101 10
Solve mixed numbers

A mixed number is the sum of a whole number and a proper fraction. This sum is implied without the use of any visible operator such as "+"; for example, in referring to two entire cakes and three quarters of another cake, the whole and fractional parts of the number are written next to each other:

An improper fraction can be thought of as another way to write a mixed number;                    Source: Wikipedia

Mixed number involves an integer plus a proper fraction. Here we consider the basic arithmetic operation on the mixed number. The mixed number is in the form of 3. The mixed number has both a whole number part and a fractional part. so the three numbers in a mixed number are

the whole number
the numerator
the denominator

Example problems:

Example 1:

Multiplication of 3 `3/7` *2 `1/3`

Change each of the mixed number to improper fractions.

2` 1/3` =`7/3`

The new representation is `24/7` * `7/3`

Cancel each of the 7s replacing them by  `7/7` =1 = 1 `24/7` *`7/3`

The problem  like this `24/7` *`7/3`

Cancel both the 3 and 24 by dividing by 3.   `3/3` =1    `24/3` = 8

The problem look like this `8/1` *`1/1`

The solution is  8.

Multiplying whole number with mixed numbers:

Multiply 5 x  8 `4/5` .

Solution:

Change the mixed number to an improper fraction 8 `4/5` = `44/5 ` and the whole number to .

The problem in the form 5*`44/5`

Cancel the the common term in below fractions `(44xx5)/5`

The result is ` 44/1` here 5 in the numerator and denominator will be cancelled, we get

= 44

Problem 2: mixed numbers and improper fractions

(ii) 4 `1/2` + `1/2`

Solution: This is mixed number is adding mixed number with improper fraction

4 `1/2` = `(4 xx2+1)/4` + `1/2`

= `9/2` + `1/2`

= `9/2` + `1/2` here the denominator are same so we can add directly, we get

= `(9+1)/2`

= `10/2` = 5 here 10 is cancelled 5 times by 2.

= 5.

To add or subtract mixed numbers
Add or subtract the fractional parts
Add or subtract the integral parts

Simplify, if necessary

Problem in the Add mixed number:

Solution:

`(4xx3+1)/3`  + `(2xx3+2)/3`

= `13/3` + `7/3.`

= `20/3 `

Subtracting mixed numberis 5 `1/2` - 2` 3/4`

Solution: the given problem both  are in the mixed number convert into proper fraction and subtract it.

= `(2xx5+1)/2` – `(4xx2+3)/4`

= `11/2` – `11/4` taking the LCM as 4

= `((11xx2)(11xx1))/4`

= `(22-11)/4 ` here subtracting the numerator 22-11 as 11

= `11/4.`

Solution: In this equation the denominator of 4 is same we can subtract directly, we get

=`(4xx3+1)/3`  +  `(4xx3+2)/3`

=`13/3` +`14/3` here denominator is same we subtract directly

`=(13+14)/3`

`=25/3`

Let us see some example problems of mixed number.

Problem 1:

Solve` 3 1/2 +5 3/4 + 7 1/4`

Solution:

We can add the given mixed numbers by using the following method.

First we can convert the mixed number to fraction.

That is, `3 1/2 = ((3xx2) +1)/ 2= 7/2`

`5 3/4 = ((5xx4) +3)/ 4= 23/4`

`7 1/4= ((7xx4) +1)/ 4= 29/4`

Then we can write the above fractions are in the form of,

`= 7/2+ 23/4+ 29/4`

Now we can add the fractions. Before we can go to adding, we can see the denominator part.

If denominator values are equal we need not to any change in the numerator. But if denominator values are different we can find the L.C.M of denominator values and then change the numerator value depends on L.C.M value.

In the above problem, denominators are different.

So, L.C.M of 2, 4, 4 = 8

`= 28/8+ 46/8+ 58/8`
`= (28+46+58)/ 8`

`= 132/8`

After simplifying,

`= 33/2 `

Problem 2:

Solve `7 3/2 -3 1/4 -2 3/5`

Solution:

We can subtract the given mixed numbers by using the following method.

First we can convert the mixed number to fraction.

That is, `7 3/2 = ((7*2) +3)/ 2= 17/2`

`3 1/4 = ((3*4) +1)/ 4= 13/4`

` 2 3/5= ((2*4) +3)/ 4= 11/5`

Then we can write the above fractions are in the form of,

`= 17/2- 13/4- 11/5`

Here denominators are different. Before we can go to subtracting, we can see the denominator part.

If denominator values are equal we need not to any change in the numerator.

But if denominator values are different we can find the L.C.M of denominator values and then change the numerator value depends on L.C.M value.

So L.C.M of 2, 4, 5 = 20

Therefore, `(17xx10)/ (2xx10) - (13xx5)/ (4xx5) - (11xx4)/ (5xx4)`

`= 170/20- 65/20- 44/20`

`= (170-65-44)/ 20`

`= 61/20`