Download operations on fractions

Operations on Fractions
Objectives:
…to add, subtract, multiply, and divide fractions.
Assessment Anchor:
7.A.3.2 – Compute accurately with and without use of a calculator
NOTES
To add or subtract fractions:
1. You MUST have a COMMON DENOMINATOR!!!!
a. If denominator is already the same, continue to step 2.
b. If denominator is different:
1. Find a common denominator (LCM).
2. Write equivalent fractions using your common
denominator.
2. Add or subtract the numerators.
a. If you are able to subtract, continue to step 3.
b. If you cannot subtract, you must BORROW!
1. Take one away from the whole number.
2. Add the numerator and denominator together to get a
NEW numerator.
3. The denominator remains the same.
3. Add or subtract the whole numbers.
4. The denominator remains the same.
***Special Situation: If the fraction part of a mixed number is improper, you
must change that improper fraction to a mixed number and add the original
whole number to it.
The most important words above are:
COMMON DENOMINATOR
Operations on Fractions
EXAMPLES
1)
3
1
2
+1
5
3
……original problem with unlike denominators
3
5
6
+1
15
15
……equivalent fractions with like denominators
4
2)
3)
11
15
……sum of original numbers
3
11
3
–1
12
4
…… original problem with unlike denominators
3
11
9
–1
12
12
…… equivalent fractions with like denominators
2
2
1
= 2
12
6
……difference of original numbers (simplified)
93 + 35
4
6
4)
55 – 31
9
6
“Getting the LCD (least common
denominator is great…but any common
denominator will do just fine!”
Operations on Fractions
MORE EXAMPLES (with borrowing)
5)
7
3
3
–1
8
4
……original problem with unlike denominators
7
3
6
–1
8
8
……equivalent fractions with like denominators
6
11
6
–1
8
8
……borrowing procedure
5
6)
5
8
……difference of original numbers
5
1
1
–4
10
4
……original problem with unlike denominators
5
2
5
–4
20
20
……equivalent fractions with like denominators
4
22
5
–4
20
20
……borrowing procedure
17
20
7)
…… difference of original numbers
13 2 – 4 1
7
2
8)
9
5
12
– 17
9
Operations on Fractions
Vocabulary alert!!
RECIPROCAL – a number that can be multiplied by
another number to make 1
MORE NOTES
To multiply or divide fractions:
1. Rewrite any whole numbers OR mixed numbers as improper
fractions.
2. IF multiplication, continue to step 3…IF division make the following
changes first:
a. Keep the first fraction the same.
b. Change the division symbol to a multiplication symbol.
c. Write the reciprocal of the second fraction.
3. Multiply the numerators.
4. Multiply the denominators.
5. Simplify final answer if possible
***Special Situation: When you have a multiplication symbol between two
fractions, you are allowed to REDUCE or CANCEL common factors before
multiplying the numerators and denominators.
EXAMPLES
9)
6
7
× 41
6
7
×
……original problem
5
126
35
21
5
=
……change to improper fraction
18
5
or 3 3
5
……multiply numerators and denominators
***SHOW CANCELLING OPTION!!!
Operations on Fractions
10)
51 × 11
……original problem
26
5
……change to improper fraction
5
4
×
130
20
5
4
13
2
=
or 6 1
2
……multiply numerators and denominators
***SHOW CANCELLING OPTION!!!
11)
11 ÷ 12
……original problem (DIVISION!)
4
3
÷
11
9
……change to improper fraction
4
3
×
9
11
……multiply by the reciprocal!!!
3
36
33
9
12
11
=
or 1 1
11
……multiply numerators and denominators
***SHOW CANCELLING OPTION!!!
12)
62 ÷4
……original problem (DIVISION!)
20
3
÷
4
1
……change to improper fraction
20
3
×
1
4
……multiply by the reciprocal!!!
3
20
12
=
5
3
or 1 2
3
……multiply numerators and denominators
***SHOW CANCELLING OPTION!!!
Operations on Fractions
13)
41 × 31
14)
71 × 31
15)
81 ÷ 62
16)
1 11 ÷ 16
4
3
3
3
2
13
7