1. 4-7 6th grade math
Equivalent Fractions

2. Objective
To find equivalent fractions and write fractions in simplest form.
Why? To help you solve addition and subtraction problems with unlike denominators.

3. California State Standards
NS 1.0 : Solve problems involving fractions … NS 2.4 : Determine the least common multiple (LCM) and the greatest common divisor (GCD)of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator … to find the reduced form for a fraction)

4. Vocabulary Equivalent Fractions
Fractions that name the same number
½ = 2/4
Simplest Form (Reduced Form) (Lowest Terms)
A fraction is in simplest form when the greatest common factor of the numerator and denominator is one.
2/4 = ½ (÷2)
Least Common Denominator (LCD)
The least common multiple of the denominators of two or more fractions
12 is the least common denominator of ¼ and 1/6
Greatest Common Divisor (GCD)
The greatest number that can be divided into both the numerator and denominator to reduce the fraction to lowest terms.
The GCD is 3 to reduce 2/6 to 1/3
Identity Property of Multiplication
The product of any number and one is that number
1 x 5 = 5

5. How to Make Equivalent Fractions
) Use what you know to find the LCM of the numbers in the denominators 2) Multiply both the numerator and denominator by the same number that changed the denominator to the new LCM 3) Check your work 12
LCM of 3 and 12 = 12
1 · 4 =
3 · 4 =
4 , 4

6. How to Find if Fractions are Equivalent
) Use what you know to find the GCF of the numbers in the denominators 2) Divide both the numerator and denominator by the same number that changed the denominator to the new GCF 3) Check your work. Do NOT simplify.
1 4
= 3 · 1; 12 = 3 · 4
GCF of 3 and 12 = 4
÷ 4 = 1
12 ÷
The fractions are equivalent or the same.

7. Simplifying Fractions24
Find the GCF of both the numerator and the denominator
Divide the numerator and denominator by the GCF
Check to be sure all numbers are prime. If not, continue to simplify
12 24 GCF of 12 and 24 = ÷ 12 = 1 24 ÷ 12 = 2 12 is reduced to

8. Try It! 12 = 22 12 = ÷ 2 = 6 22 ÷ 2 = 11 Simplify 14 = 12 28 22
22 ÷ 2 = 11
14 = 28
14 = ÷ 7 = 2 ÷ 2 = 1
÷ 7 = 4 ÷ 2 = 2
3) 24 40
24 = ÷ 8 = 3
40 ÷ 8 = 
Simplify 12 22 14 28
3) 24 40

9. 4) 38 = = ÷ 2 = ÷ 2 = 23 5) 24 = = ÷ 6 = 4 54 ÷ 6 = 9
4) ) 24 54

10. Try Some More! 8) 7 8 6 10 LCD = 30 7 · 5 = 35 8 · 3 = 24
6) 5 , 5
6 30
LCD = 30
5· 5 = , 5
6 · 5 =
25 , 5 30
7) 6 , 4
6 · 3 = 18 , 4
10 · 3 =
18 , 4
8) 7 8
6 10
LCD = 30
7 · 5 = · 3 = 24
6 · 5 = · 3 = 30
35 , 24 30
8 4
9 12
LCD = 36
8 · 4 = · 3= 12
9 · 4 = · 3= 36
32 , 12 36
Use the LCD to write each set of fractions as equivalent fractions, or fractions with the same denominator.
6) 5 , 5
7) 6 , 4
8) 7 8
6 10

11. 4 , 5 , 7
4 · · · 8
3 · · · 8
LCD = 72

12. Objective Review
To find equivalent fractions and write fractions in simplest form.
Why? You can now solve addition and subtraction problems with unlike denominators.

13. Independent Practice Complete problems 12-24
Copy original problem first.
Show all work!
If time, complete Mixed Review: 25-29
If still more time, work on Accelerated Math.