Equivalent Fractions Definitions and Examples
Introduction
In mathematical terms, an equivalent fraction is a fraction that represents the same value as another fraction. The two fractions have different denominators and numerators, but they both represent the same proportion of a whole. Here are some examples to help you better understand equivalent fractions.
What are Equivalent Fractions?
Equivalent fractions are fractions that have the same value, even though they may look different. For example, 1/2 is equivalent to 2/4 because both fractions represent the same amount: one-half.
To understand why two fractions can be equivalent, think about a pizza. If you cut a pizza into four equal slices, each slice would be one-fourth of the pizza. But if you cut the pizza into eight equal slices, each slice would be one-eighth of the pizza. So 1/4 and 1/8 are also equivalent fractions and represent the same amount—one-fourth—of the pizza.
It’s easy to create equivalent fractions. To do so, you can either multiply or divide both the numerator and denominator by the same number (but not zero). For example, if we multiply or divide both 1/2 and 2/4 by 2, we get new fractions that are also equivalent: 2/4 and 4/8. We could keep going and multiply or divide both pairs of fractions by 2 again to get 4/8 and 8/16—and so on!
How to Find Equivalent Fractions?
Equivalent fractions are two or more fractions that have the same value, even though they may have different numbers in the numerator and denominator. To find equivalent fractions, you can use a fraction strip or a number line.
To find equivalent fractions using a fraction strip:
1. Find the smallest whole number that is equal to or greater than all of the denominators of the fractions you’re working with. This number is called the least common multiple (LCM).
2. Write down the LCM.
3. Cut out a strip of paper that is as long as the LCM.
4. Label each section of the strip with one of the fractions’ denominators. The length of each section should be proportional to its corresponding denominator. For example, if one fraction has a denominator of 2 and another has a denominator of 4, then label one section “2” and label another section “4.” The section labeled “4” should be twice as long as the section labeled “2.” If necessary, mark off smaller divisions within each section to help you visualize this proportionality better.
5. Find where the numerators meet on the strip. The two or more fractions are equivalent if their numerators are in the same position on the strip relative to their respective denominators (e.g., both on top of their corresponding sections, both in the middle, etc.).
To find equivalent fractions using a number line:
How do you know if Two Fractions are Equivalent?
If two fractions have the same value, regardless of their size or denominators, then they are considered equivalent. For example, 1/2 is equivalent to 2/4 because both fractions represent the same value: one-half. To determine whether two fractions are equivalent, you can use a number of methods, including comparing like terms or converting to decimals.
When you compare like terms, you’re looking at whether the fractions have the same overall value. For example, 3/4 is not equivalent to 6/8 because when you reduce those fractions, 3/4 becomes 3/3 (one whole) while 6/8 becomes 3/4 (still not equal to one whole). To compare like terms, simply reduce each fraction to its lowest form and then compare the resulting numbers. If they’re the same, then the fractions are equivalent.
You can also convert fractions to decimals to see if they’re equal. For example, 1/4 converts to 0.25 while 2/8 converts to 0.25. As you can see, both fractions are equal in value even though their denominators are different. When converting fractions to decimals, simply divide the numerator by the denominator. If the resulting decimal is the same for both fractions, then they are equivalent.
Equivalent Fractions Chart
An equivalent fractions chart is a visual representation of different ways to express the same fraction. For example, the fraction 1/2 can be represented as 2/4, 3/6, 4/8, and so on. Each of these fractions is equal to 1/2, but they each have a different numerator and denominator.
Looking at an equivalent fractions chart can help you to see how different fractions are related to one another. It can also be a helpful tool when you’re trying to simplify a fraction or find an equivalent fraction for a given fraction.
Conclusion
In conclusion, equivalent fractions are a great way to represent fractions that have the same value but are different in terms of numerator and denominator. This concept is useful in many real-world situations, so it’s worth taking the time to understand it fully. We hope that our examples and explanations have helped you to do just that. If you’re still struggling, don’t hesitate to reach out for help from a tutor or friend who understands fractions better than you do.
