Equivalent Fractions

1
Equivalent Fractions

• Lesson 4-7

2
Bell Work
Name the greatest 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
3
Todays Math Standards

• Number Sense 1.0 (this is what we are working
  toward)
• Students compare and order positive and negative
  fractions, decimals, and mixed numbers. Students
  solve problems involving fractions, ratios,
  proportions, and percentages
• Number Sense 2.4
• 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 for a fraction).

4
Equivalent Fractions

• We use the GCF and the LCM to make equivalent
  fractions
• GCF to make smaller equivalent fractions
• Reduce
• Simplify
• Put in lowest terms
• LCM to make equivalent fractions
• Make common denominators
• Addition
• Subtraction
• Comparing (with and without number lines)

5
Key Vocabulary

• equivalent fractions
• Fractions that name the same number
• improper fraction
• A fraction whose numerator is larger than the
  denominator
• mixed number
• A whole number and a fraction

6
Equivalent Fractions
Notice how all three of the rectangles still have
these same 5 rows. The only thing that has
changed is the number of columns.
Different fractions can name the same number.
3 5
15 25
6 10


7
To create fractions equivalent to a given
fraction, multiply or divide the numerator and
denominator by the same nonzero number.
8
Find two fractions equivalent to .
1
5 ? 2
10 14
Multiply the numerator and denominator by 2.

7 ? 2
1
5 ? 3
Multiply the numerator and denominator by 3.
15 21

7 ? 3
9
15 21
5 7
10 14
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.
5 7
10
Find two fractions equivalent to .
1
6 ? 2
12 24
Multiply the numerator and denominator by 2.

12 ? 2
1
6 2 12 2
Divide the numerator and denominator by 2.
3 6

11
18 24
Write the fraction in simplest form.
Find the GCD of 18 and 24.
18 2 3 3
The GCD is 6 2 3.
24 2 2 2 3
1
18 24
3 4
Divide the numerator and denominator by 6.


12
15 45
Write the fraction in simplest form.
Find the GCD of 15 and 45.
15 3 5
The GCD is 15 3 5.
45 3 3 5
1
1 3
15 45
Divide the numerator and denominator by 15.


13
To determine if two fractions are equivalent,
simplify the fractions.
14
Determine whether the fractions in each pair are
equivalent.
4 6
28 42
and
Simplify both fractions and compare.
1
4 6
4 2 6 2
2 3


1
2 3
28 42
28 14 42 14


15
Determine whether the fractions in each pair are
equivalent.
6 10
20 25
and
Simplify both fractions and compare.
1
6 2 10 2
6 10
3 5


1
20 5 25 5
4 5
20 25


16
Determine whether the fractions in each pair are
equivalent.
Simplify both fractions and compare.
1
3 9
3 3 9 3
1 3


1
6 6 18 6
1 3


17
Determine whether the fractions in each pair are
equivalent.
4 12
9 48
and
Simplify both fractions and compare.
1
4 4 12 4
1 3
4 12


1
9 48
9 3 48 3
3 16


18
3 5
8 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
19
Converting Between Improper Fractions and Mixed
Numbers
A. Write
as a mixed number.
13 5
First divide the numerator by the denominator.
3 5
Use the quotient and remainder to write the
mixed number.
13 5
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.
3 ? 7 2
2 3
23 3


7
3
?
20
15 6
A. Write
as a mixed number.
First divide the numerator by the denominator.
Use the quotient and remainder to write the mixed
number.
3 6
15 6
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.
3 ? 8 1
1 3
25 3

8

3
?
21
To add or subtract fractions with different
denominators, you must rewrite the fractions with
a common denominator. In this case, the fractions
need to be made equivalent.
22
(No Transcript)
23
Find the Lowest Common Denominator for and
.
24 2 x 2 x 2 x 3
30 2 x 3 x 5
LCM 2 x 2 x 2 x 3 x 5
120
x 4
x 4
x 5
x 5
24
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. 6. Find the LCD, and write
equivalent fractions for and .
12 24
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. 6. Find the LCD, and write
equivalent fractions for and .
no
no
1 3
1 3
16 48
16 48
17 8
31 7
31 7
3 7
5 12
5 12
3 16
LCD 48
25
Guided Practice

• Holt Online video tutorial and practice
• Holt Online Practice
• Holt-common denominators