Equivalent FractionsThey can be defined as fractions that can have different numerators and denominators but represent the same value. For example, 9/12 and 6/8 are equivalent fractions because they both simplify to 3/4.
All equivalent fractions, in their simplest form, reduce to the same fraction, as can be seen in the example above. Explore the given lesson to get a better idea of how to find equivalent fractions and how to check if the given fractions are equivalent.
| 1. | What are equivalent fractions? |
| 2. | How do you find equivalent fractions? |
| 3. | How do you know if two fractions are equivalent? |
| 4. | Table of Equivalent Fractions |
| 5. | Frequently asked questions about equivalent fractions |
What are equivalent fractions?
Two or morefractionsThey are said to be equivalent if, in simplified terms, they correspond to the same fraction. For example, the equivalent fractions of 1/5 are 5/25, 6/30, and 4/20, which when simplified result in the same fraction, which is 1/5.
Equivalent Fractions Definition
Equivalent FractionsThey are defined as fractions that have the same value regardless of the numerator and denominator. For example, both 6/12 and 4/8 are simplified 1/2, meaning they are inherently equivalent.
Examples of equivalent fractions
Here are some examples of equivalent fractions.
Example:1/2, 2/4, 3/6, and 4/8 are equivalent fractions. Let's see how their values are the same. We will represent each of these fractions ascircleswith hatched parts. It can be seen that the shaded parts in all figures represent the same part when viewed as a whole.
Here we can see that the amount of shaded fraction is the same in all circles. Therefore 1/2, 2/4, 3/6 and 4/8 are equivalent fractions.
How do you find equivalent fractions?
Equivalent fractions can be written by multiplying or dividing bothcounterand the denominator by the same number. Therefore, simplified, these fractions reduce to the same number. Let's understand the two ways we can form equivalent fractions:
- Multiply the numerator and denominator by the same number.
- Divide the numerator and denominator by the same number.
Multiply the numerator and denominator by the same number
To find equivalent fractions for a given fraction, multiply the numerator and denominator by the same number. For example, to find an equivalent fraction of 3/4, multiply the numerator 3 and the denominator 4 by the same number, say 2. Therefore, 6/8 is an equivalent fraction of 3/4. We can find other equivalent fractions by multiplying the numerator and denominator of the given fraction by the sameNumber.
- 3/4= \(\dfrac{3 \times 3}{4 \times 3}\) =9/12
- 3/4=\(\dfrac{3 \times 4}{4 \times 4}\) =12/16
- 3/4=\(\dfrac{3 \times 5}{4 \times 5}\) =15/20
So the equivalent fractions of 3/4 are 6/8, 9/12, 12/16, and 15/20.
Divide the numerator and denominator by the same number
To find equivalent fractions for a given fraction, divide the numerator and denominator by the same number. For example, to find an equivalent fraction of 72/108, we will first find its common onefactors. We know that 2 is a common factor of 72 and 108. Therefore, an equivalent fraction of 72/108 can be found by dividing the numerator and denominator by 2. Therefore 36/54 is an equivalent fraction of 72/108. Let's see how the fraction is further simplified:
- 2 is a common factor of 36 and 54. Thus 36/54= \(\dfrac{36 \div 2}{54 \div 2}\)= 18/27
- Again, 3 is a common divisor of 18 and 27. Therefore, 18/27= \(\dfrac{18 \div 3}{27 \div 3}\)= 6/9
- Again, 3 is a common factor of 6 and 9. Therefore, 6/9=\(\dfrac{6 \div 3}{9 \div 3}\)= 2/3
Hence some equivalent fractions of 72/108 are 36/54, 18/27, 6/9 and 2/3. Here 2/3 is the simplified form of 72/108 since there is no common divisor (other than 1) of 2 and 3.
How do you know if two fractions are equivalent?
We need to simplify the given fractions to find out if they are equivalent or not. The simplification to get equivalent numbers can be done to the point where both the numerator and denominator must still be presentwhole numbers. There are several methods to determine if certain fractions are equivalent. Some of these are the following:
- equating the denominators.
- Find the decimal form of both fractions.
- method of cross multiplication.
- visual method.
Using each of these methods, let's determine if 2/6 and 3/9 are equivalent fractions.
equating the denominators
The denominators of the fractions 2/6 and 3/9 are 6 and 9. TheLeast common multiple (mcm)the denominator of 6 and 9 is 18. Let's make the denominators of both fractions equal to 18 by multiplying them by appropriate numbers.
- 2/6=\(\dfrac{2\times 3}{6\times 3}\)= 6/18
- 3/9=\(\dfrac{3 \times 2}{9 \times 2}\)= 6/18
We can see that both fractions correspond to the same fraction 6/18. Therefore the given fractions are equivalent.
Use:If the fractions are NOT equivalent, we can check the larger or smaller fraction by looking at the numerator of the two resulting fractions. Therefore, this method can also be usedcompare fractions.
Find the decimal form of both fractions
Let's find themDecimalForm the fractions 2/6 and 3/9 to see if they add up.
- 2/6= 0,3333333...
- 3/9= 0,3333333...
The decimal values of both fractions are equal and therefore they are equivalent.
cross multiplication method
To determine if 2/6 and 3/9 are equivalent,multiply crossthem. If both products are equal, the fractions are equivalent.
Since both products here are 18, the given fractions are called equivalent fractions.
visual method
Let's visualize the fractions 2/6 and 3/9 as identicalto formand check that the shaded parts of both are the same.
We can see that the shaded parts of both circles represent the same value. In other words, the shaded parts in both figures can be seen to represent the same part when viewed as a whole. Therefore the given fractions are equivalent.
Table of Equivalent Fractions
Graphs and tables are often used to better illustrate concepts because they serve as a useful reference for calculations and are easier to understand. Anchor charts and tables, like the one below, make it easier for students to understand equivalent fractions. Let's use the table below to find the equivalent fractions of 1/4.
From this table we can see that the equivalent fractions of 1/4 are: 2/8, 3/12, 4/16,...
Tips on Equivalent Fractions
- Two fractions are said to be equivalent if their values (decimal value/graph value) are equal.
- Usually we multiply the numerator and denominator of a fraction by the same number to get the equivalent fraction.
- The "cross multiplication method" is used to determine whether two fractions are equivalent or not.
- "Make denominators equal" is another way to determine if two or more fractions are equal.
☛ Related items
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Frequently asked questions about equivalent fractions
What are Equivalent Fractions in Mathematics
Two or more fractions are saidequivalent fractionsif they are independent of their numerators and have the same valuedenominator. For example, 2/4 and 8/16 are equivalent fractions because they simplify to 1/2.
What are examples of equivalent fractions?
There can be many examples of equivalent fractions, e.g. B. 8/12 and 6/9 are equivalent fractions because they simplify to the same fraction (2/3). Likewise, 4/7 and 28/49 are also equivalent fractions.
How do you find equivalent fractions?
When the given fractions are simplified and reduced to a common fraction, they can be called equivalent fractions. Apart from that, there are several other methods to determine if the given fractions are equivalent or not. Some of these are the following:
- equating the denominators.
- Find the decimal form of both fractions.
- method of cross multiplication.
- visual method.
What does it mean when two fractions are equal?
When two fractions are equivalent, it means they have the same value regardless of their different numerators and denominators. In other words, when simplified, they reduce to the same fraction.
Why are equivalent fractions important?
Equivalent fractions help us add, subtract, multiply, divide and compare fractions, which helps us solve many problems in real time.
What is an equivalent improper fraction?
an equivalentspurious breakmeans an equivalent fraction in an improper form. A fraction is improper if its numerator is greater than its denominator. For example, 3/2 is an improper fraction equal to 9/6.
How do you calculate equivalent fractions?
Any two fractions can be considered equivalent if they have the same value. There are several methods to find out if fractions are equivalent. The basic method is to reduce them. When reduced to the same fraction, they are considered equivalent.
How do you write equivalent fractions?
Equivalent fractions can be written by multiplying or dividing bothcounterand the denominator by the same number. Therefore, simplified, these fractions reduce to the same number. For example, let's write an equivalent fraction for 2/3. We multiply the numerator and denominator by 4 and get (2 × 4)/(3 × 4) = 8/12. Therefore 8/12 and 2/3 are equivalent fractions.
Give 2 fractions that equal 6/8.
To write the fraction that equals 6/8, we multiply the numerator and denominator by 2 to get (6 × 2)/(8 × 2) = 12/16. Therefore 6/8 and 12/16 are equivalent fractions. Now let's get another equivalent fraction for 6/8 by dividing it by a common number, say 2. After dividing the numerator and denominator by 2, we get (6 ÷ 2)/(8 ÷ 2) = 3 /4. Therefore 6/8 and 3/4 are equivalent fractions.
What are the equivalent fractions of 1/4?
To find equivalent fractions of 1/4, we multiply the numerator and denominator by the same number. So we're going to multiply it by 2, which will be, (1 × 2)/(4 × 2) = 2/8. Now to find another fraction equal to 1/4, we multiply by 3. This will be (1 × 3)/(4 × 3) = 3/12. So we get two fractions that equal 1/4, namely 2/8 and 3/12.
Give two fractions equal to 2/3.
To find the equivalent fractions of 2/3, we multiply the numerator and denominator by the same number. So we're going to multiply it by 5, which will be, (2 × 5)/(3 × 5) = 10/15. Now to find another fraction equal to 2/3, we multiply by 6. This will be (2 × 6)/(3 × 6) = 12/18. So we get two equivalent fractions for 2/3, and they are 10/15 and 12/18.