Video: Using Proportions to Find Unknowns

The numbers 6 and 19 are in the same proportion as 𝑥 and 22. Calculate the value of 𝑥, giving your answer as a top heavy fraction in its simplest form.

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Video Transcript

The numbers six and 19 are in the same proportion as 𝑥 and 22. Calculate the value of 𝑥, giving your answer as a top heavy fraction in its simplest form.

If the two sets of values are in the same proportion, then the ratio between each pair of values is the same. The ratio between the first pair of values is six over 19. The ratio between the second pair of values is 𝑥 over 22. And these two ratios are equal.

In order to find the value of 𝑥, we need to solve this equation. The first step is to multiply both sides of the equation by 22. This gives six multiplied by 22 over 19 is equal to 𝑥. To work out what six multiplied by 22 is, we can split 22 into 20 and two. Six multiplied by 20 is 120. And six multiplied by two is 12. The sum of these two values is 132. We have then that 132 over 19 is equal to 𝑥.

The question asked for the answer as a top heavy fraction in its simplest form. A top heavy fraction is one where the numerator is greater than the denominator. And that’s certainly true here. 132 is greater than 19. This fraction is already in its simplest form, as 132 and 19 have no common factors. 19 is a prime number. And it isn’t a factor of 132. The value of 𝑥 is 132 over 19.

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