# Recognizing Equivalent Fractions Worksheets

Equivalent fractions are values that are the same exact amount or size, but just being expressed differently. In most cases fractions are not stated in their lowest form and a simple reduction always makes the values easier to work with. This skill is something you will use just about every school year it has a wide variety of applications. It will help you solve math operations (add, subtract, multiple, divide) of fractions much quicker. You will find that it applies a great deal with anything that involves measurement. Engineers spend a good part their day recognizing equal fractional values. This series of worksheets and lessons will take students through a series of different strategies and techniques that they can use to identify fractional equivalency in values.

### Aligned Standard: Grade 3 Fractions - 3.NF.3

- Matching Step-by-step Lesson- Change models to fractions and then reduce them to their lowest form. They will come out to be equivalent in this series.
- Guided Lesson - Fill in the missing part of the equivalent values.
- Guided Lesson Explanation - I go through the detail of reducing the fractions to make them equal.
- Practice Worksheet - Find the missing part of the fraction or proportion, based on how you look at it.
- Matching Worksheet - Match the fraction to itself in lowest terms. Just draw a line to complete this.

- Answer Keys - These are for all the unlocked materials above.

### Practice Worksheets

Interpret the pie based fractions and make some of your own values by converting these visuals.

- Practice 1- Name all the fractions and draw line between the values that are equal.
- Practice 2- Fill the missing numbers to create equivalent fractions.
- Practice 3- Complete the values to make them equal. We jump between the numerator and denominator.

### Math Skill Quizzes

Writing fractions in their lowest form and some more coloring for you.

- Quiz 1- Color the diagram to make them equal. You will then create your own equal values.
- Quiz 2- Write an equal fraction to what you are given. Write them in their lowest possible form.

### How to Recognize Equivalent Fractions

In mathematics, equivalent fractions are fractions with the same value, but they do not look similar. More accurately, they are defined as integers with different numerators and denominators that represent the same proportion. Equivalent fractions, when expressed on a number line, represent the same points or distance on it. They produce the same result when reduced to their simplest forms. To recognize equivalent fractions, you must know these two tricks.

Consider this example: 1/2 = 2/4 = 4/8

These fractions are equivalent; however, they use different numbers. But how do you find that out?

## Same Number Rule

The first rule to recognizing an equivalent fraction is to multiply or divide both the numerator and denominator by the same number. If multiplying 1(numerator) and 2 (denominator) of 1/2 gives the fraction 2/4, then these fractions are equivalent. 1 x 2 / 2 x 2 = 2/4.

## Cross Multiply

Another trick is to cross multiply the fractions to find out if they are equivalent or not. Now here, cross-multiplying refers to multiplying one's numerator with the other's denominator. 2 x 8 = 4 x 4 = 16. The fractions are equivalent. Students will be able to use these worksheets to help them learn to identify fractions that are equal.

## Decimal Rule

If you convert each value to decimal, it is quick and easy to see if their values are equal. Just divide the numerator by the denominator. Back to our example: 1/2 = 0.5, 2/4 = 0.5, 4/8 = 0.5. This is a quick and easy way to get the job done but can be cumbersome with larger values.

## Reduce to Lowest Terms

This is usually the first thing I ask students to do. You should always make sure that the values you are working with are in their lowest terms. All the other methods that we have already discussed will work whether the values are in expanded or lowest terms. If we look back at our example, we can see that if we just reduced all those fractions to their lowest terms, we would be done already because they all reduce to 1/2.