Equivalent Fractions
Equivalent fractions are the fractions having the same value. Same fraction can be represented in many ways. Let us take the following example.
In picture (i) the shaded part is represented by fraction \(\frac{1}{2}\).
The shaded part in picture (ii) is represented by fraction \(\frac{2}{4}\). In picture (iii) the same part is represented by fraction \(\frac{4}{8}\). SO, the fraction represented by these shaded portions are equal. Such fractions are called equivalent fractions.
We say that \(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{4}{8}\)
Hence, for a given fraction there can be many equivalent fractions.
Making Equivalent Fractions:
We have seen in the above example that \(\frac{1}{2}\), \(\frac{2}{4}\) and \(\frac{4}{8}\) are equivalent fractions.
Therefore, \(\frac{1}{2}\) can be written as \(\frac{1}{2}\) = \(\frac{1 × 2}{2 × 2}\) = \(\frac{1 × 3}{2 × 3}\) = \(\frac{1 × 4}{2 × 4}\) and so on.
Hence, an equivalent fraction of any given fraction can be obtained by multiplying its numerator and denominator by the same number.
Same way, when the numerator and denominator of a fraction are divided by the same number, we get its equivalent fractions.
\(\frac{1}{2}\) = \(\frac{1 ÷ 1}{2 ÷ 1}\) = \(\frac{2}{4}\) = \(\frac{2 ÷ 2}{4 ÷ 2}\) = \(\frac{3}{6}\) = \(\frac{3 ÷ 3}{6 ÷ 3}\)
We have,
2/4 = (1 × 2)/(2 × 2)
3/6 = (1 × 3)/(2 × 3)
4/8 = (1 × 4)/(2 × 4)
We observe that
2/
4,
3/
6 and
4/
8 are obtained by multiplying the numerator and denominator of
1/
2 by 2, 3 and 4 respectively.
Thus, an equivalent fraction of a given fraction can be obtained by multiplying its numerator and denominator by the same number (other than zero).
2/4 = (2÷ 2)/(4 ÷ 2) = 1/2
3/6 = (3÷ 3)/(6 ÷ 3) = 1/2
4/8 = (4 ÷ 4)/(8 ÷ 4) = 1/2
We observe that if we divide the numerators and denominators of
2/
4,
3/
6 and
4/
8 each by their common factor 2, we get an equivalent fraction
1/
2.
Thus, an equivalent fraction of a given fraction can be obtained by dividing its numerator and denominator by their common factor (other than 1), if ant.
Note:
(i) Multiplying its numerator (top) and denominator (bottom) by the same number (other than 0).
(ii) Dividing its numerator (top) and denominator (bottom) by their common factor (other than 1).
For Example:
1. Write three equivalent fraction of
3/
5.
Equivalent fractions of
3/
5 are:
(3 × 2)/(5× 2) = 6/10,
(3 × 3)/(5 × 3) = 9/15,
(3 × 4)/(5 × 4) = 12/20
Therefore, equivalent fractions of
3/
5 are
6/
10,
9/
15 and
12/
20.
2. Write next three equivalent fraction of \(\frac{2}{3}\).
We multiply the numerator and the denominator by 2.
We get, \(\frac{2 × 2}{3 × 2}\) = \(\frac{4}{6}\)
Next, we multiply the numerator and the denominator by 3. We get
\(\frac{2 × 3}{3 × 3}\) = \(\frac{6}{9}\).
Next, we multiply the numerator and the denominator by 4. We get
\(\frac{2 × 4}{3 × 4}\) = \(\frac{8}{12}\).
Therefore, equivalent fractions of \(\frac{2}{3}\) are \(\frac{4}{6}\), \(\frac{6}{9}\) and \(\frac{8}{12}\).
3. Write three equivalent fraction of
1/
4.
Equivalent fractions of
1/
4 are:
(1× 2)/(4× 2) = 2/8,
(1 × 3)/(4 × 3) = 3/12,
(1× 4)/(4× 4) = 4/16
Therefore, equivalent fractions of
1/
4 are
2/
8,
3/
12 and
4/
16.
4. Write three equivalent fraction of
2/
15.
Equivalent fractions of
2/
15 are:
(2× 2)/(15 × 2) = 4/30,
(2 × 3)/(15 × 3) = 6/45,
(2× 4)/(15 × 4) = 8/60
Therefore, equivalent fractions of
2/
15 are
4/
30,
6/
45 and
8/
60.
5. Write three equivalent fraction of
3/
10.
Equivalent fractions of
3/
10 are:
(3× 2)/(10× 2) = 6/20,
(3 × 3)/(10 × 3) = 9/30,
(3× 4)/(10× 4) = 12/40
Therefore, equivalent fractions of
3/
10 are
6/
20,
9/
30 and
12/
40.
You might like these
-
To add two or more like fractions we simplify add their numerators. The denominator remains same.
-
In worksheet on addition of fractions having the same denominator, all grade students can practice the questions on adding fractions. This exercise sheet on fractions can be practiced by the students to get more ideas how to add fractions with the same denominators.
-
In worksheet on subtraction of fractions having the same denominator, all grade students can practice the questions on subtracting fractions. This exercise sheet on fractions can be practiced by the students to get more ideas how to subtract fractions with the same
-
Addition and subtraction of like fractions. Addition of Like Fractions: To add two or more like fractions we simplify add their numerators. The denominator remains same. To subtract two or more like fractions we simply subtract their numerators and keep the same denominator.
-
Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtraction with the help of a fraction number line, add the fractions with the same
-
In 4th grade fractions worksheet we will circle the like fractions, circle the greatest fraction, arrange the fractions in descending order, arrange the fractions in ascending order, addition of like fractions and subtraction of like fractions.
-
We will discuss here how to arrange the fractions in ascending order. Solved examples for arranging in ascending order: 1. Arrange the following fractions 5/6, 8/9, 2/3 in ascending order. First we find the L.C.M. of the denominators of the fractions to make the denominators
-
In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a number to convert them to like fractions. Let us consider some of the
-
Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example \(\frac{7}{13}\) > \(\frac{2}{13}\) because 7 > 2. In comparison of like fractions here are some
-
Like and unlike fractions are the two groups of fractions: (i) 1/5, 3/5, 2/5, 4/5, 6/5 (ii) 3/4, 5/6, 1/3, 4/7, 9/9 In group (i) the denominator of each fraction is 5, i.e., the denominators of the fractions are equal. The fractions with the same denominators are called
-
In worksheet on equivalent fractions, all grade students can practice the questions on equivalent fractions. This exercise sheet on equivalent fractions can be practiced by the students to get more ideas to change the fractions into equivalent fractions.
-
We will discuss here about verification of equivalent fractions. To verify that two fractions are equivalent or not, we multiply the numerator of one fraction by the denominator of the other fraction. Similarly, we multiply the denominator of one fraction by the numerator
-
In 5th Grade Fractions Worksheets we will solve how to compare two fractions, comparing mixed fractions, addition of like fractions, addition of unlike fractions, addition of mixed fractions, word problems on addition of fractions, subtraction of like fractions
-
Here we will learn Reciprocal of a fraction. What is 1/4 of 4? We know that 1/4 of 4 means 1/4 × 4, let us use the rule of repeated addition to find 1/4× 4. We can say that \(\frac{1}{4}\) is the reciprocal of 4 or 4 is the reciprocal or multiplicative inverse of 1/4
-
To divide a fraction or a whole number by a fraction or a whole number, we multiply the reciprocal of the divisor. We know that the reciprocal or the multiplicative inverse of 2 is \(\frac{1}{2}\).
● Fraction
Representations of Fractions on a Number Line
Fraction as Division
Types of Fractions
Conversion of Mixed Fractions into Improper Fractions
Conversion of Improper Fractions into Mixed Fractions
Equivalent Fractions
Interesting Fact about Equivalent Fractions
Fractions in Lowest Terms
Like and Unlike Fractions
Comparing Like Fractions
Comparing Unlike Fractions
Addition and Subtraction of Like Fractions
Addition and Subtraction of Unlike Fractions
Inserting a Fraction between Two Given Fractions
Numbers Page
6th Grade Page
From Equivalent Fractions to HOME PAGE
Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.
Share this page:
What’s this?
|
|
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.