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Description
Flashcards by Liffey Farrell, updated more than 1 year ago
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Created by Liffey Farrell
almost 7 years ago
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| Question | Answer |
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Using fractions:
Fractions show parts of whole numbers, for example, the fraction 1/4 shows a number that is 1 part out of 4, or a quarter
Image:
Fraction (image/png)
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1/4 is the same as 1 divided by 4 |
| Fractions are one way of showing numbers that are parts of a whole. Other ways are decimals and percentages. You can also convert between fractions, decimals and percentages. Like whole numbers and decimals, fractions can be either positive or negative. | Equivalent fractions: Equivalent fractions are fractions that are worth exactly the same even though they are written differently. 1/4 is worth the same as 2/8 because 2/8 will simplify to 1/4 by dividing by a common factor of 2 |
| Equivalent fractions are made by multiplying or dividing the denominator and numerator of the fraction by the same number. |
For example, to find fractions that are equivalent to 1/3, multiply the numerator and denominator by the same number
Image:
1 Over 3 (image/png)
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| Multiplying or dividing both parts of a fraction by the same number will always create equivalent fractions. There are an infinite amount of equivalent fractions that can be found because there are an infinite amount of numbers to multiply by | Adding and subtracting fractions: If fractions have the same denominator, they can be added (or subtracted) by adding (or subtracting) the numerators. |
| For instance: 2/9 + 3/9 = 5/9 or 6/11 - 4/11 = 2/11 | If two fraction do not have the same denominator, then find a common denominator by making equivalent fractions |
| Example: Work out 4/7 + 1/3 Create a common denominator by looking for the lowest common multiple of 7 and 3. This is 21 (7 x 3 = 21, 3 x 7 = 21) | Create equivalent fractions using 21 as the new common denominator 4/7 = 12/21 1/3 = 7/21 So: 4/7 + 1/3 = 12/21 + 7/21 = 19/21 |
| Multiplying and dividing fractions: - To multiply two fractions together, multiply the numerators together and multiply the denominators together. | Example 1: Work out 3/5 x 2/3 3/5 x 2/3 = 3x2 = 6 5 x 3 = 15 = 6/15 |
| 6/15 can be simplified to 2/5 (take out a common factor of 3) | If the fractions to be multiplied contain mixed numbers, first convert them to improper fractions and then multiply the numerators together and multiply the denominators together |
| Example 2: Work out 2 1/3 x 1 1/2 2 1/3 = 7/3 (2x3+1/3) and 1 1/2 = 3/2 (1x2+1/2) | 2 1/3 x 1 1/2 is the same as 7/3 x 3/2. 7x3 = 21 3x2 = 6 = 21/6 It can be simplified to 7/2 (common factor of 3) and should then be converted to a mixed number. |
| 7/2 = 3 1/2 Divide the numerator by the denominator This fraction cannot be simplified any further, so this is the final answer | Dividing fractions: To divide two fractions multiply the first fraction by the reciprocal of the second fraction. This means simply that the divide sign is swapped for a multiply sign, and the second fraction is flipped upside down. |
| Example: Work out 3/5 / 2/3 This is the same as 3/5 x 3/2 (keep the first fraction the same, change the divide sign t a multiply and write the second fraction as a reciprocal - flip it upside down) | The sum is now: 3/5 x 3/2 = 3 x 3 = 9 5 x 2 = 10 9/10 |
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