Satypal walks \displaystyle \frac{2}{3} km from a place P towards east and then there \displaystyle 1\frac{5}{7} km towards west Where will he be now from P ?

Let us denote the distance travelled towards east by positive sign so thus distance of Satypal from the point P would be \displaystyle \frac{2}{3} + \displaystyle (-1\frac{5}{7}) = \displaystyle \frac{2}{3} + \displaystyle \frac{-12}{7} = \displaystyle \frac{2\times 7}{3\times 7} + \displaystyle \frac{(-12)\times 3}{7\times 3} = \displaystyle \frac{14-36}{21} = \displaystyle \frac{-22}{ 21 } = \displaystyle -1\frac{1}{21} Since it is negative it means Satypal is at a distance \displaystyle1 \frac{1}{21} km towards west of P

Find the sum 3\dfrac{4}{5}+2\dfrac{3}{10}+1\dfrac{1}{15}

First, convert each mixed fraction into an improper fraction.We get, 3\dfrac{4}{5}=\dfrac{18}{5} 2\dfrac{3}{10}=\dfrac{23}{10} 1\dfrac{1}{15}=\dfrac{16}{15} Then, to find out \dfrac{19}{5}+\dfrac{23}{10}+\dfrac{16}{15} , we need to calculate the LCM of the denominators.LCM of 5,10\, \, and \, \, 15=30 Now,let us change each of the given fraction into an equivalent fraction having 30 as the denominator \dfrac{19}{5}\times\dfrac{6}{6}=\dfrac{114}{30} \dfrac{23}{10}\times\dfrac{3}{3}=\dfrac{69}{30} \dfrac{16}{15}\times\dfrac{2}{2}=\dfrac{32}{30} Now, \dfrac{114}{30}+\dfrac{69}{30}+\dfrac{32}{30}= \dfrac{(114+69+32)}{30} =\dfrac{215}{30} =\dfrac{43}{6} =7\dfrac{1}{6}

Sarita bought \dfrac{2}{5} meter of ribbon and Lalita \dfrac{3}{4} meter of ribbon. What is the total length of the ribbon they bought?

Length of ribbon Sarita bought = \dfrac25 meter Length of ribbon Lalita bought = \dfrac34 meter Total length of ribbon = \dfrac25 + \dfrac34 LCM of 5 & 4 is 20 \dfrac {4\times 2}{5 \times 4} + \dfrac {3\times 5}{4\times 5} = \dfrac {8}{20} + \dfrac {15}{20} = \dfrac {23} {20} Thus,they bought \dfrac {23}{20} meters of ribbon together.

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>>Class 6
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>>Fractions
>>Operations on Fractions
>> $Adding and Subtracting Like...$

Adding and Subtracting Like Fractions

Q: Solve: 4 \frac{2}{3} + 3 \frac{1}{4}

\frac{(3 \times 4) + 2}{3} + \frac{(3 \times 4) + 1}{4} = \frac{14}{3} + \frac{13}{4} = \frac{(14 \times 4) + (13 \times 3)}{12} = \frac{56 + 39}{12} = \frac{95}{12}

Q: Divide the sum of (65/12) and (8/3) by their difference.

First we have to find the sum (65/12)+(8/3) LCM of 12 and 3 is 12 Then, (65\times 1)/(12\times 1)=(65/12) and (8\times 4)/(3\times 4)=(32/12) Now, =(65+32)/12 =(97/12) Now find the difference of (65/12)-(8/3) LCM of 12 and 3 is 12 Then, (65\times 1)/(12\times 1)=(65/12) (8\times 4)/(3\times 4)=(32/12) Now, =(65-32)/12 =(33/12) Now divide (97/12)\div (33/12) =(97\times 12)\times (12/33) =(97\times 12)/(12\times 33) =(97\times 1)/(1\times 33) =(97/33)

Q: Simplify: (2/3)+(5/6)-(1/9)

LCM of 3,6,9=18 Now let us change each of the given fraction into an equivalent fraction having 18 as the denominator. (2/3)x(6/6)=(12/18) and (5/6)x(3/3)=(15/18) and (1/9)x(2/2)=(2/18) Now, =(12/18)+(15/18)-(2/18) =(12+15-2)/18 =(27-2)/18 =(25/18) =[1(7/18)]

Q: Find the sum(8/9)+(7/12)

For addition of two unlike fractions,first change them to the like fractions.LCM of 9,12=36Now,let us change each of the given fraction into an equivalent fraction having 36 as the denominator. \dfrac{8}{9}\times \dfrac{4}{4}=\dfrac{32}{36} \dfrac{7}{12}\times \dfrac{3}{3}=\dfrac{21}{36} Now.add the like fractions, =\dfrac{32}{36} +\dfrac{21}{36} =\dfrac{32+21}{36} =\dfrac{53}{36} =[1\dfrac{17}{36}]

Q: Simplify: [8(5/6)]-[3(3/8)]+[1(7/12)]

First we convert each mixed fraction into an improper fraction. \Rightarrow [8(5/6)]=(53/6) also \Rightarrow [3(3/8)]=(27/8) and \Rightarrow [1(7/12)]=(19/12) Then, (53/6)-(27-8)-(19/12) LCM of 6,8,12=24 Now, let us change each of the given fraction into an equivalent fraction having 24 as the denominator. =[(53/6)\times(4/4)]=(212/24) also =[(27/8)\times (3/3)]=(81/24) and =[(19/12)\times(2/2)]=(38/24) Now, =(212/24)-(81/24)-(38/24) =[(212-81+38)/24] =[(250-81/24)] =(169/24) =[7(1/24)]

Q: Solve: \frac{4}{3} - \frac{1}{2}

\frac{(4 \times 2) - (1 \times 3)}{6} = \frac{8 - 3}{6} = \frac{5}{6}

Maths

example

Addition of like fractions

Fractions which have same denominator are called as like fractions.
For eg:-

\frac{3}{1 6}

and

\frac{7}{1 6}

Let's see how to add them :

\frac{3}{1 6} + \frac{7}{1 6}

Since the denominators are same, we will directly add the numerators and we get

\frac{3}{1 6} + \frac{7}{1 6} = \frac{3 + 7}{1 6} = \frac{1 0}{1 6} = \frac{5 \times 2}{8 \times 2} = \frac{5}{8}

example

Subtraction of like fractions

Take two like fractions of the form

\frac{a}{b}

and

\frac{c}{b}

Now, let's see how to subtract them

\frac{a}{b} - \frac{c}{b}

Since the denominators are same, we will directly subtract the numerators
i.e.

\frac{a}{b} - \frac{c}{b} = \frac{a - c}{b}

For eg:-

\frac{3}{1 6} - \frac{7}{1 6} = \frac{3 - 7}{1 6} = \frac{- 4}{1 6} = \frac{- 1}{4}

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Adding and Subtracting Unlike Fractions

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Addition and Subtraction of Like Fractions

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Addition of like fractions

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Subtraction of like fractions

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Adding and Subtracting Unlike Fractions

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Important Questions

Satypal walks 32​km from a place P towards east and then there 175​km towards west Where will he be now from P ?

Solve: 432​+341​

Divide the sum of (65/12) and (8/3) by their difference.

Simplify: (2/3)+(5/6)-(1/9)

Find the sum (8/9)+(7/12)

Simplify: [8(5/6)]−[3(3/8)]+[1(7/12)]

4+21​+321​+976​.

Solve: 34​−21​

Find the sum 354​+2103​+1151​

Sarita bought 52​ meter of ribbon and Lalita 43​ meter of ribbon. What is the total length of the ribbon they bought?

Satypal walks $\frac{2}{3}$ km from a place P towards east and then there $1 \frac{5}{7}$ km towards west Where will he be now from P ?

Solve:
$4 \frac{2}{3} + 3 \frac{1}{4}$

Divide the sum of $(65 / 12)$ and $(8 / 3)$ by their difference.

Find the sum
(8/9)+(7/12)

Simplify: $[8 (5 / 6)] - [3 (3 / 8)] + [1 (7 / 12)]$

$4 + \frac{1}{2} + 3 \frac{1}{2} + 9 \frac{6}{7}$ .

Solve:
$\frac{4}{3} - \frac{1}{2}$

Find the sum
$3 \frac{4}{5} + 2 \frac{3}{1 0} + 1 \frac{1}{1 5}$

Sarita bought $\frac{2}{5}$ meter of ribbon and Lalita $\frac{3}{4}$ meter of ribbon. What is the total length of the ribbon they bought?