addition and subtraction of fractions

1. Similar Fractions
Fractions having the
same denominator
3
8
and
2
8
4
6
and
1
6

2. Dissimilar Fractions
Fractions having
different denominator
3
2
and
2
8
4
6
and
1
5

3. Mixed Fractions
Combination of
fraction and a whole
number
4
3
2
, 2
2
8
, 1
2
3

4. In adding similar fractions,
add the numerators and copy the
denominator. Simplify the answer if
possible.
1.
2
8
+
5
8
=
7
8
2.
3
6
+
4
6
=
7
6
or 1
1
6
3.
2
12
+
4
12
=
6
12
or
1
6

5. Proper fraction
A fraction in which the value of the
numerator is less than the
denominator.
7
8
,
1
2
,
8
12
,
3
9

6. Improper fraction
A fraction in which the value of the
numerator is greater than the
denominator.
7
6
,
5
2
,
17
12
,
13
9

7. Greatest Common Factor
The highest number that divides
exactly into two or more numbers.
The largest factor that the given
numbers share.
6: 1x6, 2x3
12: 1x12, 2x6, 3x4

8. Add & Subtract Fractions
1. Find the common denominator.
2. Make equivalent fractions using the
new common denominator.
3. Add/sub the numerators.
Denominator stays the same.
4. Simplify/reduce.
5. Leave improper fractions as is.

9. Examples
24
29
24
20
24
9
6
5
8
3




1

10. 9
2
4
9
6
3
9
8
7
3
2
3
9
8
7




2

11. 1.
1
7
+
2
5
2.
2
5
+
1
7
3.
2
5
+
2
7
4.
2
5
+
2
3
5.
1
4
+
2
3

12. 6.
2
5
−
1
7
=
7.
1
7
−
2
5
=
8.
2
5
−
2
7
=
9.
2
3
−
2
5
=
10.
2
3
−
1
4
=

13. 1.
1
7
+
2
5
=
19
35
2.
2
3
+
1
7
=
17
21
3.
2
5
+
2
7
=
24
35
4.
2
5
+
2
3
=
16
15
= 1
1
15
5.
1
4
+
2
3
=
11
12

14. 6.
2
5
−
1
7
=
9
35
7.
1
7
−
2
5
= −
9
35
8.
2
5
−
2
7
=
4
35
9.
2
3
−
2
5
=
4
15
10.
2
3
−
1
4
=
5
12

15. Multiply Fractions & Mixed #s
1. Change any mixed numbers into
improper fractions.
2. Multiply numerators.
3. Multiply denominators.
4. Simplify. (You can also simplify
before you multiply.)
5. Leave improper fractions as is.

16. Examples
16
5
3
3
48
15
6
5
8
3




11
42
11
10
5
21
11
10
5
1
4




1
2
1
2

17. Divide Fractions & Mixed #s
1. Change any mixed #s into improper
fractions.
2. Find the reciprocal of the 2nd fraction
(the divisor), rewriting the problem as
a multiplication problem.
3. Multiply.
4. Simplify. (You can also simplify
before you multiply.)
5. Leave improper fractions as is.

18. Examples
20
9
2
2
40
18
5
6
8
3
6
5
8
3






25
88
10
11
5
16
11
10
5
1
3




8
5
1
2

19. Decimal Operations - Reminders
Addition and Subtraction
◦Arrange the decimal numbers
in a column such that the
decimal points are aligned,
then add or subtract as with
whole numbers.

20. Decimal Operations - Reminders
Multiplication
◦Line up digits as in whole
numbers and multiply.
◦After multiplying as usual,
count up total places behind
decimal point, and move
decimal that number of
places.

21. Decimal Operations - Reminders
Division:
◦ Shift decimal in the divisor
(outside number) to the right so
that you are dividing by a whole
number. Shift the decimal in the
dividend the same number of
places. Now divide as usual.
◦ Keep dividing until it ends or
repeats.

22. Now in your Know It Notes:
 Reciprocal: numerator and
denominator change place (fraction
flipped over)
 Multiplicative inverse: a number and
its reciprocal are called multiplicative
inverses
 A number times its reciprocal = 1

23. Important Stuff about Zero
 Zero times a number = zero
 Zero divided by a number = zero
 A number divided by zero = undefined
◦ How could you make zero groups of
something? It is not possible, so we get
“undefined” instead.