their simplestand 948
412
forms are not equal.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
85 = 13
5
85is an improper
fraction. Its numerator is greater than itsdenominator.
135is a mixed
number. Itcontains both awhole numberand a fraction.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
(A) Write
Additional Example 4: Converting Between Improper Fractions and Mixed Numbers
135 as a mixed number.
First divide the numerator by the denominator.
135
= 2 35
Use the quotient and remainder to write the mixed number.
(B) Write 723 as an improper fraction.
First multiply the denominator and whole number,and then add the numerator.
2233
+
= 3 7 + 23 = 23
3Use the result to write the improper fraction.
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Check It Out! Example 4
(A) Write 156 as a mixed number.
First divide the numerator by the denominator.
156 = 2 3
6Use the quotient and remainder to write the mixed number.
(B) Write 813 as an improper fraction.
First multiply the denominator and whole number,and then add the numerator.
113388
+
= 3 8 + 13 = 25
3
Use the result to write the improperfraction.
12
= 2
Holt CA Course 1
3-4 Equivalent Fractions and Mixed Numbers
Lesson Quiz
1. Write two fractions equivalent to .
2. Determine if and are equivalent.
3. Write the fraction in simplest form.
4. Write as a mixed number.
5. Write 4 as an improper fraction.
1224
1648
37
317
18217
8
13
no
12
36
,
5 12
4 10
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