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Put the ratio five-sixths to 1.5 to three-tenths in its simplest form.
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We recall that a ratio is written in its simplest form when all of our values are integers with no common factor except one.
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We will begin this question by turning the decimal 1.5 into a top-heavy or improper fraction.
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1.5 is the same as one and a half.
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As there are two-halves in a whole, 1.5 is the same as three-halves or three over two.
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This means that we can rewrite the ratio as five-sixths to three-halves to three-tenths.
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We need to ensure that these three values are integers.
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In order to convert them into integers, we need to begin by finding the lowest common denominator.
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This will be the lowest common multiple of six, two, and ten.
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This is equal to 30 as the lowest number in the six, two, and 10 times table is 30.
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We can then multiply each of our three fractions by 30.
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Our first term becomes five-sixths multiplied by 30.
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As 30 divided by six is equal to five, we’re left with five multiplied by five.
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This gives us the integer 25.
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We can repeat this process for the second and third terms in our ratio.
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The second term simplifies to three multiplied by 15.
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This is equal to 45.
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The third term simplifies to three multiplied by three.
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This is equal to nine.
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25, 45, and nine have no common factor apart from one.
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This means that the ratio five-sixths to 1.5 to three-tenths written in its simplest form is 25 to 45 to nine.