Which of the following groups of fractions is equivalent to seven over 17?
What are equivalent fractions? Equivalent fractions are created by multiplying or dividing the numerator and the denominator of a fraction by the same amount. Here’s an example. If we take seven over 17 and multiply it by two over two, seven times two equals 14. 17 times two equals 34. And that means 14 over 34 is an equivalent fraction to seven over 17.
We can do the same thing with three. Seven seventeenths times three over three equals 21 over 51. Option b is the only option with two of these equivalent fractions. Option d is flipping the fractions. But 34 over 14 is not the same thing as 14 over 34. 18 over eight is not equivalent to seven over 17. The fraction 18 over eight is an improper fraction. It’s greater than one. And seven over 17 is a proper fraction. And that means it’s less than one.
On option a, they’ve added one to the numerator and a one to the denominator. But doing this does not create equivalent fractions. We can only create equivalent fractions by multiplying or dividing the numerator and the denominator by the same amount.