SUBTRACTION OF FRACTION
Example #1:
A recipe needs 3/4 teaspoon black pepper and 1/4 red pepper. How
much more black pepper does the recipe need?
This fraction word problem requires subtraction
Solution:
The fact that the problem is asking how much more black pepper the
recipe needs is an indication that 3/4 is bigger than 1/4
However, it does not hurt to check!
3/4 - 1/4 = 2/4 = 1/2
The black pepper is 1/2 of a teaspoon more than the red pepper.
Example #2:
A football player advances 2/3 of a yard. A second player in the same
team advances 5/4 of a yard. How much more yard did the second
player advance?
Again, we need to perform subtraction to solve this problem.
Solution
5/4 - 2/3 = 15/12 - 8/12 = 7/12
6/12 is = 1/2, so 7/12 is just a bit more than half.
So, the second player advanced by about about half of a yard more
Example #3:
John lives 3/8 mile from the Museum of Science. Sylvia leaves 1/4 mile
from the Museum of Science. How much closer is Sylvia from the
museum?
Solution
The fact that the word problem is saying how much closer Sylvia is is
an indication that 1/4 is smaller than 3/8
3/8 - 1/4 = 3/8 - 2/8 = 1/8
Sylvia is closer to the library by 1/8 mile.
You can also say that John is further away by 1/8 mile.
Example #4
changing both fractions to a common denominator (see comments on the
right)
EXAMPLE #5
Changing them to simple fractions we find:
Now, changing both fractions to a common denominator (see comments on
the right)we can solve it as:
This fraction can be further simplified as:
Example: 6
Martha spent
of her allowance on food and shopping. What fraction of her allowance
had she left?
Solution:
She had
of her allowance left.
Example: 7
of a group of children were girls. If there were 24 girls, how many children were there
in the group?
Solution:
3 units = 24
1 unit = 24 3 = 8
5 units = 5 8 = 40
There were 40 children in the group.
Example: 8
Sam had 120 teddy bears in his toy store. He sold
he receive?
Solution:
Step 1: Find the number of teddy bears sold.
He sold 80 teddy bears.
Step 2: Find how much money he received.
80 12 = 960
of them at $12 each. How much did
He received $960.
ADDITION OF FRACTIONS
Example 1: Add fractions with like (same) denominators
1
____
Add the fractions
4
Solution to example 1:
2
+
____
When the fractions have the same denominator, we add the numerators and
keep the same denominator
1
____
2
+
____
3
=
____
Example 2: Add fractions with unlike (different) denominators.
4
____
Add the fractions
+
7
2
____
Solution to example 2:
step 1: Find the lowest common multiple (LCM) of the two denominators.
The LCM of 7 and 5 is 35.
step 2: Write equivalent fractions with a lowest common denominator (LCD)
equal to the LCM.
4
____
7
and
4x5
=
____
7x5
20
=
____
35
2x7
=
____
14
____
____
5x7
35
step 3: Replace the given fractions by their equivalent and add the fractions with
like denominator.
4
2
+
____
20
____
14
____
____
35
35
step 3: Reduce the fraction if possible.
The fraction obtained above cannot be further reduced.
Example 3: Add fractions mixed numbers.
2
Add the mixed numbers
____
3
Solution to example 3:
step 1: Add the whole numbers 3 + 2 = 5
step 2: Find the LCD, equivalent fractions with common denominator and add the
fractions.
2
5
+
____
14
____
____
15
+
21
step 3: Reduce and write the fraction as a mixed number if possible.
29
____
21
8
=
____
21
____
21
step 4: Add the whole number obtained in step 1 and the mixed number obtained
in step 3
8
5
8
=
____
____
21
21
Example 1:
14+14
Step 1. The bottom numbers (the denominators) are already the same. Go straight to step 2.
Step 2. Add the top numbers and put the answer over the same denominator:
14+14=1+14=24
Step 3. Simplify the fraction:
24=12
In picture form it looks like this:
14
14
24
... and do you see how 2 4 is simpler as 1 2 ? (see Equivalent Fractions.)
Example 2:
13+16
Step 1: The bottom numbers are different. See how the slices are different sizes?
12
13
16
We need to make them the same before we can continue, because we can't add them like that.
The number "6" is twice as big as "3", so to make the bottom numbers the same we can multiply
the top and bottom of the first fraction by 2, like this:
2
13
26
Important: you multiply both top and bottom by the same amount,
to keep the value of the fraction the same
Now the fractions have the same bottom number ("6"), and our question looks like this:
26
16
The bottom numbers are now the same, so we can go to step 2.
Step 2: Add the top numbers and put them over the same denominator:
26+16=2+16=36
In picture form it looks like this:
26
16
36
Step 3: Simplify the fraction:
36=12
In picture form the whole answer looks like this:
26
16
36
12
MULTIPLICATION OF FRACTIONS
Problem 1: Reduce the fraction
Answer. Rewrite the fraction with the numerator and the denominator factored and then locate
the fraction within the mix that has a value of 1.
The fraction
can be written as
The fraction
is equivalent to the fraction .
Problem 2: Multiply
and reduce the answer.
Answer. Multiply the numerators and multiply the denominators, but leave them in factored
form. Then reduce the fraction by factoring the numerator and the denominator and located the
fraction within the mix that has a value of 1. See the following steps:
The answer to the problem is
Problem 3: Multiply
and reduce the answer.
Answer. You cannot work this problem because the fraction is undefined. If one part of a
problem is undefined, the entire problem is undefined. You cannot work it; there is no answer.
Problem 4: Multiply
and reduce the answer.
Answer. Multiply the numerators and multiply the denominators and keep the results in factored
form. Look for the fraction in the mix that has a value of 1. See the following steps:
The answer to the problem is
Problem 5: Multiply
and reduce the answer.
Answer. The fraction has a value of zero because the numerator is zero. Since zero times any
number equals zero, then the answer is 0.
Problem 6: Multiply
and reduce the answer.
Answer. Multiply the numerators and multiply the denominators, but leave them in factored
form
. Then reduce the answer by factoring the numerator and the
denominator and locate the fraction within the mix that has(have) a value of 1.
The answer to the problem is
Problem 7: Multiply
and reduce the answer.
Answer. Multiply the numerators and multiply the denominators, but leave them in factored
form
Then reduce the fraction by factoring the numerator and the denominator and located the fraction
within the mix that has a value of 1. The fraction
can be written as
This can be reduced further to
The fraction
cannot be reduced further because the numerator and denominator do not
share any common factors. Therefore the answer is
DIVISION OF FRACTIONS
Example 3
Find 1
Solution:
1
2
2
1 5
=
x
5
2 2
1x5
5
=
2x2
4
=1
Change the sign to x.
Invert (turn upside down) the divisor.
Multiply the numerators.
Multiply the denominators.
1
4
Change the result to a mixed fraction.
Example 4
Find 2
2
3
Solution:
2 2 3
= x
3 1 2
Write 2 as
2
, invert the divisor and change the sign to x.
1
2x3
6
=
1x2
2
Multiply the numerators.
Multiply the denominators.
3
=3
1
Simplify the result.
Example 5
Find
3
8
Solution:
3
8
6=
3
8
6
1
3 1
x
8 6
3x1
1x1
1
=
=
8x6
8 x 2 16
Write 6 as
6
.
1
Invert the divisor and change the sign to x.
Multiply the numerators and the denominators.
Simplify before multiplying (divide 3 and 6 by 3).
Example 6
Find 2
1
2
1
2
1 5
=
10 2
=2
1
10
1
= x0
2 11
5
11
10
Convert mixed fractions to
improper fractions.
Invert the divisor and change the sign to x
5 x 10
5x5
=
2 x 11
1 x11
Simplify before multiplying
(divide 10 and 2 by 2)
25
3
= 2
11
11
Change the result to a mixed fraction.
