This lesson is for third through fifth grade students who have an knowledge of identical fractions making use of models, an understanding of multiplication and division facts, and also of multiplying and also dividing fractions. Student will usage multiplication and division to show equivalent fractions.

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Key Understandings

If you multiply or divide both numerator and denominator by the very same number, the new fraction will be indistinguishable to the initial fraction.


Denominator: The bottom part of a fraction. The denominator to represent the total variety of equal components in the whole or the set.

Numerator: The top component of a fraction. The numerator represents how many pieces of the entirety that room being discussed.

Equivalent Fractions: fountain that reduce to the very same number and also have an same value. They are fractions that name the very same amount in different ways.

Simplifying: reducing to lowest terms.

Lowest terms/Simplest Form: The numerator and also denominator of a fraction in lowest terms have no typical factors except one.



Review vocabulary and also what student know about equivalent fractions. Display models of tantamount fractions and also explain that even though the numerators and denominators in the fractions space different, the fractions stand for the exact same amount, which means they room equivalent.

Use models to display the fractions 1/2 and also 2/4, or attract them for students. Have students point out what castle know around the fractions. Command them to view that there space twice as numerous pieces in the illustration of 2/4 than in the illustration of 1/2, yet they represent the same amount.

Review the numbers that are multiplied by one same the same number. Ask student to provide a few examples the one together a fraction, because that example: 3/3, 4/4, 2/2. Compose 1/2 x 2/2 = 2/4, and show the the numerator and denominator space doubled to present the brand-new fraction. Define that this is another method to uncover equivalent fractions.

Multiply the numerator and denominator by the very same number to discover an indistinguishable fraction. Or, divide the numerator and also denominator through the very same number. It"s vital to create fractions as "stacked", no side-by-side. This will help students as soon as multiplying and dividing.

Show a few examples:

3/12 x 4/4 = 12/48 3/12 (division sign) 3/3 = 1/4 every one of these fractions are equivalent because they name the exact same amount: 1/4

After a few examples, have students think around a dominance for this principle. They should have the ability to tell you the if you main point or division both numerator and denominator by the exact same number, the new portion will be identical to the initial fraction. The just time this won"t work is if students multiply by zero.

Explain that periodically fractions have to be change the name to do them easier to job-related with. Emphasize that the fractions will certainly still same the very same amount, or it is in equivalent, but the numerator and also denominator will be various from the initial fraction.

To simplify fractions, uncover a common factor that will certainly divide evenly right into the numerator and also denominator. Because that example, show the college student this fraction: 12/18

Find the factors of the numerator and also denominator. The determinants of 12 room 2, 3, 4, and 6. The components of 18 space 2, 3, 6, and also 9. The usual factors room 2, 3, and also 6.

To leveling the fraction, divide by 6, because 6 is the greatest usual factor. Display students exactly how to divide the fraction: 12/18 (division sign) 6/6 = 2/3

Explain the a fraction is in simplest form if 1 is the only usual factor of the numerator and also denominator. Have students determine if this portion is in most basic form. 2/3 is the simplest type of 12/18.

In order to mitigate a fraction to its shortest terms, define that students deserve to divide by any type of common factor, and continue till it"s in lowest terms, or they can divide through the greatest typical factor. Because that example, students could divide the fraction 12/18 through 2/2, and then divide by 3/3 to present the portion in easiest form. Or students might divide 12/18 through 6/6 and also show the portion 2/3 in one step.

Discuss the an interpretation of the word equivalent and what makes fractions equivalent. Have students write in your journals exactly how they can uncover equivalent fractions. Have them answer the question: exactly how do you understand when you have a portion in most basic form?

Guided practice

Have students exercise finding tantamount fractions both by multiplying the numerators and denominators and also by dividing the numerators and denominators by the greatest common factors. Administer students with number of fractions and ask them to find equivalent fountain by multiplying. Some examples could be 2/3,1/4, or 3/5.

Have students additionally simplify fractions. Some examples could be 6/30 = 1/5, 4/6 = 2/3, or 15/20 = 3/4.

Another method to have students exercise would it is in to produce flash cards of identical fractions, and play a video game such together concentration, where students find and also match the equivalent fractions.

Sharing concepts

Discuss what students learned when finding tantamount fractions. Have actually them share tactics they used.

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Independent exercise

Give students several fractions and also have them discover equivalent fractions utilizing both multiplication and division.