Mixed Fraction

A mixed fraction is a combination of a whole number & a proper fraction.

Or

A fraction which has quotient, remainder & divisor as 2¹/₅.

## 1. Example of Mixed Fraction

There are many examples of mixed fractions-

**2³/₅, 5⁶/₇, 7⁸/₉, .......etc.**

Where the red colour showed

**quotient**, the blue colour showed the**remainder**& orange colour showed**divisor**.## 2. How to convert a mixed fraction into an improper fraction?

**1.) Convert mixed fraction**

**2³/₅**

**into an improper fraction.**

Solve:-

**= 2³/₅**

*{To get the numerator of the improper fraction, we multiply quotient 2 &*

*divisor 5*

*then we add remainder 3 in the answer}*

*{To get the denominator of the improper fraction we write divisor 5 of given mixed fraction in the division of numerator}*

As below-

= {(2×5)+3}÷5

= {10+3}÷5

= 13÷5

= or 13/5

We get an improper fraction 13/5.

**2.) Convert mixed fraction**

**5⁶/₇**

**into an improper fraction.**

Solve:-

**=**

**5⁶/₇**

*{To get the numerator of the improper fraction, we multiply quotient 5 &*

*divisor 7*

*then we add remainder 6 in the answer}*

*{To get the denominator of the improper fraction we write divisor 7 of given mixed fraction in the division of numerator}*

As below-

= {(5×7)+6}÷7

= {35+6}÷7

= 41÷7

= or 41/7

We get an improper fraction 41/7.

## 3. How to do subtraction of Mixed Fractions?

**1.) Subtract mixed fraction 1**

**⁶/₇ from**

**2³/₇**

Solve:-

*{ To subtract mixed fractions we need to convert it into improper fractions. So first we convert given mixed fractions into improper fractions}*

*=*2³/₇ - 1⁶/₇

= (17/7) - (13/7)

*{Now we will subtract this improper fraction to get an answer}*

= (17 - 13) / 7

= 4/7

We get our answer 4/7.

**2.) Subtract mixed fraction 11¹**

**/₅ from 23³**

**/₅**

Solve:-

*{ To subtract mixed fractions we need to convert it into improper fractions. So first we convert given mixed fractions into improper fractions}*

*=*23³/₅ - 11¹/₅

= (118/5) - (55/5)

*{Now we will subtract this improper fraction to get an answer}*

= (118 - 55) / 5

= 63/5

We get our answer 63/5.

### We can do the addition of mixed fractions as above subtraction.

## 4. How to do Multiplication of Mixed Fractions?

**1.) Multiply mixed fraction 5⁶/₇ & 7⁸/₉.**

Solve:-

*{Also in multiplication, we need to convert mixed fractions into improper fractions}*

*=*5⁶/₇ × 7⁸/₉

= (41/7) × (71/9)

*{Now multiply both numerators to each other & both denominators to each other}*

= (41×71) / (7×9)

*=*2911 / 63

**2.) Multiply mixed fraction 1²/₃ & 3³/₄.**

Solve:-

*{Also in multiplication, we need to convert mixed fractions into improper fractions}*

*=*1²/₃ × 3³/₄

= (5/3) × (15/4)

*{Now multiply both numerators to each other & both denominators to each other}*

= (5×15) / (3×4)

*=*75 / 12

## 5. How to do Division of Mixed Fractions?

**1.) Divide mixed fraction 4³/₄ from**

**3²/₃.**

Solve:-

*{First, we will convert mixed fractions into improper fractions}*

*=*

**4³/₄ ÷ 3²/₃**

= (19/4) ÷ (11/3)

*{Now we do reciprocal of (11/3) into (3/11) & change sign ÷ to ×)*

*=*(19/4) × (3/11)

*{Now we multiply both numerators to each other & multiply both denominators to each other & then divide both answers}*

= (19×3) / (4×11)

= 57 / 44

We get our answer 57/44.

**2.) Divide mixed fraction**

**3⁴/₅**

**from**

**1³/₅**

**.**

Solve:-

*{First, we will convert mixed fractions into improper fractions}*

*=*

**3⁴/₅ ÷ 1³/₅**

= (19/5) ÷ (8/5)

*{Now we do reciprocal of (8/5) into (5/8) & change sign ÷ to ×)*

*=*(19/5) × (5/8)

*{Now we multiply both numerators to each other & multiply both denominators to each other & then divide both answers}*

= (19×5) / (5×8)

= 95 / 40

We get our answer 95/40.