What Does Equivalent Mean in Math?

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  • 0:03 Equal Pieces of Cake
  • 0:46 Equivalent Numbers
  • 2:29 Converting Decimals…
  • 3:33 Lesson Summary
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Lesson Transcript
Instructor: Bethany Calderwood

Bethany has taught special education in grades PK-5 and has a master's degree in special education.

Equivalent numbers are used to make different math problems easier to complete. In this lesson, you'll learn the meaning of equivalent numbers, as well as how to find some of your own.

Equal Pieces of Cake

Mom made mini cakes for dessert. She gave Chris one-half of a cake, Leila three-sixths of a cake, and Jim four-eighths of a cake. Chris said it wasn't fair because Jim got four pieces of cake, while he only got one. Leila said it wasn't fair because Chris' half of the cake was bigger than her three pieces. Jim said he thought all their portions were the same. Who was right?

equivalent fractions

Look at this picture. One half, three-sixths, and four-eighths are all fractions that show the same amount of cake! The picture shows that two-fourths, eight-sixteenths, and five-tenths are also equal to the same amount of cake. This is because all of the portions are equivalent fractions.

Equivalent Numbers

Equivalent means equal in value, function, or meaning. In math, equivalent numbers are numbers that are written differently but represent the same amount. In the picture of the boxes, the same amount of each box is colored in, but because each box is divided into a different number of sections, the number is written differently.

Equivalent Fractions

Equivalent fractions can be found by multiplying both the numerator (top number) and denominator (bottom number) by the same number. They can also be found by reducing a fraction to its simplest terms.

In order to add or subtract fractions, they need to have like denominators. That means the fractions must have the same number on the bottom of each fraction. To add or subtract fractions, it's often necessary to use equivalent fractions. Look at this problem.

addition equation

As they stand now, the fractions 1/4 and 1/3 cannot be added, but as equivalent fractions of 3/12 and 4/12, they can be added.

Equivalent Decimals

When you're working with decimals, sometimes it is helpful to add a zero as a placeholder. This is okay if the zero is placed to the right of the decimal point after the last number. A decimal and a zero can also be added after a whole number, which is often done to facilitate long division and multiplication. Here are a few examples of equivalent decimals, or decimals that have the same value:

  • 3.4 = 3.40
  • 5 = 5.0
  • 2.62 = 2.620

These are not equivalent because adding a zero changes the value of the number:

  • 3.4 and 3.04
  • 9.4 and 90.4
  • 4.55 and 4.505

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