Read the following problem: "Find an equivalent fraction for 4/9 with a denominator of 36."
Write an equation with the facts from the word problem, setting the fraction 4/9 equal to a fraction with x as the unknown numerator and 36 as the denominator: 4/9 = x/36.
Cross-multiply the fractions and set the products equal to each other: 144 = 9x.
Divide both sides of the equation by 9 to isolate the variable: 144 ÷ 9 = 16 and 9x ÷ 9 = x. Therefore, x = 16, meaning that the second numerator is 16. The set of equivalent fractions are 4/9 = 16/36. To double check your answer, you know that 9 times 4 equals 36, so if you multiply 4 times 4, you have the product 16, making it a true statement.
Read the following problem: "Find an equivalent fraction for 18/33 with a numerator of 6." Set up an equation with the facts from the word problem: 18/33 = 6/x.
Cross-multiply the fractions and set the products equal to each other: 18x = 198.
Divide both sides of the equation by 18: x = 11. As a result, 18/33 = 6/11.