Table of Contents

Last modified on June 26th, 2024

A mixed number, also called a mixed fraction, consists of a whole number and a proper fraction.Â Mixed numbers represent quantities that are more than one whole but less than the next whole number.

${1\dfrac{2}{3}}$, ${1\dfrac{2}{5}}$, ${4\dfrac{5}{7}}$, ${2\dfrac{1}{6}}$, and ${1\dfrac{3}{4}}$ are a few examples of mixed number.

It has two main parts: the whole number and the fractional part. The fractional part again consists of a numerator and a denominator.

- Whole number
- Fractional part

- Numerator
- Denominator

Here are a few more real-life examples of mixed numbers:

- When serving a cake or a pie at home, we express the parts of a whole as mixed fractions.
- A piece of wood of ${3\dfrac{3}{7}feet}$ long is expressed in mixed fraction
- A fully filled glass of milk and a half-filled glass is represented in mixed fraction as ${1\dfrac{1}{2}}$.

To convert a mixed number to an improper fraction, we first multiply the denominator with the whole number, then add the resultant product with the numerator.

Let us convert ${1\dfrac{2}{5}}$ to improper fraction.

Here, we will multiply the denominator 5 by the whole number 1

1 Ã— 5 = 5

Now, on adding the numerator of the mixed number 2 to the result 5,

2 + 5 = 7

Keeping the denominator the same and placing the sum in the numerator, we get the improper fraction

${\dfrac{7}{5}}$

To convert a mixed number to a decimal, we change the number to an improper fraction and then divide the numerator by the denominator.

Let us convert ${1\dfrac{3}{8}}$ to decimal number.

Here, converting ${1\dfrac{3}{8}}$ into improper fraction, we get

${\dfrac{\left( 1\times 8\right) +3}{8}}$ = ${\dfrac{11}{8}}$

Now, by dividing the numerator 11 by the denominator 8, we get

11 Ã· 8 = 1.375

To convert a mixed number to a decimal, we convert the fractional part to a decimal and then add the result to the whole number part.

Again, we convert ${1\dfrac{3}{8}}$ to decimal number.

Here, the fractional part is ${\dfrac{3}{8}}$

On dividing the numerator 3 by the denominator 8, we get

3 Ã· 8 = 0.375

Now, on adding the result to the whole number part 1, we get

1 + 0.375 = 1.375

To add mixed numbers, we first convert them into improper fractions and simplify them.

Let us add ${4\dfrac{5}{7}+1\dfrac{2}{3}}$

First, converting the mixed numbers ${4\dfrac{5}{7}}$ and ${1\dfrac{2}{3}}$ to improper fractions, we get

${4\dfrac{5}{7}}$ = ${\dfrac{\left( 4\times 7\right) +5}{7}}$ = ${\dfrac{33}{7}}$

${1\dfrac{2}{3}}$ = ${\dfrac{\left( 1\times 3\right) +2}{3}}$ = ${\dfrac{5}{3}}$

Now, if the denominators are the same, we add the numerators. However, if they are different, we take the LCM of the denominators and then simplify

Here, the denominators are 7 and 3, that are different.

The LCM of 7 and 3 is 21

Now, ${\dfrac{33}{7}+\dfrac{5}{3}}$

= ${\dfrac{33\times 3}{7\times 3}+\dfrac{5\times 7}{3\times 7}}$

= ${\dfrac{99}{21}+\dfrac{35}{21}}$

= ${\dfrac{99+35}{21}}$

= ${\dfrac{134}{21}}$

= ${6\dfrac{8}{21}}$

To subtract, we follow the same steps as addition.

Converting the mixed numbers ${4\dfrac{5}{7}}$ and ${1\dfrac{2}{3}}$ to improper fractions, we get

${4\dfrac{5}{7}}$ = ${\dfrac{\left( 4\times 7\right) +5}{7}}$ = ${\dfrac{33}{7}}$

${1\dfrac{2}{3}}$ = ${\dfrac{\left( 1\times 3\right) +2}{3}}$ = ${\dfrac{5}{3}}$

Here, the denominators are 7 and 3, that are different.

The LCM of 7 and 3 is 21

${4\dfrac{5}{7}-1\dfrac{2}{3}}$

= ${\dfrac{\left( 4\times 7\right) +5}{7}-\dfrac{\left( 1\times 3\right) +2}{3}}$

= ${\dfrac{33}{7}-\dfrac{5}{3}}$

= ${\dfrac{33\times 3}{7\times 3}-\dfrac{5\times 7}{3\times 7}}$

= ${\dfrac{99}{21}-\dfrac{35}{21}}$

= ${\dfrac{99-35}{21}}$

= ${\dfrac{64}{21}}$

= ${3\dfrac{1}{21}}$

To multiply improper fractions, we first convert the mixed numbers to improper fractions and then multiply the numerators and denominators separately.

Let us multiply ${3\dfrac{2}{5}}$ and ${2\dfrac{7}{8}}$

Converting the mixed numbers ${3\dfrac{2}{5}}$ and ${2\dfrac{7}{8}}$ to improper fractions, we get:

${3\dfrac{2}{5}}$ = ${\dfrac{\left( 3\times 5\right) +2}{5}}$ = ${\dfrac{17}{5}}$

${2\dfrac{7}{8}}$ = ${\dfrac{\left( 2\times 8\right) +7}{8}}$ = ${\dfrac{23}{8}}$

Now, multiplying the numerators and the denominators separately, we get

${\dfrac{17}{5}\times \dfrac{23}{8}}$

= ${\dfrac{17\times 23}{5\times 8}}$

= ${\dfrac{391}{40}}$

= ${9\dfrac{31}{40}}$

Dividing mixed fractions is easy. First, we convert the mixed numbers to improper fractions and then multiply the first fraction by the reciprocal of the second fraction.

Let us divide ${3\dfrac{2}{5}}$ by ${2\dfrac{7}{8}}$

Converting the mixed numbers** **${3\dfrac{2}{5}}$ and ${2\dfrac{7}{8}}$ to improper fractions,we get:

${3\dfrac{2}{5}}$ = ${\dfrac{\left( 3\times 5\right) +2}{5}}$ = ${\dfrac{17}{5}}$

${2\dfrac{7}{8}}$ = ${\dfrac{\left( 2\times 8\right) +7}{8}}$ = ${\dfrac{23}{8}}$

Then, multiplying the first fraction by the reciprocal of the second fraction

${\dfrac{17}{5}\times \dfrac{8}{23}}$

= ${\dfrac{17\times 8}{5\times 23}}$

= ${\dfrac{136}{115}}$

**Convert the fraction ${\dfrac{13}{12}}$ into a mixed number.**

Solution:

Given ${\dfrac{13}{12}}$

On dividing the numerator 13 by the denominator 12, we get

13 Ã· 12

The quotient is 1

The remainder is 1

As we know,Â

${Quotient\dfrac{Remainder}{Divisor}}$

Thus, ${\dfrac{13}{12}}$ = ${1\dfrac{1}{12}}$

**Add the mixed numbers ${2\dfrac{3}{5}}$ and ${1\dfrac{4}{9}}$**

Solution:

Here, ${2\dfrac{3}{5}+1\dfrac{4}{9}}$

= ${\dfrac{\left( 2\times 5\right) +3}{5}+\dfrac{\left( 1\times 9\right) +4}{9}}$

= ${\dfrac{13}{5}+\dfrac{13}{9}}$

= ${\dfrac{13\times 9}{5\times 9}+\dfrac{13\times 5}{9\times 5}}$

= ${\dfrac{117}{45}+\dfrac{65}{45}}$

= ${\dfrac{117+65}{45}}$

= ${\dfrac{182}{45}}$

= ${4\dfrac{2}{45}}$

Last modified on June 26th, 2024