Download Fractions Study Guide

Fractions Study Guide
Picture Fractions: You should be able to use pictures to show fractions, or find
fractions from pictures.
Example:
Practice:
1.Draw a picture showing 4/5.
2. What fraction of the pizza was eaten?
Comparing Fractions: There are two ways to see which fractions is bigger: The Rules
and Finding Equivalent Fractions.
The Rules
Fraction Type
Numerators are
1
Same Numerator
Same
denominator
Practice:
3. 1/5 1/8
Test
Check
denominators
Check
denominators
Check numerator
Comparison
Smaller number on bottom is bigger
fraction
Smaller number on bottom is bigger
fraction
Bigger number on top is bigger
fraction.
4. 3/10 3/7
5. 9/10 9/15
Example
1/3 > 1/5
2/3 > 2/7
4/5 >2/5
Comparing Fractions Continued…
Finding Equivalent Fractions: Find the least common denominator of both fractions
by looking for the Least Common Multiple of the denominators. Then multiply to make
equivalent fractions. Compare.
Example: Compare 2/4 and 1/3.
Step 1: Find their least common multiple:
2/4 4,8,12
1/3 3,6,9,12
Step 2: Multiply to make equivalent fractions.
2 x3 6
--- = --4 x3 12
1 x4 4
--- = ---3 x4 12
Step 3: Compare 6/12 > 4/12 so 2/4 >1/3
Practice:
6. 2/6 1/2
7. 1/3 5/8
8. 3/4 7/10
Reducing Fractions: Find the greatest common factors of the denominators. Use the
greatest common factor to divide both fractions.
Example: 8/12
1,2,4,8
1,2,3,4,6,12
8 ÷4 2
--- = ---12 ÷ 4 3
Practice:
9. 25/60
10. 12/40
11. 12/28
Improper Fractions: There are two ways to change an Improper Fractions into a
Mixed Number: Drawing a Picture or Dividing.
Drawing a Picture: The denominator tells you how many are in one whole. So, you
draw the number the numerator says in groups of the denominator.
Example: 14/8 = 1 6/8 or 1 3/4
1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8
8/8=1
1/8 1/8 1/8 1/8 1/8 1/8
6/8
Practice Drawing Pictures:
12. 5/2
13. 7/4
14. 17/6
Dividing: Divide the numerator by the Denominator. Write the remainder as a fraction.
__1_r6
Example: 14/8 8) 14
so 14/8= 1 6/8 or 1 ¾
Practice:
15. 15/8
16. 13/4
17. 8/3
Mixed Numbers: There are two ways to turn a mixed number into an improper
fraction: Drawing a Picture or Multiplication and Addition.
Drawing a Picture: Using the denominator draw picture of how many whole and parts
you have. Then count each part to find the improper fraction.
2 5/12
12/12
12/12
1/12 1/12 1/12 1/12 1/12
12/12 + 12/12 +5/12 = 29/12
Practice:
18. 2 2/4
19. 3 11/12
20. 2 2/7
Mixed Numbers to Improper Fractions Continued…
Multiplication and Addition Method: Multiply the denominator by the whole number.
Then, add the numerator.
Example: 2 5/12
Step 1: 12 x 2 = 24
Step2: 24+5=29
So, 2 5/12 = 29/12
Practice:
21. 2 3/8
22. 4 5/7
23. 2 1/6
Adding and subtracting fractions with LIKE denominators: Just add or subtract the
numerators, keep the denominators the same and simplify.
Example: 3/8 + 2/8 = 5/8 or 3/8 – 2/8 = 1/8
Practice:
24. 7/7 -5/7
25. 2/5 +1/5
26. 3/8 +5/8
Adding and Subtracting fractions with UNLIKE denominators: First find the least
common multiple of the two denominators to make the least common denominator.
Then, make equivalent fractions using your new common denominator. Finally add or
subtract and then simplify.
Example: 2/3 + 4/5
2/3 - 3,6,9,12,15
4/5  5,10,15
2 x5 10
-- = --3 x5 15
4 x3 12
-- = --5 x3 15
10/15+12/15=22/15, so 1 7/15
Practice:
27. 3/8 + 2/5
28. 7/8 + 2/3
29. 4/5 – ½
Adding and Subtracting Mixed Numbers: There are two ways to solve these
problems: Improper Fractions or Adding/Subtracting whole number and fractions
separately.
Improper Fractions: To remember how to find improper fractions, look at that section.
Example: 2 5/12 + 1 ½
Step 1: Make improper fractions.
2 5/12 =29/12
1 ½ = 3/2
Step 2: Find the Least Common Denominator
2,4,6,8,10,12
12
Step 3: Make Equivalent Fractions
3 x6 18
--- = ---2 x6 12
Step 4: Add or Subtract
29/12 + 18/12 =47/12
Step 5: Simplify
47 ÷ 12 =3 11/12
Practice:
30. 2 2/4 + 1 1/6
31. 1 2/6 + 2 2/5
32. 1 10/11 + 3 11/12
Adding/Subtracting whole number and fractions separately
Example: 2 5/12 + 1 ½
Step 1: Add whole numbers
2+1=3
Step 2: Find the least common denominator for the fractions.
2,4,6,8,10,12
12
Step 3: Make Equivalent Fractions
1 x6 6
--- = ---2 x6 12
Step 4: Add the Fractions
5/12+6/12=11/12
Step 5: Add the new fraction to the whole number you got in Step 1.
3 + 11/12 = 3 11/12
Practice:
33. 1 6/12 + 2 2/7
34. 3+2 2/7
35. 1 2/4 + 3 11/12