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# Fractions1

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### Fractions1

1. 1. Outline What is a fraction? Addition and Subtraction Multiplication Division An Introduction to fractions January 21, 2010 An Introduction to fractions
2. 2. Outline What is a fraction? Addition and Subtraction Multiplication Division What is a fraction? Whole Numbers Halves, Quarters and Eighths Addition and Subtraction Multiplication Division An Introduction to fractions
3. 3. Outline What is a fraction? Whole Numbers Addition and Subtraction Halves, Quarters and Eighths Multiplication Division Whole Numbers - Integers Whole numbers are numbers that have no decimal points. These numbers can also be called integers. The integers are the set of all whole numbers (both positive and negative. i.e. An Introduction to fractions
4. 4. Outline What is a fraction? Whole Numbers Addition and Subtraction Halves, Quarters and Eighths Multiplication Division Whole Numbers - Integers Whole numbers are numbers that have no decimal points. These numbers can also be called integers. The integers are the set of all whole numbers (both positive and negative. i.e. ..., −3, −2, −1, 0, 1, 2, 3, ... An Introduction to fractions
5. 5. Outline What is a fraction? Whole Numbers Addition and Subtraction Halves, Quarters and Eighths Multiplication Division Whole Numbers - Integers Whole numbers are numbers that have no decimal points. These numbers can also be called integers. The integers are the set of all whole numbers (both positive and negative. i.e. ..., −3, −2, −1, 0, 1, 2, 3, ... At this stage we will deal only with the positive integers which are sometimes called the Naturals. i.e. An Introduction to fractions
6. 6. Outline What is a fraction? Whole Numbers Addition and Subtraction Halves, Quarters and Eighths Multiplication Division Whole Numbers - Integers Whole numbers are numbers that have no decimal points. These numbers can also be called integers. The integers are the set of all whole numbers (both positive and negative. i.e. ..., −3, −2, −1, 0, 1, 2, 3, ... At this stage we will deal only with the positive integers which are sometimes called the Naturals. i.e. 0, 1, 2, 3, ... An Introduction to fractions
7. 7. Outline What is a fraction? Whole Numbers Addition and Subtraction Halves, Quarters and Eighths Multiplication Division Representing whole numbers and fractions We will represent whole numbers by circles, and fractions by parts of those circles. i.e. Figure: Represents the number ’3’ and Figure: Represents the number ’2 1 ’ 2 An Introduction to fractions
8. 8. Outline What is a fraction? Whole Numbers Addition and Subtraction Halves, Quarters and Eighths Multiplication Division Halves, Quaters and Eighths We can represent two diﬀerent fractions by two diﬀerent circles. Two fractions are equal if the shaded area in each circle is the same. i.e. 3 6 Figure: 4 and 8 While the two fractions contain diﬀerent numbers, they must actually be equal. An Introduction to fractions
9. 9. Outline What is a fraction? Addition and Subtraction Multiplication Division Common Denominators Before we can add or subtract any fractions, we must always ensure that both fractions have common denominators. (The denominator is the number on the bottom of a fraction) Example 1/2 + 1/8 In this example we must make sure that the number on the bottom of both fractions is the same. The easiest way to do this is to change the 1/2 into 4/8. Recall that these two fractions are in fact equal. = 4/8 + 1/8 Now we simply add the numerators (top number) of both fractions. = 5/8 Try a few examples yourself. An Introduction to fractions
10. 10. Outline What is a fraction? Addition and Subtraction Multiplication Division Questions Try these questions yourself: 1/4 + 3/8 = 1/2 + 3/8 = 1/4 + 1/8 = 3/4 + 5/8 = 2/3 + 3/4 = An Introduction to fractions
11. 11. Outline What is a fraction? Addition and Subtraction Multiplication Division Multiplication of fractions Multiplying fractions is much easier than adding or subtracting. All you need to do to multiply two fractions is multiply the numerators, and the denominators. i.e. Just multiply straight across. Example 2 3 5 × 4 = 2×3 5×4 = 6 20 = 3 10 We must be careful to always reduce a fraction to it’s lowest possible form. An Introduction to fractions
12. 12. Outline What is a fraction? Addition and Subtraction Multiplication Division Questions 3 2 8 × 5 = 2 6 9 × 7 = 5 8 3 × 7 = An Introduction to fractions
13. 13. Outline What is a fraction? Addition and Subtraction Multiplication Division Division Dividing fractions is very similar to multiplication, however we must do one small step to begin with. We start by saying that all whole numbers can be written as a fraction. i.e. 3 can be written as 3 . Now if we divide a number by say three, it is the same as 1 taking one third of the original number. Example 12 ÷ 3 = 4 1 and 12 × 1 = 4 3 From this example it seems that dividing by any fraction is the same as multiplying by the inverse (upside down) fraction. This is in fact the case. If you ever need to divide a fraction, simply change the divide to a multiply andAn Introductionsecond fraction upside turn the to fractions
14. 14. Outline What is a fraction? Addition and Subtraction Multiplication Division Questions 4 5 ÷27 7 3 ÷45 12 5 ÷ 17 4 An Introduction to fractions