1. Fractions Basics
By Howard Rones

2. Numerator and Denominator
Easy to remember! The Denominator is DOWN and the Numerator is NORTH.

3. Equivalent fractions represent the same fractional part of a whole.
1/2
2/4
4/8
Equivalent fractions represent the same fractional part of a whole.

4. Equivalent Fractions
Look at these fraction bars. What fractions are equivalent to1/3?
Here’s 1/3. 1 2 4 = = 3 6 12
Here’s 2/6.
Here’s 4/12.

5. Equivalent Fractions
Look at these fraction bars. What fractions are equivalent to ¾?
Look at these fraction bars. What fractions are equivalent to ¾?
Here’s 3/4. 3 6 9 = = 4 8 12
Here’s 6/8.
Here’s 9/12.

6. Fractions Equivalent to 1
What fraction of the pizza is shaded? In each picture, one whole pizza is shaded. 4 8 =1 =1 4 8 6 =1 6
When the numerator and denominator are the same, the fraction is equal to 1.

7. Naming Equivalent Fractions
Write three fractions that are equivalent to 2/3. 2 2 4 2 3 6 = = X X 3 2 6 3 3 9
one
one
In each case, we just multiplied by ONE so the new fraction must be equivalent to 2/3. 2 4 8 = X 3 4 12
one

8. Proper Fractions
A proper fraction represents a part of a whole. The numerator must be smaller than the denominator. Examples: 4 3 1 5 11 9

9. Improper Fractions
Improper fractions represent one whole or more than one whole. 4
is shaded blue. 4 4
is an improper fraction. 4

10. Improper Fractions 53 53 Each orange section is 1/3 of the rectangle.
There are 5 sections shaded is shaded 53 53
is improper.

11. Improper Fractions
Improper fractions have numerators that are equal to or greater than the denominator. 6 23 9 5 11 9
…are all improper fractions.

12. Simplifying Fractions
If the numerator and denominator have a COMMON FACTOR other than one, it can be simplified. Here, the 12 and the 15 have a COMMON FACTOR of 3. We can simplify by dividing the numerator and denominator by 3. 12 3 4 ÷ = 15 3 5 ÷

13. Simplifying Fractions
Here, the 15 and the 25 have a COMMON FACTOR of 5. We can simplify by dividing the numerator and denominator by 5. 15 5 3 ÷ = 25 5 5 ÷

14. Simplifying Fractions
Here, the 14 and the 49 have a COMMON FACTOR of 7. We can simplify by dividing the numerator and denominator by 7. 14 7 2 ÷ = 49 7 7 ÷

15. Simplifying Fractions
We see the 40 and 60 both end in a zero. We can divide them both by 10.
Then, we see the 4 and 6 are both even so we divide both by 2. Stop when the GCF is 1. 40 10 4 2 2 ÷ ÷ = = 60 10 6 2 3 ÷ ÷

16. Simplifying Fractions
Here, the 12 and the 18 have COMMON FACTORS of 2, 3 and is the GREATEST common factor (GCF). If we divide by 6, we can simplify in one step. If we use the 2 or 3, it will take more steps. 12 6 2 ÷ = 18 6 3 ÷

17. Are these fractions equal?5 10 ? 6 12
If two fractions are equal, their cross products are equal.
5 X 12 = 60
6 X 10 = 60 5 10 ? 6 12
60 = 60 The fractions are equal.

18. Are these fractions equal?5 10 ? 7 11
If two fractions are equal, their cross products are equal.
5 X 11 = 55
7 X 10 = 70 5 10 ? 7 11
55 ≠ 70. The fractions are not equal.

19. More Equivalent Fractions
Find the missing number in these equivalent fractions. 5 ? = 7 21
Think…7 X ? = X 3 = 21 so I’ll multiply the numerator and denominator by 3. 5 3 15 = X 7 3 21

20. More Equivalent Fractions
Find the missing number in these equivalent fractions. 3 24 = 4 ?
Think…3 X ? = X 8 = 24 so I’ll multiply the numerator and denominator by 8. 3 8 24 = X 4 8 32

21. More Equivalent Fractions
Find the missing number in these equivalent fractions. 15 3 = 25 ?
Think…15 ÷ ? = ÷ 5 = 3 so I’ll divide the numerator and denominator by 5. 15 5 3 = ÷ 25 5 5

22. Changing Improper Fractions to Mixed or Whole Numbers
To change an improper fraction to a mixed number or whole number, think of it as a division problem. 5
= 5 ÷ 3 = 3 ) 5 3 1
2/3
3 ) 5 5 2
= 1
- 3 3 3 2

23. Changing Improper Fractions to Mixed or Whole Numbers
To change an improper fraction to a mixed number or whole number, think of it as a division problem. 16
= 16 ÷ 4 = 4 ) 16 4 4
4 ) 16 16
= 4
- 16 4

24. Changing Mixed Numbers to Improper Fractions
Here’s the “shortcut”. Follow the colors! 2 1 = 3
1 X 3 + 2 5 = 3 3

25. Changing Mixed Numbers to Improper Fractions
Last one. Follow the colors! 4 3 = 5
3 X 5 + 4 19 = 5 5

26. Farewell
Now that you know all the basics, you are ready to learn how to add, subtract and multiply fractions. We’ll leave division for your 6th grade teacher.