Finding Equivalent Fractions

What does Equal Equal?

Before students can test to see if two numbers are equivalent, they need to have a firm grasp of what ‘equivalent’ means. Equivalence is different for fractions than it is for whole numbers. Make sure your students update their understanding of the multiplicative identity property of one, first.

Once students understand that multiplying by 3/3 is the same as multiplying by 5/5, you can show your students how to multiply fractions  by one to make a row of equivalent fractions.Take a look at page 15 from A Fresh Look at Equivalent Fractions.

Let your students use the familiar format of a multiplication table to generate equivalent fractions. Explain that fractions equivalent to one are along the top in black. Then along the left side there are unit fractions. The green numbers show the products.

Give your students copies of a blank multiplication table (page 19) and let them get some easy practice multiplying fractions.

Challenge them to prove that the numbers in each row are equivalent to each other. They should be experts at that after having demonstrated the equivalencies between one and all its variations. Let them convince you that 5/10 is equivalent to 7/14, but not too quickly. Remember, the more they explain the more they learn and remember.

Again explore the limits of fractions that are equivalent to one-half. What if the numerator were 1 billion? What if the denominator were 200?

There are different attributions to one of my favorite quotes, it fits into several situations such as this. “Don’t have your students practice until they get it right, have them practice until they cannot get it wrong.”