This document provides an overview of fractions including: - Defining fractions as parts of a whole and representing them as a/b - Explaining equivalent fractions and how to simplify fractions by dividing the numerator and denominator by their greatest common factor - Describing the different types of fractions such as proper, improper, and mixed fractions - Covering the key operations of adding, subtracting, multiplying, and dividing fractions including converting fractions to have a common denominator when needed - Providing examples for simplifying, converting between fraction types, and performing the different fraction operations

1. Chapter I
Algebra Review
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2. Chapter I
Algebra Review
1. The Real Number System
2. Sets
3. Interval Notation
4. Integer Exponents
5. Fractions, Decimals and Percentages
6. Ratios and Proportions
7. Simple and Compound Interest
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3. 5.1 SIMPLIFICATION OF FRACTIONS
5.2 TYPES OF FRACTIONS
5.3 FRACTION OPERATIONS
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4. Fractions
• Definition 5.1:
A fraction is basically a part of an entire thing. It is not a
whole number, but a part of something.
Fractions are Rational numbers, written as a/b.
For example:
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5. Activity
• Write the fraction of the yellow squares below, and then write
the fraction of the red squares.
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6. Equivalent Fractions
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7. Equivalent Fractions
• Example.1 Example.2
•
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8. Simplifying Fractions
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9. 5.1 SIMPLIFICATION OF FRACTIONS
• To simplify a fraction, divide the numerator and the
denominator by the greatest number that both the numbers
can be divided by.
Divide the numerator and the denominator by 4
The numerator and denominator both can be
divided by the number 4.
• When you simplify a fraction, keep dividing the numerator and
the denominator until you cannot go any further, making the
fraction as simple as possible.
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10. Example:1
Figure 1
• In the first picture of figure 1, the fraction of the pizza that is
eaten is
1
6
. This is because there are six slices of pizza and one
slice of pizza has been eaten out of 6 slices of pizzas.
• In the second picture of figure 1, the fraction of the eaten
pizza is
2
6
because two slices of pizzas have been taken away
out of 6 different slices of pizzas. The fraction
2
6
can be
simplified and written as
1
3
.
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11. Example :2
• If you have the fraction
24
108
You can keep dividing the numerator and the
denominator by 2 to get
2
9
.
• If you have the fraction
8
12
You can divide the numerator and the denominator by 4
to get
2
3
.
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12. Questions for you -Simplify:
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13. 5.2 Types of Fractions
• Proper and Improper
• Fraction Fraction
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14. Mixed Fractions
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15. Mixed Fractions
•
EXAMPLES:
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16. Example: 3
Write as fraction form
•1.
•2.
•3.
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17. Qs: SHOW THAT-
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18. 5.3 FRACTION OPERATIONS
• Rule for Multiplying Fractions
To multiply two different fractions, you can simply
multiply the two numerators together, and then multiply the
denominators together. After that, simplify the fraction if
needed.
•
𝑎
𝑏
×
𝑐
𝑑
=
𝑎×𝑐
𝑏×𝑑
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19. 5.3 FRACTION OPERATIONS
• Rule for Dividing Fractions
A reciprocal of a fraction is basically when you flip the fraction
around. The numerator becomes the denominator, and the
denominator becomes the numerator. For example, the reciprocal of
2
3
would be
3
2
.
• Dividing two fractions is also quite easy. To divide two fractions, take
the reciprocal of the second fraction and multiply it with the first
fraction.
• For example:
To divide
3
5
by
2
3
,
First find the reciprocal of the second fraction. The reciprocal of
2
3
is
3
2
.
Now multiply
3
5
×
3
2
=
9
10
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20. Activity
• Perform the operations in simplest form :
•
8
3
÷
2
3
=
•
6
4
×
5
7
=
•
3
4
×
2
11
=
•
5
7
÷
4
2
=
•
3
5
÷
2
9
=
•
3
2
×
2
13
=
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21. 5.3 Addition and Subtraction
of Fractions
• In order to add or subtract two different fractions, the
denominators of both the fractions must be the same.
1
3
+
2
3
=
1 + 2
3
=
3
3
• The fraction can be simplified to 1, so when you add both the
fractions, the answer is 1.
• However, if the denominators are not the same, then you
have to convert the fraction into its equivalent form by finding
the Least Common Denominator (LCD). Once you find the LCD,
you can simply add/subtract the two fractions
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22. 5.3 ADDING Fractions
•
2
5
+
1
2
First of all, find the LCD of the two
denominators.
• The LCD is 10, because 10 is a least common factor of both 5
and 2. So turn both denominators to 10. Note: Whatever you
do the denominator; do the same to the numerator.
•
2×2
5×2
+
1×5
2×5
=
4
10
+
5
10
Now that the denominators are
the same, you can
• simply add both the fractions together.
•
4
10
+
5
10
=
9
10
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23. 5.3 Subtraction of Fractions
• When subtracting two fractions, make sure that the two
fractions have the same denominators. If they don’t have the
same denominators, then again convert the fractions into its
equivalent form by finding the Least Common Denominator.
•
5
8
−
2
8
=
5−2
8
The denominators are the same, so you
=
3
8
can simply subtract the numerators.
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24. 5.3 SUBTRACTING Fractions
•
3
4
−
2
3
The Least Common Denominator is 12, because
it is the least common factor of 4 and 3.
So in order to subtract the two fractions, turn the denominator
to 12, and whatever you do to the denominator, do the same to
the numerator.
•
3×3
3×4
−
2×4
3×4
=
9
12
−
8
12
Now the denominators are the same, you can simply subtract
the numerators.
•
9
12
−
8
12
=
9−8
12
=
1
12
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25. Activity
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26. Activity
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27. Fractions: Summary
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