# Conversion of Improper Fractions into Mixed Fractions

In conversion of improper fractions into mixed fractions, we follow the following steps:

Step I:

Obtain the improper fraction.

Step II:

Divide the numerator by the denominator and obtain the quotient and remainder.

Step III:

Write the mixed fraction as: Quotient$$\frac{Remainder}{Denominator}$$.

Let us convert $$\frac{7}{5}$$ into a mixed number.

As you know if a fraction has same number as numerator and denominator, it makes a whole. Here in $$\frac{7}{5}$$ we can take out $$\frac{5}{5}$$ to make a whole and the remaining fraction we have is $$\frac{2}{5}$$. So, $$\frac{7}{5}$$ can be written in mixed numbers as 1$$\frac{2}{5}$$.

$$\frac{5}{5}$$ = 1                        +                           $$\frac{2}{5}$$

$$\frac{7}{5}$$ = $$\frac{5}{5}$$ + $$\frac{2}{5}$$ = 1 + $$\frac{2}{5 }$$ = 1$$\frac{2}{5}$$

 Actually, $$\frac{7}{5}$$ means 7 ÷ 5. When we divide 7 by 5 we get 1 as quotient and 2 as remainder. To convert an improper fraction into a mixed number we place the quotient 1 as the whole number, the remainder 2 as the numerator and the divisor 5 as the denominator of the proper fraction.

For Example:

1. Express each of the following improper fractions as mixed fractions:

(i) $$\frac{17}{4}$$

We have,

Therefore, Quotient = 4, Remainder = 1, Denominator = 4.

Hence, $$\frac{17}{4}$$ = 4$$\frac{1}{4}$$

(ii) $$\frac{13}{5}$$

We have,

Therefore, Quotient = 2, Remainder = 3, Denominator = 5.

Hence, $$\frac{13}{5}$$ = 2$$\frac{3}{5}$$

(iii) $$\frac{28}{5}$$

We have,

Therefore, Quotient = 5, Remainder = 3, Denominator = 5

Hence, $$\frac{28}{5}$$ = 5$$\frac{3}{5}$$.

(iv) $$\frac{28}{9}$$

We have,

Therefore, Quotient = 3, Remainder = 1, Denominator = 9

Hence, $$\frac{28}{9}$$ = 3$$\frac{1}{9}$$.

(v) $$\frac{226}{15}$$

We have,

Therefore, Quotient = 15, Remainder = 1, Denominator = 15

Hence, $$\frac{226}{15}$$ = 15$$\frac{1}{15}$$.

Conversion of an Improper Fraction Into a Mixed Fraction:

2. Let us convert 22/5 into an mixed fraction.

Divide the numerator 22 by the denominator 5.

The quotient 4 gives the whole number. The remainder 2 is the numerator of the fractions.

The denominator of the fraction remains the same. So, $$\frac{22}{5}$$ = 4$$\frac{2}{5}$$

3. Convert $$\frac{41}{3}$$ into mixed fraction.

Divide the numerator 41 by the denominator 3.

The quotient 13 gives the whole number. The remainder 2 is the numerator of the fractions.

The denominator of the fraction remains the same.

So, $$\frac{41}{3}$$ = 13$$\frac{2}{3}$$

Worksheet on Conversion of Improper Fractions into Mixed Fractions:

1. Convert the following into Improper Fractions:

(i) $$\frac{11}{9}$$

(ii) $$\frac{24}{5}$$

(iii) $$\frac{26}{8}$$

(iv) $$\frac{59}{9}$$

(v) $$\frac{64}{7}$$

1. (i) 1$$\frac{2}{9}$$

(ii) 4$$\frac{4}{5}$$

(iii) 3$$\frac{2}{8}$$

(iv) 6$$\frac{5}{9}$$

(v) 9$$\frac{1}{7}$$

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