1. 2-9 Equivalent Fractions and Mixed Numbers Warm Up Problem of the Day
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. 2-9 Equivalent Fractions and Mixed Numbers Warm Up
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Warm Up
Name a common factor for each pair.
1. 5 and and 12
3. 20 and and 14
5. 6 and and 15
Possible answers: 5 3 4 2 2 1

3. 2-9 Equivalent Fractions and Mixed Numbers Problem of the Day
Course 2
2-9
Equivalent Fractions and Mixed Numbers
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

4. Course 2
2-9
Equivalent Fractions and Mixed Numbers
Learn to identify, write, and convert between equivalent fractions and mixed numbers.

5. Insert Lesson Title Here
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Insert Lesson Title Here
Vocabulary
equivalent fractions
improper fractions
mixed number

6. 2-9 Equivalent Fractions and Mixed Numbers
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. 3 5 6 10 15 25 = =

7. 2-9 Equivalent Fractions and Mixed Numbers
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. 3 5 6 10 15 25 =
To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same number.

8. Additional Example 1: Finding Equivalent Fractions
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Additional Example 1: Finding Equivalent Fractions 5 7
Find two fractions equivalent to .
5 · 2 10 14 =
Multiply numerator and
denominator by 2.
7 · 2
5 · 3 15 21
Multiply numerator and
denominator by 3. =
7 · 3

9. Insert Lesson Title Here
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Insert Lesson Title Here
Check It Out: Example 1 6 12
Find two fractions equivalent to
6 · 2 12 24 =
Multiply numerator and
denominator by 2.
12 · 2
6 ÷ 2
12 ÷ 2 3 6
Divide numerator and
denominator by 2. =

10. Additional Example 2: Writing Fractions in Simplest Form
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Additional Example 2: Writing Fractions in Simplest Form 18 24
Write the fraction in simplest form.
Find the GCF of 18 and 24.
18 = 2 • 3 • 3
The GCF is 6 = 2 • 3.
24 = 2 • 2 • 2 • 3 18 24
18 ÷ 6
24 ÷ 6 3 4
Divide the numerator and
denominator by 6. = =

11. 2-9 Equivalent Fractions and Mixed Numbers Check It Out: Example 2 15
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Check It Out: Example 2 15 45
Write the fraction in simplest form.
Find the GCF of 15 and 45.
15 = 3 • 5
The GCF is 15 = 3 • 5.
45 = 3 • 3 • 5 15 45
15 ÷ 15
45 ÷ 15 1 3
Divide the numerator and
denominator by 15. = =

12. Additional Example 3A: Determining Whether Fractions are Equivalent
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Additional Example 3A: Determining Whether Fractions are Equivalent
Determine whether the fractions in each pair are equivalent. 4 6 28 42
and
Both fractions can be written with a denominator of 3. 4 6
4 ÷ 2
6 ÷ 2 2 3 = = 28 42
28 ÷ 14
42 ÷ 14 2 3 = =
The numerators are equal, so the fractions are
equivalent.

13. Additional Example 3B: Determining Whether 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. 6 10 20 25
and
Both fractions can be written with a denominator of 50. 6 10
6 · 5
10 · 5 30 50 = = 20 25
20 · 2
25 · 2 40 50 = =
The numerators are not equal, so the fractions are
not equivalent.

14. Insert Lesson Title Here
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Insert Lesson Title Here
Check It Out: Example 2A
Determine whether the fractions in each pair are equivalent.
and 3 9 6 18
Both fractions can be written with a denominator of 3. 3 9
3 ÷ 3
9 ÷ 3 1 3 = = 6 18
6 ÷ 6
18 ÷ 6 1 3 = =
The numerators are equal, so the fractions are
equivalent.

15. Insert Lesson Title Here
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Insert Lesson Title Here
Check It Out: Example 2B
Determine whether the fractions in each pair are equivalent. 4 12 9 48
and
Both fractions can be written with a denominator of 96. 4 12
4 · 8
12 · 8 32 96 = = 9 48
9 · 2
48 · 2 18 96 = =
The numerators are not equal, so the fractions are
not equivalent.

16. 2-9 Equivalent Fractions and Mixed Numbers 8 5 3 5 = 1 8 5 3 5
Course 2
2-9
Equivalent Fractions and Mixed Numbers 8 5 3 5
is an improper 1
is a mixed
fraction. Its
numerator is
greater than its
denominator.
number. It
contains both a
whole number
and a fraction. 8 5 3 5
= 1

17. 2-9 Equivalent Fractions and Mixed Numbers 
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Additional Example 4: Converting Between Improper Fractions and Mixed Numbers 13 5
A. Write
as a mixed number.
First divide the numerator by the denominator. 13 5 3 5
Use the quotient and remainder to
write a mixed number.
= 2 2 3
B. Write 7
as an improper fraction.
First multiply the denominator and whole number,
and then add the numerator. +
Use the result to
write the improper
fraction. 2 3
3 · 7 + 2 23 3 = = 7 3 

18. 2-9 Equivalent Fractions and Mixed Numbers 8  Check It Out: Example 4
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Check It Out: Example 4 15 6
A. Write
as a mixed number.
First divide the numerator by the denominator. 15 6 3 6 1 2
= 2
Use the quotient and remainder to
write a mixed number.
= 2 1 3
B. Write 8
as an improper fraction.
First multiply the denominator and whole number,
and then add the numerator. +
Use the result to
write the improper
fraction. 1 3
3 · 8 + 1 25 3 8 = = 3 

19. Insert Lesson Title Here
Course 2
2-9
Equivalent Fractions and Mixed Numbers
Insert Lesson Title Here
Lesson Quiz 12 24 1 2, 3 6
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.
5 12
4 10 no 16 48 1 3 17 8 1 8 2 31 7 3 7