37+( 611)+( 811)+(522) =198462+( 252462)+( 176462)+(105462) (Note that 462 is the LCM of 7, 11, 21, and 22) =198 252 176+105462= 125462 We can also solve it ...

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Commutative Property

Find 37+-611+...

Question

Find $\frac{3}{7} + (\frac{- 6}{11}) + (\frac{- 8}{21}) + (\frac{5}{22})$ .

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Solution

$\frac{3}{7} + (\frac{- 6}{11}) + (\frac{- 8}{11}) + (\frac{5}{22})$

$= \frac{198}{462} + (\frac{- 252}{462}) + (\frac{- 176}{462}) + (\frac{105}{462})$

(Note that 462 is the LCM of 7, 11, 21, and 22)

$= \frac{198 - 252 - 176 + 105}{462} = \frac{- 125}{462}$

We can also solve it as

$\frac{3}{7} + (\frac{- 6}{11}) + (\frac{- 8}{11}) + \frac{5}{22} = [\frac{3}{7} + (\frac{- 8}{21})] + [\frac{- 6}{11} + \frac{5}{22}]$

(by using commutative and associativity)

$= [\frac{9 + (- 8)}{21}] + [\frac{- 12 + 5}{22}] = \frac{1}{21} + (\frac{- 7}{22}) = \frac{22 - 147}{462} = \frac{- 125}{462}$

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Similar questions

Simplify: 3/7+(−6/11)+(−8/21)+5/22

Find: $\frac{5}{22} + \frac{3}{7} - \frac{8}{21} - \frac{6}{7}$

$\frac{3}{7} + (\frac{- 6}{11}) + (\frac{- 8}{21}) + (\frac{5}{22})$ $= (\frac{- 125}{462})$ . If true enter $1$ else $0$ .

Simplify:

(1)

(2)

(3)

(4)

(5)

(6)

Q. A student was asked to simplify the following

\frac{7}{5 - 2 \frac{2}{3}} \div \frac{3 - \frac{2}{3 - 1 \frac{1}{2}}}{4 - 1 \frac{1}{2}} - \frac{5}{7} \times ⎡ ⎣ \frac{7}{10} + 1 \frac{1}{5} \times \frac{3 \frac{1}{3} - 2 \frac{1}{2}}{2 \frac{5}{21} - 2} ⎤ ⎦

+ \frac{\frac{3}{1.6} + \frac{5}{3.2}}{\frac{5}{4.8} + \frac{1}{9.6}}

His answer was

3 \frac{1}{5}

Find the percentage error in the answer.

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Find 37+(−611)+(−821)+(522).

Find $\frac{3}{7} + (\frac{- 6}{11}) + (\frac{- 8}{21}) + (\frac{5}{22})$ .