fundamentals of fraction solving

1. MATHEMATICS
Lecturer: Jewin Joyce C. Laureta

2. FRACTIONS

3. DEFINITION OF TERMS:
• LCD (Least Common Denominator) - the smallest number of all
the common multiples of denominators.
• Numerator - A numerator is the number above the line in a
fraction and it represents how many parts of the whole you have.
• Denominator - The denominator is the number below the line in
a fraction and it represents how many equal parts the whole is
divided into.

4. ADDITION AND SUBTRACTION
OF PROPER FRACTIONS

5. RULES IN ADDING AND SUBTRACTING
FRACTIONS WITH SIMILAR
DENOMINATOR
1. When dealing with fractions with similar denominator, just add/subtract the
numerator and then copy the given denominator.
Examples:
ADDITION:
𝟑
𝟓
+
𝟏
𝟓
=
𝟒
𝟓
SUBTRACTION:
𝟑
𝟓
−
𝟏
𝟓
=
𝟐
𝟓

6. RULES IN ADDING AND SUBTRACTING
FRACTIONS WITH DISSIMILAR
DENOMINATOR
When dealing with fractions that have dissimilar denominator,
1. Find first the LCD
2. Divide the LCD by both the denominators and then multiply each distinct quotients with their
respective numerators.
3. Proceed to addition/subtraction of numerators and just copy the new denominator.
4. Always reduce answers to lowest term.
Examples:
𝟐
𝟑
+
𝟏
𝟗
𝟏
𝟐
−
𝟏
𝟏𝟎

7. MULTIPLICATION OF
FRACTIONS

8. RULES IN MULTIPLYING FRACTIONS
In multiplying fractions, just multiply both the numerators and
both the denominators.
Examples:
𝟐
𝟑
𝒙
𝟏
𝟗
=
𝟐
𝟐𝟕
𝟑
𝟓
𝒙
𝟐
𝟔
=
𝟔
𝟑𝟎
=
𝟏
𝟓

9. DIVISION OF FRACTIONS

10. RULES IN DIVIDING FRACTIONS
Find the reciprocal of the divisor and then proceed to
multiplication.
Examples:
𝟐
𝟑
÷
𝟑
𝟒
=
𝟐
𝟑
×
𝟒
𝟑
=
𝟖
𝟗

11. SAMPLE PROBLEMS:

12. In my fruit basket, there are 13 pieces of fruit, 5 of which
are apples.
How can we express the number of apples as a fraction?
PROBLEM NO. 1

13. 𝟓
𝟏𝟑
• 5 – The number of apples (5) corresponds to the numerator (the number
which expresses the number of parts that we wish to represent).
• 13 – The total number of fruits (13) corresponds to the denominator (the
number which expresses the number of total possible parts).
ANSWER TO PROBLEM NO. 1

14. Maria spent
𝟏
𝟑
of the money her grandparents gave her on an
adventure book. She also spent
𝟏
𝟗
of the money on a bag of
candy.
What fraction of the payment has Maria spent?
PROBLEM NO. 2

15. 𝟒
𝟗
Use the rules in adding fractions with dissimilar denominator.
ANSWER TO PROBLEM NO. 2

16. Rachel took
𝟏
𝟐
hour to paint a table and
𝟏
𝟑
hour to paint a
chair. How much time did she take in all?
PROBLEM NO. 3

17. Time taken to paint a table =
𝟏
𝟐
hour
Time taken to paint a chair =
𝟏
𝟑
hour
Total time taken =
𝟏
𝟐
+
𝟏
𝟑
=
𝟓
𝟔
hour
ANSWER TO PROBLEM NO. 3

18. One half of the students in a school are girls, three fifth
of these girls are studying in lower classes. What fraction
of girls are studying in lower classes?
PROBLEM NO. 4

19. Fraction of girls studying in school =
𝟏
𝟐
Fraction of girls studying in lower classes =
𝟑
𝟓
of
𝟏
𝟐
=
𝟑
𝟓
x
𝟏
𝟐
=
𝟑 (𝟏)
𝟓 (𝟐)
=
𝟑
𝟏𝟎
ANSWER TO PROBLEM NO. 3

20. EXERCISES:

21. Shelly walked
1
3
km. Kelly walked
4
15
km. Who walked
farther? How much farther did one walk than the other?
PROBLEM NO. 1

22. A frog took three jumps. The first jump was
2
3
m long, the second was
5
6
m long and the third was
1
3
m long. How far did the frog jump in all?
PROBLEM NO. 2

23. Sam had 120 teddy bears in his toy store. He sold
2
3
of
them at $12 each. How much did he receive?
PROBLEM NO. 3

24. At the animal shelter
4
6
of the animals are cats. Of the cats
1
2
are male. What fraction of the animals at the shelter are
male cats?
PROBLEM NO. 4

25. Grace thought that a plane journey would take
7
10
hr but the actual
journey took
1
5
hr longer. How long did the actual journey take?
PROBLEM NO. 5

26. Daniel uses
3
4
of a roll of wrapping paper to wrap five
equal-sized presents. What fraction of the roll of
wrapping paper does each present use?
PROBLEM NO. 6

27. Meera uses
4
5
of a bag of chocolate chips to make eight
muffins. What fraction of the bag of chocolate chips does
each muffin contain?
PROBLEM NO. 7