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A ratio is a way of showing proportions of amounts. For example, if there are double the number of green marbles compared with the number of yellow marbles, then we can show this by writing 2:1. This would be read as: 'the ratio of green marbles to yellow marbles is two to one'. Two parts of the marbles are green and one part is yellow, but: what is 'part(s) of' as a fraction? It's easy: 2 + 1 = 3, so 2⁄3 are green, and 1⁄3 is yellow.
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4 + 3 = 7. You DON'T have to know what the total number of items is in order to find the fractional amounts of each type of item
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You need only use the numbers in the numerators to form the ratio: the fractions MUST sum to 1
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1:1 means that half are boys and half are girls because 1 + 1 = 2 ∴ the fractional parts are each one half
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Divide the ratio 4:8 by 4 to give 1:2. This means that there is 1 brown rat for every 2 black rats ∴ there are half as many brown rats = 12. CHECK 12:24 = 1:2 (dividing by 12). Your answer MUST preserve (keep) the same ratio. ALWAYS try to REDUCE your ratios so as to get '1' in one of the terms of the ratio. Incidentally, 12 + 24 = 36 rats in all!
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16:20 = 4:5 (divide by 4), 8:10 = 4:5 (divide by 2), 1:1.25 = 4:5 (multiply by 4) ∴ they all have the same ratio of 4:5. You can also have decimal ratios!
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2:3 = 1:1.5 (dividing by 2). This means that there is 1 blue pen for every 1.5 red pens ∴ there are 1.5 as many red pens as there are blue pens = 1.5 × 20 = 30. CHECK 20:30 = 1:1.5 (dividing by 20). Your answer MUST preserve (keep) the same ratio. ALWAYS try to REDUCE your ratios so as to get a '1' in one of the terms of the ratio. Incidentally, 20 + 30 = 50 pens in all!
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2 + 3 = 5 ∴ the fractional parts are 2⁄5 × 100 = 40 amateur paintings & 3⁄5 × 100 = 60 professional paintings. CHECK 40:60 = 2:3 (dividing by 20). Your answer MUST preserve (keep) the same ratio
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Form the ratio 14:8 = 7:4 which is NOT the same as 4:7. All the others form ratios that can be reduced to 4:7
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8:56 = 1:7 (dividing by 8)
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1.25:4 = 5:16 (multiplying by 4)
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