The document outlines the objectives and methods for teaching addition, subtraction, multiplication, and division of fractions and mixed numbers. It provides detailed instructions for solving problems involving similar and dissimilar fractions, as well as steps for performing operations with mixed numbers. Additionally, it includes exercises for students to practice these concepts.

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