Question

simplification of 3/7 +-6/11+-8/21+5/22​

Answer 1

★ How to do :-

Here, we are given with four fractions in which we are asked to simplify those all fractions. We are given with only one mathematical sign that is the addition sign. We should add all those fractions together. As we know that we cannot add the fractions directly. First, we should convert the unlike fractions to like fractions by the method of taking LCM of all the denominators. Then, we can only add the numerators. But, in this question we solve this question differently. We use an other method called as the rearrangement property. In this method, we can rearrange the given fraction as we want according to the denominators of all fractions. Then, we group two numbers each in a bracket to solve them separately. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \dfrac{3}{7} + \dfrac{(-6)}{11} + \dfrac{(-8)}{21} + \dfrac{5}{22}}$

Rearrange the fractions as we want.

${\sf \leadsto \bigg( \dfrac{3}{7} + \dfrac{(-8)}{21} \bigg) + \bigg( \dfrac{(-6)}{11} + \dfrac{5}{22} \bigg)}$

LCM of 7 and 21 is 21.

LCM of 11 and 22 is 22.

${\sf \leadsto \bigg( \dfrac{3 \times 3}{7 \times 3} + \dfrac{(-8)}{21} \bigg) + \bigg( \dfrac{(-6) \times 2}{11 \times 2} + \dfrac{5}{22} \bigg)}$

Multiply the numerators and denominators of both fractions.

${\sf \leadsto \bigg( \dfrac{9}{21} + \dfrac{(-8)}{21} \bigg) + \bigg( \dfrac{(-12)}{22} + \dfrac{5}{22} \bigg)}$

Write both numerators with a common denominator.

${\sf \leadsto \bigg( \dfrac{9 + (-8)}{21} \bigg) + \bigg( \dfrac{(-12) + 5}{22} \bigg)}$

Add the numbers on both brackets.

${\sf \leadsto \dfrac{1}{21} + \dfrac{(-7)}{22}}$

LCM of 21 and 22 is 462.

${\sf \leadsto \dfrac{1 \times 22}{21 \times 22} + \dfrac{(-7) \times 21}{22 \times 21}}$

Multiply the numerators and denominators of both fractions.

${\sf \leadsto \dfrac{22}{462} + \dfrac{(-147)}{462}}$

Write the second number with one sign.

${\sf \leadsto \dfrac{22 + (-147)}{462} = \dfrac{22 - 147}{462}}$

Subtract the numbers.

${\sf \leadsto \dfrac{(-125)}{462}}$

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${\red{\underline{\boxed{\bf So, \: the \: answer \: when \: simplified \: is \: \dfrac{(-125)}{462}.}}}}$

Answer 2

ƛղʂաҽɾ :-

⛄ɢɪᴠᴇɴ⛄

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• $\dfrac{3}{7} + \dfrac{( - 6)}{11}+ \dfrac{( - 8)}{21} + \dfrac{5}{22}$

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⛄ᴛᴏ ꜰɪɴᴅ⛄

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• ᴛʜᴇ ꜱɪᴍᴘʟɪꜰɪᴇᴅ ᴀɴꜱᴡᴇʀ.

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ʂσɭυƚıσɳ :-

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ʀᴇᴀʀʀᴀɴɢᴇ ᴛʜᴇ ɢɪᴠᴇɴ ꜰʀᴀᴄᴛɪᴏɴ:-

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$\hookrightarrow ( \dfrac{3}{7} + \dfrac{( - 8)}{21} ) + ( \dfrac{( - 6)}{11} + \dfrac{ 5}{22} )$

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➥ʟᴄᴍ ᴏꜰ 7 & 21 ɪꜱ 21

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$\hookrightarrow ( \dfrac{3 \times 3}{7 \times 3} ) + (\dfrac{( - 8)}{21} )$

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$\hookrightarrow \dfrac{9}{21} + \dfrac{( - 8)}{21}$

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➥ ʟᴄᴍ ᴏꜰ 11 & 22 ɪꜱ 22

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$\hookrightarrow \dfrac{( - 6 \times 2)}{11 \times 2} + \dfrac{5}{22}$

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$\hookrightarrow \dfrac{( - 12)}{22} + \dfrac{5}{22}$

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ᴡʀɪᴛᴇ ʙᴏᴛʜ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀꜱ ᴡɪᴛʜ ᴀ ᴄᴏᴍᴍᴏɴ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ

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$\hookrightarrow \dfrac{ 9 + ( - 8)}{21} + \dfrac{( - 12) + 5}{22}$

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ᴀᴅᴅ ᴛʜᴇ ɴᴜᴍʙᴇʀꜱ

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$\hookrightarrow \dfrac{1}{21} + \dfrac{( - 7)}{22}$

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ʟᴄᴍ ᴏꜰ 21 & 22 ɪꜱ 462

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$\hookrightarrow \dfrac{1 \times 22}{21 \times 22} + \dfrac{( - 7) \times 21}{22 \times 21}$

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$\hookrightarrow \dfrac{22}{462} + \dfrac{( -147 )}{462}$

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$\hookrightarrow \dfrac{22 + ( - )}{462}$

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$= \dfrac{ - 125}{462}$

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