Only to be used for arranged hours
Math 84
Activity # 14
Your Name: __________________
“Addition and Subtraction With Signed Fractions”
Task 1: Addition of signed fractions
Using multiples for the least common denominator.
5 −2
+
18 27
Step 1: If necessary simplify the fractions to only one sign preferably in the
numerator.
Step 2: Find the LCD using multiples.
1,
2,
3,
4,
5
Note: The 3rd multiple is circled.
18, 36, 54, 72, 90…
27, 54, 81 …
Note: The 2nd multiple is circled.
Step 3: Finding equivalent fractions with the LCD.
5
3
×
=
18
3
2
−2
×
=
27
2
15
54
In the multiples of 18 the LCM is the 3rd circle so multiply by
−4
54
In the multiples of 27 the LCM is the
2
2nd circle so multiply by
2
Step 4: Add.
5 −2
+
18 27
Equivalent Fractions
with the LCD
   →
Adding and keeping
15 − 4
15 + (− 4 ) 11
the LCD
+
    →
=
54 54
54
54
Step 5: Write the answer in lowest terms. (Prime factor the numerator and
denominator.)
11
11
=
54 2 ⋅ 3 ⋅ 3 ⋅ 3
No common factors, its already in lowest terms.
3
3
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Task 2: Subtraction of signed fractions
− 7 17
−
14 36
Step 1: Using the rule.
a − b = a + (− b )
− 7 17
− 7 (− 17 )
−
⇒ Using the rule ⇒
+
14
36
14 36
Step 2: Find the LCD using multiples.
1,
2,
3,
4,
5,
6,
7
14, 28, 42, 56, 70, 84, 98, …
36, 72, 108 , 144, 180…
Since it is taking time to find the LCM using this method, let’s try another method.
14
2
7
36
2
2
3
3
LCM 2
2
3
3
7
LCM = LCD = 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 7 = 252
Step 2: Finding the equivalent fractions.
14
2
2
3
3
7
36
2
2
3
3
7
LCM 2
2
3
3
7
Note the missing numbers for 14 are circled, the product of the missing
− 7 18 − 126
× =
14 18
252
numbers is
2 ⋅ 3 ⋅ 3 = 18
− 17 7 − 119
× =
36 7
252
Note the missing number for 36 is circled. With the missing number, 7,
convert to an equivalent fraction.
Only to be used for arranged hours
Step 3: ADD.
− 7 − 17
+
14
36
Equivalent Fractions
the LCD
with

 →
Adding and keeping
− 126 − 119
− 126 + (− 119 ) − 245
+
the
LCD
   →
=
252
252
252
252
Step 5: Write the answer in lowest terms. (Prime factor the numerator and
denominator.)
− 35
5 ⋅ 7 ⋅ 71
− 245
− 35
35
; Note that the answer can be
=
or −
=
252
2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 71
36
36
36
Problem:
or
11 − 14
+
12 16
Step 1: If necessary simplify the fractions to only one sign preferably in the
numerator.
Step 2: Find the LCD.
Step 3: Finding equivalent fractions with the LCD.
Step 4: Add.
Step 5: Write the answer in lowest terms.
35
.
− 36
Only to be used for arranged hours
Exercises: Perform the operation. Write the answer in lowest terms.
1) −
4)
7)
12 − 14
+
60 18
5 14
+
9 21
5 − 11
+
20 16
2)
3 − 15
+
4 38
5) 4
8)
3
1
−2
21
15
20  − 13 
−

52  8 
3)
−2
3
4
−1
15
21
1 16
6) − 12 −
9 12
9) −
11 16
+
12 21