Question Video: Evaluating Algebraic Expressions by Direct Substitution with Fractions Mathematics • 7th Grade

Video Transcript

Evaluate 𝑥 divided by 𝑦 if 𝑥 equals two over nine and 𝑦 equals six over seven.

To answer this question, we can begin by noting that we are asked to find the quotient of two fractions. We can answer this question by recalling that dividing by a fraction is the same as multiplying by its reciprocal. In particular, 𝑎 over 𝑏 divided by 𝑐 over 𝑑 is equal to 𝑎 over 𝑏 times 𝑑 over 𝑐. This is of course provided that we are not dividing by zero.

We want to apply this formula to find 𝑥 divided by 𝑦, that is, two over nine divided by six over seven. We can apply the formula with 𝑎 equal to two, 𝑏 equal to nine, 𝑐 equal to six, and 𝑑 equal to seven. Or we can just take the reciprocal of the fraction we are dividing by to obtain two over nine multiplied by seven over six.

We can now recall that we can multiply fractions together by multiplying their numerators and denominators separately. This gives us two times seven over nine times six. We could evaluate these products. However, we can also note that there is a shared factor of two in the numerator and denominator. Canceling this shared factor gives us one times seven over nine times three. Finally, we can evaluate the products in the numerator and denominator to find that 𝑥 divided by 𝑦 is equal to seven over 27.