Simplify each of the following and write as a rational number of the form pq-i 34-56-78ii 23-56-79iii -112-76-58iv -45-710-815v -910-2215-13-20vi 53-3-2-73-3

(i) #160;34+56+ 78=1824+2024+ 2124=18+20+( 21)24=18+20 2124=1724(ii) #160;23+ 56+ 79=1218+ 1518+ 1418=12+( 15)+( 14)18=12 15 1418= 1718(iii) #160; 112+76+ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VI

Mathematics

Associative Property

Simplify each...

Question

Simplify each of the following and write as a rational number of the form $\frac{p}{q}$ :
(i) $\frac{3}{4} + \frac{5}{6} + \frac{- 7}{8}$
(ii) $\frac{2}{3} + \frac{- 5}{6} + \frac{- 7}{9}$
(iii) $\frac{- 11}{2} + \frac{7}{6} + \frac{- 5}{8}$
(iv) $\frac{- 4}{5} + \frac{- 7}{10} + \frac{- 8}{15}$
(v) $\frac{- 9}{10} + \frac{22}{15} + \frac{13}{- 20}$
(vi) $\frac{5}{3} + \frac{3}{- 2} + \frac{- 7}{3} + 3$

Open in App

Solution

(i) Given $\frac{3}{4} + \frac{5}{6} + \frac{- 7}{8} = \frac{18 + 20 - 21}{24}$ [LCM of 4, 6, 8 is 24]
$= \frac{17}{24}$
(ii) Given $\frac{2}{3} + \frac{- 5}{6} + \frac{- 7}{9}$ = $\frac{12 - 15 - 14}{18}$
= $\frac{- 17}{18}$
(iii) Given $\frac{- 11}{2} + \frac{7}{6} + \frac{- 5}{8}$ = $\frac{- 132}{24} + \frac{28}{24} + \frac{- 15}{24}$
$= \frac{(- 132) + 28 + (- 15)}{24}$
$= \frac{- 132 + 28 - 15}{24}$
$= \frac{- 119}{24}$
(iv) Given $\frac{- 4}{5} + \frac{- 7}{10} + \frac{- 8}{15}$
$= \frac{(- 24) + (- 21) + (- 16)}{30}$
$= \frac{- 24 - 21 - 16}{30}$
$= \frac{- 61}{30}$
(v) Given $\frac{- 9}{10} + \frac{22}{15} + \frac{13}{- 20}$ $= \frac{- 54}{60} + \frac{88}{60} + \frac{- 39}{60}$
$= \frac{(- 54) + 88 + (- 39)}{60}$
$= \frac{- 54 + 88 - 39}{60}$
$= \frac{- 5}{60} = - \frac{1}{12}$
(vi) Given $\frac{5}{3} + \frac{3}{- 2} + \frac{- 7}{3} + 3 = \frac{10 + (- 9) + (- 14) + 18}{6}$
$= \frac{10 - 9 - 14 + 18}{6}$
$= \frac{5}{6}$

Suggest Corrections

Similar questions

Q. Express each of the following as a rational number of the form

\frac{p}{q} :

(i)

\frac{- 8}{3} + \frac{- 1}{4} + \frac{- 11}{6} + \frac{3}{8} - 3

(ii)

\frac{6}{7} + 1 + \frac{- 7}{9} + \frac{19}{21} + \frac{- 12}{7}

(iii)

\frac{15}{2} + \frac{9}{8} + \frac{- 11}{3} + 6 + \frac{- 7}{6}

(iv)

\frac{- 7}{4} + 0 + \frac{- 9}{5} + \frac{19}{10} + \frac{11}{14}

(v)

\frac{- 7}{4} + \frac{5}{3} + \frac{- 1}{2} + \frac{- 5}{6} + 2

Q. Simplify the following using laws of indices:

(3^{- \frac{1}{2}} \times 2^{- \frac{1}{3}}) \div (3^{- \frac{3}{4}} \times 2^{- \frac{5}{6}})

Q. Simplify each of the following and express each as a rational number:

{(\frac{- 2}{3})}^{5} \times {(\frac{- 3}{7})}^{3}

Q. Simplify each of the following and express each as a rational number:

{(\frac{2}{3})}^{2} \times {(\frac{- 3}{5})}^{3} \times {(\frac{7}{2})}^{2}

Q. Two rational numbers between

\frac{2}{3} and \frac{5}{3}

are
(a)

\frac{1}{6} and \frac{2}{6}

(b)

\frac{1}{2} and \frac{2}{1}

(c)

\frac{5}{6} and \frac{7}{6}

(d)

\frac{2}{3} and \frac{4}{3}

Join BYJU'S Learning Program

Simplify each of the following and write as a rational number of the form pq:(i) 34+56+−78(ii) 23+−56+−79(iii) −112+76+−58(iv) −45+−710+−815(v) −910+2215+13−20(vi) 53+3−2+−73+3