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The numbers six and 19 are in the same proportion as 𝑥 and 22.
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Calculate the value of 𝑥, giving your answer as a top heavy fraction in its simplest form.
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If the two sets of values are in the same proportion, then the ratio between each pair of values is the same.
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The ratio between the first pair of values is six over 19.
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The ratio between the second pair of values is 𝑥 over 22.
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And these two ratios are equal.
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In order to find the value of 𝑥, we need to solve this equation.
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The first step is to multiply both sides of the equation by 22.
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This gives six multiplied by 22 over 19 is equal to 𝑥.
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To work out what six multiplied by 22 is, we can split 22 into 20 and two.
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Six multiplied by 20 is 120.
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And six multiplied by two is 12.
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The sum of these two values is 132.
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We have then that 132 over 19 is equal to 𝑥.
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The question asked for the answer as a top heavy fraction in its simplest form.
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A top heavy fraction is one where the numerator is greater than the denominator.
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And that’s certainly true here.
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132 is greater than 19.
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This fraction is already in its simplest form, as 132 and 19 have no common factors.
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19 is a prime number.
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And it isn’t a factor of 132.
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The value of 𝑥 is 132 over 19.