Question
Find $\frac{3}{7}+\left(\frac{-6}{11}\right)+\left(\frac{-8}{21}\right)+\left(\frac{5}{22}\right)$
✓
Answer
We have, $\frac{3}{7}+\left(\frac{-6}{11}\right)+\left(\frac{-8}{21}\right)+\left(\frac{5}{22}\right)$
$=\frac{198}{462}+\left(\frac{-252}{462}\right)+\left(\frac{-176}{462}\right)+\left(\frac{105}{462}\right)$[$\because$ $462$ is the $LCM$ of $7, 11, 21$ and $22$]
$=\frac{198-252-176+105}{462}$
$=\frac{-125}{462}$
Alternatively: We can also solve it as.
$\frac{3}{7}+\left(\frac{-6}{11}\right)+\left(\frac{-8}{21}\right)+\frac{5}{22}$
$=\left[\frac{3}{7}+\left(\frac{-8}{21}\right)\right]+\left[\frac{-6}{11}+\frac{5}{22}\right]$
$=\left[\frac{9+(-8)}{21}\right]+\left[\frac{-12+5}{22}\right]$[$\because$$LCM$ of $7$ and $21$ is $21$; $LCM$ of $11$ and $22$ is $22$]
$=\frac{1}{21}+\left(\frac{-7}{22}\right)$
$=\frac{22-147}{462}$
$=\frac{-125}{462}$
$=\frac{198}{462}+\left(\frac{-252}{462}\right)+\left(\frac{-176}{462}\right)+\left(\frac{105}{462}\right)$[$\because$ $462$ is the $LCM$ of $7, 11, 21$ and $22$]
$=\frac{198-252-176+105}{462}$
$=\frac{-125}{462}$
Alternatively: We can also solve it as.
$\frac{3}{7}+\left(\frac{-6}{11}\right)+\left(\frac{-8}{21}\right)+\frac{5}{22}$
$=\left[\frac{3}{7}+\left(\frac{-8}{21}\right)\right]+\left[\frac{-6}{11}+\frac{5}{22}\right]$
$=\left[\frac{9+(-8)}{21}\right]+\left[\frac{-12+5}{22}\right]$[$\because$$LCM$ of $7$ and $21$ is $21$; $LCM$ of $11$ and $22$ is $22$]
$=\frac{1}{21}+\left(\frac{-7}{22}\right)$
$=\frac{22-147}{462}$
$=\frac{-125}{462}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Gunpowder contains $75\%$ nitre and $10\%$ sulphur. Find the amount of the gunpowder which carrier $9\ kg$ nitre. What amount of gunpowder would contain $2.3\ kg$ sulphur?
→If from a two-digit number, we subtract the number formed by reversing its digits then the result so obtained is a perfect cube. How many such numbers are possible? Write all of them.
The external dimensions of a closed wooden box are $62\ cm, 30\ cm$ and $18\ cm$. If the box is made of $2\ cm$-thick wood, find the capacity of the box.
→Find the amount of $Rs. 4096$ for $18$ months at $12\frac{1}{2}\%$ per annum, the interest being compounded semi-annually
→Diagonals of parallelogram $\text{ABCD}$ intersect at $O$ as shown in the figure. $\text{XY}$ contains $O$, and $\text{X, Y}$ are points on opposite sides of the parallelogram. Give reasons for each of the following:
$i. \text{OB}=\text{OD}$
$ii. \angle\text{OBY}=\angle\text{ ODX}$
$iii. \angle\text{BOY}=\angle\text{DOX}$
$iv. \triangle\text{BOY}=\triangle\text{DOX}$
Now, state if $\text{XY}$ is bisected at $O$.
→$i. \text{OB}=\text{OD}$
$ii. \angle\text{OBY}=\angle\text{ ODX}$
$iii. \angle\text{BOY}=\angle\text{DOX}$
$iv. \triangle\text{BOY}=\triangle\text{DOX}$
Now, state if $\text{XY}$ is bisected at $O$.
The area of a trapezium is $216m^2$ and its height is $12m.$ If one of the parallel sides is $14m$ less than the other, find the length of each of the parallel sides.
→Harpreet borrowed $Rs. 20000$ from her friend at $12\%$ per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after $2$ years.
→Living on your own, Sanjay is looking for one bedroom apartment on rent. At Neelgiri apartments, rent for the first two months is $20\%$ off. The one bedroom rate at Neelgiri is ₹ 6000 per month.
At Savana apartments the first month is $50\%$ off. The one bedroom rate at Savana apartments is ₹ $7000$ per month. Which apartment will be cheaper for the first two months and by how much?
→At Savana apartments the first month is $50\%$ off. The one bedroom rate at Savana apartments is ₹ $7000$ per month. Which apartment will be cheaper for the first two months and by how much?
Divide the following polygons into parts (triangles and trapezium) to find out its area.
Multiply the following :
$\left(x^2-5 x+6\right),(2 x+7)$
→$\left(x^2-5 x+6\right),(2 x+7)$