# Question Video: Using the Properties of Proportion to Find the Value of an Algebraic Fraction Mathematics

If 𝑎/𝑏 = 43/14 and 𝑎/𝑐 = 43/12, find the value of 𝑐/𝑏.

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### Video Transcript

If 𝑎 over 𝑏 is equal to 43 over 14 and 𝑎 over 𝑐 is equal to 43 over 12, find the value of 𝑐 over 𝑏.

This question is actually far simpler than it might first appear. Let’s begin by considering the two fractions we are given. We’re told that 𝑎 over 𝑏 is equal to 43 over 14. 𝑎 over 𝑐 is equal to 43 over 12. In both of these fractions, the numerator 𝑎 is equal to 43. This means that we can write the values of 𝑎, 𝑏, and 𝑐 as a ratio. When 𝑎 is equal to 43, 𝑏, the denominator of the first fraction, is 14. We also know that when 𝑎 is equal to 43, 𝑐 is equal to 12.

We need to focus on these last two terms as we want to find the value of 𝑐 over 𝑏. When 𝑏 is equal to 14, we know that 𝑐 is equal to 12. Therefore, 𝑐 over 𝑏 is equal to 12 over 14. As these two values are even, they’re both divisible by two. The fraction, therefore, simplifies to six over seven or six-sevenths. If 𝑎 over 𝑏 is equal to 43 over 14 and 𝑎 over 𝑐 is equal to 43 over 12, then 𝑐 over 𝑏 is equal to 6 over 7.