Are you interested in equivalent fractions? This web page gives you clear information about equivalent fractions. It will explain the definition of an Equivalent fraction. By going through the article you can also check the examples of verifying equivalent fractions. With this Knowledge, you can also solve similar problems very easily.
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Equivalent Fractions
Equivalent fractions are the fractions with different numerators and different denominators but they have the same value. At one glance, you can not tell whether the fractions are equivalent or not. It is difficult to know whether the two fractions have the same value.
For example \(\frac { 4 }{ 14 } \), \(\frac { 6 }{ 21 } \)
How to Verify Equivalent Fractions?
Here you can check the examples of verifying the equivalent fractions.
To verify whether the two fractions are equivalent or not, multiply the numerator of one fraction by the denominator of another fraction. Also, multiply the denominator of one fraction by the numerator of another fraction. If the products are the same after the multiplication then the fractions are said to be equivalent.
Verifying Equivalent Fractions Examples with Answers
Example 1:
Verify whether the fractions \(\frac { 4 }{ 6 } \), \(\frac { 8 }{ 12 } \) are equivalent?
Solution:
\(\frac { 4 }{ 6 } \)⤨ \(\frac { 8 }{ 12 } \)
Multiply the numerator of the first fraction by the denominator of the other is
i.e. 4×12=48
The product of the denominator of the first fraction and the numerator of the other is
i.e. 6×8=48
The products are the same.
So \(\frac { 4 }{ 6 } \), \(\frac { 8 }{ 12 } \) are equivalent fractions.
Example 2:
Check whether the fractions \(\frac { 3}{ 6 } \), \(\frac { 2 }{ 4 } \) are equivalent?
Solution:
\(\frac { 3 }{ 6 } \)⤨ \(\frac { 2 }{ 4 } \)
Multiply the numerator of first fraction by the denominator of the other is
i.e. 3×4=12
The product of the denominator of the first fraction and the numerator of the other is
i.e. 6×2=12
The products are the same.
So \(\frac { 3 }{ 6 } \), \(\frac { 2 }{ 4 } \) are equivalent fractions.
Example 3:
Check whether the fractions \(\frac { 6 }{ 9 } \), \(\frac { 2 }{ 3 } \)are equivalent fractions?
Solution:
\(\frac { 6 }{ 9 } \)⤨ \(\frac { 2 }{ 3 } \)
Multiply the numerator of first fraction by the denominator of the other is
i.e. 6×3=18
The product of the denominator of the first fraction and the numerator of the other is
i.e. 9×2=18
The products are the same.
So \(\frac { 6 }{ 9 } \), \(\frac { 2 }{ 3 } \) are equivalent fractions.
Example 4:
Check whether the fractions \(\frac { 12 }{ 9 } \), \(\frac { 4 }{ 3 } \)are equivalent fractions?
Solution:
\(\frac { 12 }{ 9 } \)⤨ \(\frac { 4 }{ 3 } \)
Multiply the numerator of first fraction by the denominator of the other is
i.e. 12×3=36
The product of the denominator of the first fraction and the numerator of the other is
i.e. 9×4=36
The products are the same.
So \(\frac { 12 }{ 9 } \), \(\frac { 4 }{ 3 } \) are equivalent fractions.
Example 5:
Check whether the fractions \(\frac { 2 }{ 5 } \), \(\frac { 5 }{ 2} \)are equivalent fractions?
Solution:
\(\frac { 2 }{ 5 } \)⤨ \(\frac { 5 }{ 6 } \)
Multiply the numerator of first fraction by the denominator of the other is
i.e. 2×6=12
The product of the denominator of the first fraction and the numerator of the other is
i.e. 5×5=25
The products are not the same.
So \(\frac { 2 }{ 5 } \), \(\frac { 5 }{ 2 } \) are not equivalent fractions.
Example 6:
Check whether the fractions \(\frac { 3 }{ 5 } \), \(\frac { 6 }{ 10} \)are equivalent fractions?
Solution:
\(\frac { 3 }{ 5 } \)⤨ \(\frac { 6 }{ 10 } \)
Multiply the numerator of first fraction by the denominator of the other is
i.e. 3×10=30
The product of the denominator of the first fraction and the numerator of the other is
i.e. 5×6=30
The products are the same.
So \(\frac { 3 }{ 5 } \), \(\frac { 6 }{ 10 } \) are equivalent fractions.
Example 7:
Check whether the fractions \(\frac { 7 }{ 42} \), \(\frac { 8 }{ 48} \)are equivalent fractions?
Solution:
\(\frac { 7 }{ 42 } \)⤨ \(\frac { 8 }{ 48} \)
Multiply the numerator of first fraction by the denominator of the other is
i.e. 7×48=336
The product of the denominator of the first fraction and the numerator of the other is
i.e. 42×8=336
The products are the same.
So \(\frac { 7 }{ 42 } \), \(\frac { 8 }{ 48 } \) are equivalent fractions.
Example 8:
Check whether the fractions \(\frac { 1 }{ 7 } \), \(\frac { 2 }{ 14} \)are equivalent fractions?
Solution:
\(\frac { 1 }{ 7 } \)⤨ \(\frac { 2 }{ 14 } \)
Multiply the product of the numerator of first fraction by the denominator of the other is
i.e. 1×14=14
The product of the denominator of the first fraction and the numerator of the other is
i.e. 7×2=14
The products are the same.
So \(\frac { 1 }{ 7 } \), \(\frac { 2}{ 14 } \) are equivalent fractions.
Example 9:
Check whether the fractions \(\frac { 5 }{ 25} \), \(\frac { 6 }{ 30} \)are equivalent fractions?
Solution:
\(\frac { 5 }{ 25 } \)⤨ \(\frac { 6 }{ 30 } \)
Multiply the product of the numerator of first fraction by the denominator of the other is
i.e. 5×30=150
The product of the denominator of the first fraction and the numerator of the other is
i.e. 25×6=150
The products are the same.
So \(\frac { 5 }{ 25 } \), \(\frac { 6}{ 30} \) are equivalent fractions.
Example 10:
Check whether the fractions \(\frac { 3 }{ 20} \), \(\frac { 4 }{ 50} \)are equivalent fractions?
Solution:
\(\frac { 3 }{ 20 } \)⤨ \(\frac { 4 }{ 50 } \)
Multiply the product of the numerator of first fraction by the denominator of the other is
i.e. 3×50=150
The product of the denominator of the first fraction and the numerator of the other is
i.e. 20×4=80
The products are not the same.
So \(\frac { 3}{ 20 } \), \(\frac { 4}{ 50} \) are not equivalent fractions.