Lesson 1.9 a adding and subtracting rational numbers

To or like fractions, add
or subtract the and
write the sum over the .

To or like fractions:
1. Add or subtract the numerators 2. Retain the denominator. 3. Simplify if possible.
Example 1:
1
4
+
2
4
=
3
4
/ the
numerators.
1+2
Retain the
.
Simplify if possible.

Example 1:
1
4
+
2
4
=
3
4

Example 2:
5
11
−
2
11
=
3
11
/ the
numerators.
5 − 2
Retain the
.

Example 2:
5
11
−
2
11
=
3
11

Example 3:
−
3
9
+
4
9
=
1
9
/ the
numerators.
−3 + 4
Retain the
.

Example 3:
+
4
9
=
1
9
−
3
9

Example 4:
−
4
7
+
2
7
=
−2
7
/ the
numerators.
−4 + 2
Retain the
.
−
2
7

Example 4:
−
4
7
+
2
7
= −
2
7

Example 5:
5
6
+
−3
6
=
2
6
/ the
numerators.
5 − 3
Retain the
.
=
1
3

Example 5:
5
6
+
−3
6
=
2
6
=
1
3

Example 6:
1
13
−
−4
13
=
5
13
/ the
numerators.
1 + 4
Retain the
.

Example 6:
1
13
−
−4
13
=
5
13

Example 7:
2
3
5
+ 1
1
5
=
4
5
/ the
numerators.
3 + 4
Retain the
.
Add/subtract the
whole numbers
3
2 + 1

Example 7:
2
3
5
+ 1
1
5
=
4
5
3

1.
3
2
+ 1
1
2
2.
5
21
−
16
21
3.
9
13
+
−4
13
4. −
2
8
−
4
8
5. −
5
6
−
1
6
= 3
= −
11
21
=
5
13
= −
3
4
= −1

To or rational numbers with different denominators:
1. Denominators should be alike. Find LCD. Change to improper fractions if possible.
2. Convert all to equivalent fractions.
3. Simplify now if ready.
Example 1:
1
9
+
2
3
Denominators should
be alike. Find LCD.

Example 1:
1
9
+
2
3
Denominators should
be alike. Find LCD.
Least Common Multiple
9: 9, 18, 27, 36, 45, …
3: 3, 6, 9, 12, 15, …

Example 1:
1
9
+
2
3
Denominators should
be alike. Find LCD.
9: 9, 18, 27, 36, 45, …
3: 3, 6, 9, 12, 15, …
LCD: 9

Example 1:
1
9
+
2
3
=
LCD: 9 Convert all to . Change
each denominator to the LCD.
1
9
What should be
multiplied to the
denominator to
have the LCD?

Example 1:
1
9
+
2
3
=
1
9
+
6
9

Example 1:
1
9
+
2
3
=
1
9
+
6
9
What should be
multiplied to the
denominator to
have the LCD?
× 3
× 3
Simplify!

Example 1:
1
9
+
2
3
=
1
9
+
6
9× 3
× 3
Simplify!

Example 1:
LCD: 9
Simplify.
1. Add the
numerators.
2. Retain
denominator.
1
9
+
2
3
=
1
9
=
7
9
× 3
× 3
+
6
9
1 + 6

Example 1:
LCD: 9
1
9
+
2
3
=
1
9
=
7
9
× 3
× 3
+
6
9
Simplify.
1. Add the
numerators.
2. Retain
denominator.

Example 1:
1
9
+
2
3
=
1
9
=
7
9
× 3
× 3
+
6
9

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
Changing mixed fraction to
improper fraction.
Multiply the denominator
and whole number
12
3
4
=
51
4
48
4 12

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
improper fraction.
Add up the product to the
numerator. The result will be the
new numerator.
12
3
4
=
51
4
48
48 + 3

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
improper fraction.
Copy the denominator
12
3
4
=
51
4

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
Break the
groupings.

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
+(−)
Break the
groupings.

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
Denominators
should be alike.
Find LCD.

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
Denominators
should be alike.
Find LCD.
4: 4, 8, 12, 16, …
2: 2, 4, 6, 8, …
LCD: 4

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
LCD: 4
=
51
4
−
2
4
What should be
multiplied to the
denominator to
have the LCD?
Convert all to . Change

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
What should be
multiplied to the
denominator to
have the LCD?
LCD: 4

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
What should be
multiplied to the
denominator to
have the LCD?
LCD: 4
× 2
× 2

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
Simplify!
LCD: 4
× 2
× 2

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
Now we’re ready!
1. Subtract the
numerator.
2. Copy denominator
LCD: 4
× 2
× 2
=
49
4
51 − 2

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
Now we’re ready!
1. Subtract the
numerator.
2. Copy denominator
LCD: 4
× 2
× 2
=
49
4

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
For final answers.
Change to mixed
fractions.
× 2
× 2
=
49
4
= 12
1
4

Example 2:
12
3
4
+ −
1
2
=
51
4
−
1
2
=
51
4
−
2
4
× 2
× 2
=
49
4
= 12
1
4

1.
1
2
+ −
1
4
2.
7
8
−
3
16
3.
2
3
−
3
4
4. 1
7
5
− −
9
10
5. 3
3
4
− 1
5
8
+ 1
1
2

1.
1
2
+ −
1
4
2.
7
8
−
3
16
3.
2
3
−
3
4
4. 1
7
5
− −
9
10
5. 3
3
4
− 1
5
8
+ 1
1
2
=
1
4
=
11
16
= −
1
12
=
33
10
𝑜𝑟 3
3
10
=
5
8

Lesson 1.9 a adding and subtracting rational numbers

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Lesson 1.9 a adding and subtracting rational numbers