Exercise 3D
Q1 | Ex-3D | Class 7 | Rational Numbers | SChand | New Learning Composite Maths | Chapter 4 | myhelper
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Question 1
Find Each Sum
(a) $\frac{1}{2}+\left(\frac{7}{-8}\right)$
Sol :
$=\frac{1}{2} -\frac{7}{8}$
$=\frac{4-7}{8}=\frac{-3}{8}$
(b) $-\frac{1}{4}+\left(\frac{7}{-12}\right)$
Sol :
$=\frac{-1}{4}-\frac{7}{12}$
$=\frac{-3-7}{12}=\frac{-10}{12}$
$=\frac{-5}{6}$
(c) $\frac{43}{5}+\left(-\frac{71}{10}\right)$
Sol :
$=\frac{43}{5}-\frac{71}{70}$
$=\frac{86-71}{10}=\frac{15}{10}=\frac{3}{2}$
(d) $-1\frac{7}{15}+\left(-\frac{19}{30}\right)$
Sol :
$=-\frac{22}{15}-\frac{19}{30}$
$=\frac{-44-19}{30}=\frac{-63}{30}$
$=-2\frac{1}{10}$
Q2 | Ex-3D | Class 7 | Rational Numbers | SChand | New Learning Composite Maths | Chapter 4 | myhelper
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Question 2
Subtract:
(a) $\frac{1}{13} \text{ from } -\frac{5}{26}$
Sol :
$=\frac{-5}{26}-\frac{1}{13}$
$=\frac{-5\times 1-1\times 2}{26}$
$=\frac{-5-2}{26}=-\frac{7}{26}$
(b) $\frac{8}{-15} \text{from } \frac{-11}{30}$
Sol :
$=\frac{-11}{30}-\left(\frac{8}{-15}\right)$
$=\frac{-11}{30}+\frac{8}{15}$
$=\frac{-11\times 1+8\times 2}{30}=\frac{-11+16}{30}$
$=\frac{+5}{30}=\frac{1}{6}$
(c) $1\frac{4}{25} \text{ from } -3\frac{7}{50}$
Sol :
$=-3\frac{7}{50}-1\frac{4}{25}$
$=-\frac{157}{50}-\frac{29}{25}$
$=-\frac{215}{50}=-\frac{43}{10}$
(d) $-1\frac{3}{11} \text{ from } 3\frac{5}{22}$
Sol :
$=3\frac{5}{22}-\left(-1\frac{3}{11}\right)$
$=\frac{71}{22}+\frac{14}{11}$
$=\frac{99}{22}=4\frac{1}{2}$
Q3 | Ex-3D | Class 7 | Rational Numbers | SChand | New Learning Composite Maths | Chapter 4 | myhelper
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Question 3
Add.
(a) $\frac{7}{-8} \text{ and } \frac{5}{11}$
Sol :
$=\frac{7}{-8}+\frac{5}{11}=\frac{-77+40}{88}$
$=-\frac{37}{88}$
(b) $1\frac{2}{3} \text{ and } -2\frac{1}{5}$
Sol :
$=\frac{5}{3}-\frac{11}{5}$
$=\frac{25-33}{15}=-\frac{8}{15}$
(c) $-1\frac{3}{7} \text{ and } 1\frac{3}{8}$
Sol :
$=-1\frac{3}{7}+1\frac{3}{8}$
$=\frac{10}{7}+\frac{11}{8}$
$=\frac{-80-77}{56}$
$=-\frac{3}{56}$
(d) $-14 \frac{7}{11} \text{ and } -35\frac{9}{10}$
Sol :
$=-14\frac{7}{11}+\left(-35\frac{9}{10}\right)$
$=\frac{-161}{11}-\frac{359}{10}$
$=\frac{-5559}{110}=-50\frac{59}{110}$
Q4 | Ex-3D | Class 7 | Rational Numbers | SChand | New Learning Composite Maths | Chapter 4 | myhelper
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Question 4
(a) $\frac{3}{7} \text{ from } \frac{5}{-9}$
Sol :
$=\frac{5}{-9}-\frac{3}{7}$
$=-\frac{5}{9}-\frac{3}{7}$
$=\frac{-35-27}{63}=\frac{-62}{63}$
(b) $\frac{-9}{22} \text{ from } \frac{-5}{21}$
Sol :
$=-\frac{5}{21}-\left(-\frac{9}{22}\right)$
$=-\frac{5}{21}+\frac{9}{22}$
$=\frac{-110+189}{462}$
$=\frac{79}{462}$
(c) $-1\frac{1}{7} \text{ and } -2\frac{3}{10}$
Sol :
$=-2\frac{3}{10}-\left(-1\frac{1}{7}\right)$
$=-\frac{23}{10}+\frac{8}{7}$
$=\frac{-161+80}{70}=-\frac{81}{70}$
$=-1\frac{11}{70}$
(d) $-6\frac{5}{8} \text{ from } 1\frac{4}{11}$
Sol :
$=\frac{15}{11}+\frac{53}{8}$
$=\frac{120+583}{88}=\frac{703}{88}$
$=7\frac{87}{88}$
Q5 | Ex-3D | Class 7 | Rational Numbers | SChand | New Learning Composite Maths | Chapter 4 | myhelper
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Question 5
Find the sum.
(a) $\frac{-17}{20}+\left(-\frac{19}{25}\right)$
Sol :
$=-\frac{17}{20}-\frac{19}{25}$
$=\frac{-85-76}{100}=\frac{-161}{100}$
$=-1\frac{61}{100}$
(b) $1\frac{5}{8}+\frac{9}{-12}$
Sol :
$=1\frac{5}{8}+\frac{9}{-12}$
$=\frac{13}{8}-\frac{9}{12}$
$=\frac{39-18}{24}=\frac{21}{24}$
(c) $-2\frac{5}{6}+2\frac{9}{14}$
Sol :
$=-\frac{17}{6}+\frac{37}{14}$
$=\frac{-119+111}{42}$
$=-\frac{8}{42}$
$=-\frac{4}{21}$
Q6 | Ex-3D | Class 7 | Rational Numbers | SChand | New Learning Composite Maths | Chapter 4 | myhelper
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Question 6
Subtract:
(a) $-1\frac{3}{8} \text{ from } 5\frac{7}{12}$
Sol :
$=\frac{67}{12}+\frac{11}{8}$
$=\frac{134+33}{24}$
$=\frac{167}{24}=6\frac{23}{24}$
(b) $-1\frac{4}{15} \text{ from } \frac{11}{-20}$
Sol :
$=\frac{11}{-20} -\left(-1\frac{4}{15}\right)$
$=-\frac{11}{20}+\frac{19}{15}$
$=\frac{-33+76}{60}=\frac{43}{60}$
(c) $4\frac{7}{10} \text{ from } \frac{18}{-25}$
Sol :
$=\frac{18}{-25}-4\frac{7}{10}$
$=\frac{-8}{25}-\frac{47}{10}$
$=\frac{-36-235}{50}=\frac{-271}{50}$
$=-5\frac{21}{50}$
Q7 | Ex-3D | Class 7 | Rational Numbers | SChand | New Learning Composite Maths | Chapter 4 | myhelper
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Question 7
Simplify:
(a) $-10+ \left(-6\frac{1}{5}\right)$
Sol :
$=-16\frac{1}{5}$
(b) $-\frac{19}{80}-(-3)$
Sol :
$=2\frac{61}{80}$
(c) $\frac{18}{-19}+1\frac{1}{38}-2\frac{7}{57}$
Sol :
$=-2\frac{5}{114}$
(d) $-\frac{5}{17}+\left(-\frac{2}{5}\right)$
Sol :
$=\frac{-59}{85}$
(e) $6 + \frac{9}{-11}$
Sol :
$=5\frac{2}{11}$
(f) $-\frac{5}{18}+\frac{17}{-24}+1\frac{29}{36}– 2$
Sol :
$=\frac{-85}{72}$
Q8 | Ex-3D | Class 7 | Rational Numbers | SChand | New Learning Composite Maths | Chapter 4 | myhelper
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Question 8
$\frac{5}{-9}-\frac{7}{-12}-2-\left(-\frac{-5}{-6}\right)$
Sol :
$=-\frac{5}{9}+\frac{7}{12}-2+\frac{5}{6}$
$=\frac{-20-21-72+30}{36}=-\frac{41}{36}=-1\frac{5}{36}$
Q9 | Ex-3D | Class 7 | Rational Numbers | SChand | New Learning Composite Maths | Chapter 4 | myhelper
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Question 9
Subtract $\left(\frac{3}{7}+\frac{5}{-9}\right)$ from the negative of $\frac{8}{-63}$
Sol :
$\frac{8}{-63}-\left(\frac{3}{7}+\frac{5}{-9}\right)$
$=-\frac{8}{63}-\left(\frac{3}{7}-\frac{5}{9}\right)$
$=\frac{-8}{63}-\frac{3}{7}+\frac{5}{9}$
$=\frac{-8-27+35}{63}$
=0
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