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Math for Kids23 chapters | 325 lessons

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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.

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?

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** 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** 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.

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.

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

Sometimes a math equation contains fractions but requires decimals for the computation; or the equation contains decimals but requires fractions. In these cases, it is helpful to know how to convert decimals to fractions and fractions to decimals by finding equivalent numbers.

A knowledge of place value enables you to easily find the fraction equivalent for a decimal number.

- In the number 0.3, the 3 is in the tenths place, so the number is read three-tenths. This is equivalent to the fraction 3/10.
- In the number 0.05, the 5 is in the hundredths place, so the number is read five-hundredths. This is equivalent to the fraction 5/100.

The fraction equivalents for other decimals can be found in a similar manner.

To find the decimal equivalent of a fraction, read the fraction line as 'divided by', and divide the numerator by the denominator.

- The fraction 4/5 can be read as four divided by five (4 / 5), which is 0.8
- The fraction 1/4 can be read as one divided by four (1/4), which is 0.25

**Equivalent numbers** represent the same value or amount. You can find equivalent fractions by multiplying both the numerator and denominator by the same number, or by reducing a fraction to its simplest terms. **Equivalent decimals** can be made by adding one or more zeroes onto the end of the number. You can convert decimals to fractions by looking at what place the number is in the decimals, such as tenths or hundredths, and then putting that number over the place number. When converting a fraction to a decimal number, divide the numerator by the denominator.

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52 in chapter 4 of the course:

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Math for Kids23 chapters | 325 lessons

- Subtraction: Lesson for Kids
- Expanded Form: Lesson for Kids
- Logic Problems: Lesson for Kids
- How to Do Long Multiplication: Lesson for Kids
- What is Multiplication? - Lesson for Kids
- Addition: Lesson for Kids
- Multiplication Properties Lesson for Kids
- Math Card Games for Kids
- Telling Time: Activities & Games for Kids
- Telling Time: Lesson for Kids
- Counting Money: Lesson for Kids
- Telling Time to the Minute: Lesson for Kids
- Divisibility Rules for 10: Lesson for Kids
- Divisibility Rules for 2: Lesson for Kids
- Divisibility Rules for 5: Lesson for Kids
- Division Lesson for Kids: Definition & Method
- Long Division Steps: Lesson for Kids
- Estimation: Lesson for Kids
- Lattice Method of Multiplication
- What Are Different Ways to Multiply? 3:52
- Different Ways to Divide
- What is a Theorem? - Definition & Examples 3:11
- What is Subtraction with Regrouping?
- How to Divide a Whole Number by a Decimal
- What is Addition With Regrouping?
- Finding the Missing Addend
- Metric System vs. Imperial System
- History of the Metric System: Lesson for Kids
- How Money is Made: Lesson for Kids
- What is the Chinese Multiplication Method?
- The Column Addition Method
- 4 Digit Subtraction with Regrouping
- How to Multiply Using Expanded Form 3:52
- How to Write Numbers in Expanded Form 3:58
- Famous Mathematicians: Lesson for Kids
- How to Write Decimals in Expanded Form 3:30
- Length Lesson for Kids: Definition & Measurement
- 4 Digit Addition with Regrouping
- Expanded Notation Method for Division
- Expanded Notation Method for Multiplication 3:23
- Multiplication & Division Fact Families
- Addition & Subtraction Fact Families
- 4 Digit by 1 Digit Multiplication
- Metric Conversions: Lesson for Kids
- How to Divide by Double Digit Numbers
- Two-Step Math Word Problems 4:03
- How to Borrow in Math
- Math Word Problems: Lesson for Kids
- How to Learn Times Tables
- The Box Method for Multiplication 2:29
- 4 Digit by 2 Digit Multiplication
- What Does Equivalent Mean in Math? 4:13
- Go to Math Basics for Elementary School

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