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1. BUSINESS MATHEMATICS

2. ADDITION, SUBTRACTION, MULTIPLICATION,
DIVISION OF FRACTIONS

3. Lesson Objectives
At the end of the lesson, the students should be able to:
1. add similar and dissimilar fractions, and mixed
numbers;
2. subtract similar and dissimilar fractions, and mixed
numbers;
3. multiply fraction by another fraction, whole number,
and mixed number; and
4. divide fractions by another fraction, whole numbers
by fractions, and mixed numbers by mixed numbers.

4. Addition of Fractions
Similar Fractions
• add the numerators and retain the denominator
• reduce fractions to lowest terms
1
8
+
2
8
+
5
8
=
1 + 2 + 5
8
= 𝟏
2
4
+
3
4
+
1
4
=
2 + 3 + 1
4
=
6
4
= 𝟏
𝟏
𝟐

5. Addition of Fractions
Dissimilar Fractions
• convert dissimilar fractions to similar (using LCD)
• perform addition of similar fractions
5
8
+
1
4
→
5
8
+
2
8
=
𝟕
𝟖
1
2
+
1
3
+
1
4
→
6
12
+
4
12
+
3
12
=
13
12
= 𝟏
𝟏
𝟏𝟐

6. Addition of Fractions
Mixed Numbers
• add the whole numbers, then add fractional parts
2
1
2
+ 5
1
3
= (2+5) +
3
6
+
2
6
= 𝟕
𝟓
𝟔
• or change into improper fractions then add
2
1
2
+ 5
1
3
→
5
2
+
16
3
→
15
6
+
32
6
=
47
6
= 𝟕
𝟓
𝟔

7. Subtraction of Fractions
Similar Fractions
• subtract the numerators and copy the denominator
• reduce fractions to lowest terms
15
16
−
8
16
=
15 − 8
16
=
𝟕
𝟏𝟔
5
8
−
3
8
=
(5 − 3)
8
=
2
8
=
𝟏
𝟒

8. Subtraction of Fractions
Dissimilar Fractions
• convert dissimilar fractions to similar (using LCD)
• perform subtraction of similar fractions
2
3
−
1
4
→
8
12
−
3
12
=
𝟓
𝟏𝟐
5
6
−
1
8
→
20
24
−
3
24
=
𝟏𝟕
𝟐𝟒

9. Subtraction of Fractions
Mixed Numbers
8
2
5
− 3
1
5
= (8 − 3) +
2
5
−
1
5
= 𝟓
𝟏
𝟓
12
2
3
− 8
1
4
→ 12
8
12
− 8
3
12
= 𝟒
𝟓
𝟏𝟐
23
1
8
− 15
3
4
→ 23
1
8
− 15
6
8
→ 22
9
8
− 15
6
8
= 𝟕
𝟑
𝟖

10. Subtraction of Fractions
Mixed Numbers and Whole Numbers
14 − 3
3
4
→ 13
4
4
− 3
3
4
= 𝟏𝟎
𝟏
𝟒
25 − 6
3
8
→ 24
8
8
− 6
3
8
= 𝟏𝟖
𝟓
𝟖
18
2
5
− 7 = 𝟏𝟏
𝟐
𝟓

11. Fraction by Another Fraction
=
1 × 1
2 × 7
=
𝟏
𝟏𝟒
=
𝟏
𝟑𝟔
2
1
1
8
×
4
7
Multiplication of Fractions
5
12
×
2
8
×
4
15
6
1
2
1
3
1

12. Multiplication of Fractions
Fraction by a Whole Number
=
1 × 3
2 × 1
=
3
2
= 𝟏
𝟏
𝟐
=
5 × 3
1 × 1
=
15
1
= 𝟏𝟓
2
4
× 3 →
2
4
×
3
1
2
1
25 ×
3
5
→
25
1
×
3
5
1
5

13. Multiplication of Fractions
Whole Number by a Mixed Number
2 × 3
1
4
→ 2 ×
13
4
=
26
4
= 𝟔
𝟏
𝟐
17 × 5
1
8
→ 17 ×
41
8
=
697
8
= 𝟖𝟕
𝟏
𝟖

14. Multiplication of Fractions
Mixed Number by a Mixed Number
2
3
4
× 1
1
2
→
11
4
×
3
2
=
33
8
= 𝟒
𝟏
𝟖

15. Division of Fractions
Fraction by another Fraction
2
3
÷
3
4
→
2
3
×
4
3
=
𝟖
𝟗
=
12
5
= 𝟐
𝟐
𝟓
12
17
÷
5
17
→
12
17
×
17
5
1
1

16. Division of Fractions
Whole Numbers and Fraction
5 ÷
2
3
→
5
1
×
3
2
=
15
2
= 𝟕
𝟏
𝟐
6 ÷
1
4
→
6
1
×
4
1
=
24
1
= 𝟐𝟒

17. Division of Fractions
Mixed Numbers
• always change mixed numbers to improper
fractions and proceed with division
8
1
4
÷ 2
1
8
→
33
4
÷
17
8
→
33
4
×
8
17
= 𝟑
𝟏𝟓
𝟏𝟕
25
1
5
÷ 5
1
3
→
126
5
÷
16
3
→
126
5
×
3
16
= 𝟒
𝟐𝟗
𝟒𝟎
8
63
1
2

18. Exercises:
Perform the indicated operation.
1.
1
4
+
3
8
+
1
6
−
2
3
2. 8 − 5
1
2
+ 2
2
5
3. 3 ×
6
27
÷
2
23
4.
3
4
× 3 +
5
6
÷
5
6
5.
17
24
×
6
7
+
3
14
÷
3
5