Fraction: A fraction is a part of a whole or a collection and it consists of a numerator and denominator.
Example: If we serve1 part of a cake with 8 equal parts, we have served ^{1}⁄_{8} of the cake.
Let us see how to solve operations involving fractions.
While adding or subtracting two fractions; we need to make sure that the denominators are the same.
Steps:
Add or subtract the numerators.
Keep the denominator the same.
Reduce the answer, if possible.
Example: Solve ^{1}⁄_{4 }+ ^{1}⁄_{4}
Example: Subtract ^{1}⁄_{4} from ^{3}⁄_{4}
If the denominators are not the same:
First, make them the same
Then add or subtract like fractions with the same denominators.
Example: To solve ^{1}⁄_{4} + ^{1}⁄_{2} , we first make the denominators the same.
We change the denominator 2 and make it 4 by multiplying it by 2. However, we need to multiply the numerator and denominator both by 2 to keep the value of the fraction unchanged.
Multiplying ^{1}⁄_{2} ✕ ^{2}⁄_{2} = ^{2}⁄_{4}
Since the denominators are the same we can now add both the fractions.
Similarly, we use these rules for subtraction.
To multiply two fractions we simply multiply the numerators and denominators.
Example:
^{2}⁄_{3} ✕ ^{3}⁄_{15} = ?
First, simplify the fraction ^{3}⁄_{15} to its lowest term.
While dividing two fractions:
Inverse the second fraction, that is, interchange its numerator and denominator to get the reciprocal.
Multiply the first fraction by the reciprocal of the second fraction.
Example:
Fractions with a numerator larger than the denominator are called improper fractions. When we solve improper fractions, the result can be a mixed number (a fraction with a whole number and a proper fraction).
Example:
^{38}⁄_{7 }= ?
38 ÷ 7 = 5 Quotient and 3 Remainder
5
5 ^{3}⁄_{7}
Therefore, ^{38}⁄_{7} = 5 ^{3}⁄_{7}
Thus, by solving an improper fraction ^{38}⁄_{7} we get a mixed number 5 ^{3}⁄_{7}
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