Adding and Subtracting Fractions with Sample Questions

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NEO Thu, Jan 27, 2022 10:32 AM UTC

This pdf covers following topics of fractions:
Adding with like denominators
Adding with unlike denominators
Subtracting with like denominators
Subtracting with unlike denominators

1. Adding and Subtracting Fractions
There are four main operations that we can do with numbers: addition (+), subtraction (–),
multiplication (x), and division (÷). You will be assessed on your ability to add and
subtract fractions.
In order to add or subtract, fractions must have common denominators.
ADDING FRACTIONS
1. Adding with Common Denominators
To add fractions, if the denominators are the same, we simply add the
numerators and keep the same denominators.
Add
1 and 5
e.g.
12 12
Since the denominators are common, simply add the numerators. 1 + 5 = 6
12 12 12
Notice that we must reduce the answer, if possible. = 1
2
2. Adding When One Denominator is a Multiple of the Other
2 5
e.g. Add and
9 27
Notice that the denominators are not common. Also notice that 27 is a multiple
of 9 (since 9 x 3 = 27). So, we make the lowest common denominator ( LCD)
27.
2 (x3) = 6
9 27
Therefore: 2 + 5 is the same as 6 + 5
9 27 27 27
Carpentry: Adding and Subtracting Fractions – Study Guide 1FB/2014 Page 1

2. We can now add the top 2 numbers, so the answer is = 11
27
3. Adding Any Fraction
Add 7 and 13
12 15
We must find a common denominator by examining multiples of the
largest denominator. In the example above we find that the LCD = 60.
7 (x5) + 13 (x4) = 35 + 52
12 15 60 60
= 87 Then simplify = 1 9
60 20
When adding mixed numbers, add the whole numbers and the fractions
separately. Find common denominators and add.
Add 1
5 and 2 3
6 8
1 5 ( = 1 20 ) + 2 3 (= 2 9 ) total equals 3 29
6 24 8 24 24
If an improper fraction occurs in the answer, change it to a common
fraction by doing the following.
3 29 = 3 + 1 5 = 4 5
24 24 24
Carpentry: Adding and Subtracting Fractions – Study Guide 1FB/2014 Page 2

3. SUBTRACTING FRACTIONS
1. Common Fractions
As in addition, we must have common denominators in order to subtract.
Find the LCD; change the fractions to equivalent fraction with the LCD as
the denominator. Then subtract the numerators, but keep the same
5 3 2 1
- = or
8 8 8 4
2 3 16 9 7
- = - =
3 8 24 24 24
2. Mixed Numbers
When subtracting whole numbers, subtract the whole numbers, and then subtract
the fractions separately.
5 3 2
3 -1 = 2
9 9 9
However, if the common fraction we are subtracting is smaller than the other
common fraction, we must borrow the number “1” from the large whole number.
2 7 2 9
i.e. 4 =3+ + , or 3
7 7 7 7
2 5 9 5 4
4 - 2 = 3 -2 = 1
7 7 7 7 7
3 2
To subtract 1 from 6 , first change the common fractions to equivalent
4 3
8 9 -
fractions with the LCD. Since is smaller than , borrow from 6.
12 12
2 3 8 9
6 - 1 =6 -1
3 4 12 12
Carpentry: Adding and Subtracting Fractions – Study Guide 1FB/2014 Page 3

4. 8 12 8 20
6 = 5 + = 5
12 12 12 12
20 9 11
5 -1 = 4
12 12 12
ADDING AND SUBTRACTING FRACTIONS WITH FEET AND INCHES
The most important thing to remember when you are working with feet and inches is that they do
NOT follow the decimal system. Your measurements will not be correct if you try to make an
inch into a decimal or vice versa.
There are 12 inches (“) in 1 foot (‘)
You will be asked to calculate measurements in feet and inches; for example, in the practice test,
you were asked to calculate the length of a board that has been cut into 3 pieces. The pieces
3 1 ,6 3 and 7 4 . You are also told that is used up for each saw cut (kerf)
So, you need to calculate:
3 1 +6 3 +7 4 + +
Add the feet first: 3’ + 6’ + 7’ = 16’
Now add the inches: 1” + 3” + 4” = 8”
Now add the fraction of inches: + + + +
We know that we have to make all of these fractions have the same denominator before we can
add them. The only one that is different is . To covert this into sixths, we can multiply the top
and bottom by 2. (x2) =
So, + + + + =
The final answer is 16’ + 8” + ” = 16’ 9 ”
Carpentry: Adding and Subtracting Fractions – Study Guide 1FB/2014 Page 4

5. Practice: 1: Adding Fractions
a) Add the following:
1 2 4 3 4 2
1) + 2) + 3) +
5 5 5 5 9 9
3 3 3 2 1 1 3
4) + + 5) + 6) +
4 4 4 3 9 2 8
1 5 2 4 1 1
7) + 8) + 9) 3 +4
4 16 3 15 2 4
2 1 1 4 3 1
10) 9 + 3 11) 8 + 4 12) 2 +6
3 6 2 5 4 2
1 5 1 3 2 4
13) 4 + 6 14) 6 + 8 15) 7 +
3 6 3 4 3 5
2 1 3
16) 8 + 6 + 1
3 4 8
Practice 2: Subtracting Fractions
a) Subtract the following:
9 1 14 1 5 3
1) - 2) - 3) -
12 8 15 6 6 8
7 2 2 1 1 1
4) - 5) 9 - 6 6) 4 -1
9 3 3 6 2 4
3 5 11 2 1 2
7) - 8) - 9) 6 - 2
4 8 12 3 3 3
1 3 5 6 3 11
10) 13 - 5 11) 5 - 4 12) 4 - 1
4 4 7 7 4 12
Answers on the next page
Carpentry: Adding and Subtracting Fractions – Study Guide 1FB/2014 Page 5

6. Remember that your answers may be slightly different from those given below, because of rounded
decimals and the route you took to reach your answer.
If you find any errors on the study material, please email [email protected]
Practice 1: Adding Fractions
3 7 2 2 9 1 7 7 9 14 3 5
1) 2) or 1 3) 4) or 2 5) 6) 7) 8) 9) 7 10) 12
5 5 5 3 4 4 9 8 16 15 4 6
3 1 1 1 7 7
11) 13 12) 9 13) 11 14) 15 15) 8 16) 16
10 4 6 12 15 24
Practice 2: Subtracting Fractions
5 23 11 1 1 1 1 1 2 1
1) 2) 3) 4) 5) 3 6) 3 7) 8) 9) 3 10) 7
8 30 24 9 2 4 8 4 3 2
6 5
11) 12) 2
7 6
Carpentry: Adding and Subtracting Fractions – Study Guide 1FB/2014 Page 6

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