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Equivalent Fractions

- Lesson 4-7

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

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).

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)

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

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

To create fractions equivalent to a given

fraction, multiply or divide the numerator and

denominator by the same nonzero number.

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

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

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

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.

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.

To determine if two fractions are equivalent,

simplify the fractions.

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

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

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

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

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

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

?

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

?

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.

(No Transcript)

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

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

Guided Practice

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