2-9 equivalent fractions and mixed numbers course 2 warm up warm up problem of the day problem of...
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2-9 Equivalent Fractions and Mixed Numbers
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
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
Course 2
2-9 Equivalent Fractions and Mixed Numbers
2
2 1
Possible answers:
Problem of the Day
Find a number less than 100 for which all three statements are true:• Divide by 3. Remainder of 2.• Divide by 4. Remainder of 3.• Divide by 5. Remainder of 4.
59
Course 2
2-9 Equivalent Fractions and Mixed Numbers
Learn to identify, write, and convert between equivalent fractions and mixed numbers.
Course 2
2-9 Equivalent Fractions and Mixed Numbers
Vocabulary
equivalent fractionsimproper fractionsmixed number
Insert Lesson Title Here
Course 2
2-9 Equivalent Fractions and Mixed Numbers
In some recipes the amounts of ingredients are given as fractions, and sometimes those fractions do not equal the fractions on a measuring cup. Knowing how fractions relate to each other can be very helpful.
Different fractions can name the same number.
35 = = 15
256
10
Course 2
2-9 Equivalent Fractions and Mixed Numbers
=
To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same number.
Course 2
2-9 Equivalent Fractions and Mixed Numbers
In the diagram = . These are called
equivalent fractions because they are different expressions for the same nonzero number.
35
610
1525
Find two fractions equivalent to .
Additional Example 1: Finding Equivalent Fractions
57
5 · 27 · 2
= 1014
Multiply numerator and denominator by 2.
Course 2
2-9 Equivalent Fractions and Mixed Numbers
5 · 37 · 3 = 15
21Multiply numerator and denominator by 3.
Check It Out: Example 1
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Find two fractions equivalent to .
6 · 212 · 2
= 1224
Multiply numerator and denominator by 2.
6 ÷ 212 ÷ 2
= 36
Divide numerator and denominator by 2.
Course 2
2-9 Equivalent Fractions and Mixed Numbers
612
Write the fraction in simplest form.
Additional Example 2: Writing Fractions in Simplest Form
1824
Find the GCF of 18 and 24.
The GCF is 6 = 2 • 3.
Course 2
2-9 Equivalent Fractions and Mixed Numbers
=1824
Divide the numerator and denominator by 6.
18 = 2 • 3 • 3
24 = 2 • 2 • 2 • 3
18 ÷ 624 ÷ 6 = 3
4
Write the fraction in simplest form.
Check It Out: Example 2
1545
Find the GCF of 15 and 45.
The GCF is 15 = 3 • 5.
Course 2
2-9 Equivalent Fractions and Mixed Numbers
=1545
Divide the numerator and denominator by 15.
15 = 3 • 5
45 = 3 • 3 • 5
15 ÷ 1545 ÷ 15 = 1
3
Determine whether the fractions in each pair are equivalent.
Additional Example 3A: Determining Whether Fractions are Equivalent
and 46
2842
Both fractions can be written with a denominator of 3.
46 = 4 ÷ 2
6 ÷ 2 = 23
2842
= 28 ÷ 1442 ÷ 14 = 2
3
The numerators are equal, so the fractions are equivalent.
Course 2
2-9 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
Both fractions can be written with a denominator of 50.
= 6 · 510 · 5 = 30
502025
= 20 · 225 · 2 = 40
50The numerators are not equal, so the fractions are not equivalent.
610
Course 2
2-9 Equivalent Fractions and Mixed Numbers
Check It Out: Example 2A
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Both fractions can be written with a denominator of 3.
39 = 3 ÷ 3
9 ÷ 3 = 13
= 6 ÷ 618 ÷ 6 = 1
3
The numerators are equal, so the fractions are equivalent.
Course 2
2-9 Equivalent Fractions and Mixed Numbers
and 39
618
618
Determine whether the fractions in each pair are equivalent.
Check It Out: Example 2B
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and 412
948
Both fractions can be written with a denominator of 96.
= 4 · 812 · 8 = 32
96
948
= 9 · 248 · 2 = 18
96
The numerators are not equal, so the fractions are not equivalent.
412
Course 2
2-9 Equivalent Fractions and Mixed Numbers
Determine whether the fractions in each pair are equivalent.
85= 13
5
85 is an improper
fraction. Its numerator is greater than itsdenominator.
1 35
is a mixednumber. Itcontains both awhole numberand a fraction.
Course 2
2-9 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 a mixed number.
B. Write 7 23 as an improper fraction.
First multiply the denominator and whole number,and then add the numerator.
2233
+
= 3 · 7 + 23 = 23
3
Use the result to write the improperfraction.
Course 2
2-9 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 36
Use the quotient and remainder to write a mixed number.
B. Write 8 13 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.
Course 2
2-9 Equivalent Fractions and Mixed Numbers
12
= 2
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.
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1224
1648
37
317
182
12,
Course 2
2-9 Equivalent Fractions and Mixed Numbers
36
178
5 12
4 10
13
no