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Math for Kids23 chapters | 325 lessons

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Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Your number line can actually help you figure out equivalent fractions if you know what steps to take to break up your number line in the right way. Learn how in this how-to lesson.

In this lesson, we'll talk about equivalent fractions and how using a number line can help us find them. Our **equivalent fractions** are different ways to write the same fraction. For example, 1/2 and 2/4 are equivalent fractions. If you simplify 2/4 by dividing both the numerator and denominator by 2, you'll get 1/2, the same as the other one.

- 1/2 = 2/4

Remember, our number line is a line with evenly spaced tick marks that show us our numbers.

To work with equivalent fractions, we begin with one fraction such as 1/2. To find the equivalent fractions, we'll follow these steps.

We'll first need to locate our fraction on the number line. To do this, you'll need to divide the first tick mark into even pieces. If you are looking for the fraction 1/2, you'll need to divide the first tick mark (the space between the number 0 and 1) into two even pieces. If you are looking for 1/3, then you'll need to divide the first tick mark into three even pieces. So, the denominator tells you how many even pieces to divide that first tick mark into and the numerator tells you which of those tick marks your fraction is. Place a small tick mark to mark your dividers.

So, 1/2 has you dividing your first tick mark into two even spaces. You place a small tick mark in the middle of your line between the number 0 and the number 1. The numerator 1 tells you that your fraction is the first of the small tick marks (the only small tick mark in this case).

Now, to find our equivalent fractions, we'll need to divide the divisions we made from step 1 into two even spaces.

So, for your 2/4, you'll be dividing the two divisions you made in step 1 in half. So you'll have four equal spaces between your number 0 and your number 1 now.

To find out what our equivalent fraction is, we'll now need to read our number line.

For your 1/2, you remember that the 1/2 is the middle separation between the number 0 and the number 1. But for this number line, you now have four separations. So this means the denominator is now 4. The middle line between 0 and 1 is the second small tick mark, so the numerator is 2. This means that 1/2 and 2/4 are equivalent fractions.

If you want to find more equivalent fractions, keep repeating steps 2 and 3.

You've found your answer to be 2/4. An equivalent fraction to 1/2 is 2/4.

If you want to find another equivalent fraction, you could follow step 4 and repeat steps 2 and 3 with your number line that already has the four splits between the number 0 and the number 1. This time, you'll divide each of those four spaces into two even spaces. You'll end up with eight even spaces now. This means your denominator is now 8. The numerator that corresponds to the 1/2 location is 4/8. So that means 4/8 is also an equivalent fraction. You can keep repeating steps 2 and 3 to find infinitely more.

- 1/2 = 2/4 = 4/8

You can also stack number lines of equal scale over one another to see the equivalency visually. As you can see above, the equivalent fractions are obvious next to one another.

Let's try another example.

This time, let's start with the fraction 2/3.

To find this fraction, you'll need to separate your first tick mark, the space between the number 0 and the number 1, into three equal spaces. Your 2/3 fraction then is the second small tick mark.

Now, to find the equivalent fractions, you divide each of your newly created divisions into two equal spaces. You now have six even spaces. So your denominator is now 6. Your 2/3 is now 4/6.

So 2/3 and 4/6 are equivalent fractions.

To find more, you would separate each of your six divisions in half again. You now have twelve divisions. Your 2/3 now becomes 8/12. So now you have another equivalent fraction.

- 2/3 = 4/6 = 8/12

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Math for Kids23 chapters | 325 lessons

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- Comparing Fractions: Lesson for Kids
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- Fractions to Decimals: Lesson for Kids
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- Numerator & Denominator Lesson for Kids
- Decimals: Lesson for Kids
- Multiplying Fractions by Whole Numbers: Lesson for Kids 3:04
- How to Simplify Fractions: Lesson for Kids
- Improper Fractions: Lesson for Kids
- What is a Benchmark Fraction on a Number Line? 3:48
- How to Add Mixed Fractions with Different Denominators
- Multiplying Compound Fractions
- Simplifying Compound Fractions
- Dividing Compound Fractions
- Adding Compound Fractions
- Subtracting Compound Fractions
- How to Subtract Fractions with Variables
- Multiplying Fractions with Like Denominators
- Subtracting Fractions with Like Denominators
- Reducing Fractions: Rules & Practice
- Definition of Simplest Form: Lesson for Kids
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- How to Subtract Fractions with Unlike Denominators
- Rules for Subtracting Fractions
- Rules for Multiplying Fractions
- Rules for Dividing Fractions
- Ordering Fractions on a Number Line
- Locating Fractions on a Number Line
- How to Add & Subtract Two Fractions with Like Denominators
- How to Find Equivalent Fractions on a Number Line
- Go to Fractions for Elementary School

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