fractions dr. farhana shaheen

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Chapter IAlgebra Review

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Chapter I

Algebra Review1. The Real Number System2. Sets3. Interval Notation4. Integer Exponents5. Fractions, Decimals and Percentages6. Ratios and Proportions7. Simple and Compound Interest 2

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5.1 SIMPLIFICATION OF FRACTIONS 5.2 TYPES OF FRACTIONS5.3 FRACTION OPERATIONS

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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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Activity• Write the fraction of the yellow squares below, and then write

the fraction of the red squares.

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Equivalent Fractions

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Equivalent Fractions

• Example.1 Example.2 •

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Simplifying Fractions

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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. 9

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Example:1

Figure 1

• In the first picture of figure 1, the fraction of the pizza that is eaten is . 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 because two slices of pizzas have been taken away out of 6 different slices of pizzas. The fraction can be simplified and written as .

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Example :2• If you have the fraction

You can keep dividing the numerator and the denominator by 2 to get .

• If you have the fraction You can divide the numerator and the denominator by 4

to get .

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Questions for you -Simplify:

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5.2 Types of Fractions• Proper and Improper• Fraction Fraction

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Mixed Fractions

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Mixed Fractions

• EXAMPLES:

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Example: 3Write as fraction form

•1.

•2.

•3. 16

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Qs: SHOW THAT-

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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.

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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 would be .• 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 by , First find the reciprocal of the second fraction. The reciprocal of is . Now multiply

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Activity• Perform the operations in simplest form :

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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.

• 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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5.3 ADDING Fractions• 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.

• Now that the denominators are the same, you can

• simply add both the fractions together.

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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.

• The denominators are the same, so you can simply subtract the numerators.

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5.3 SUBTRACTING Fractions• 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.

Now the denominators are the same, you can simply subtract the numerators.

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Activity

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Activity

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Fractions: Summary

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