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Maths 3 Marks Question

Rational Numbers · CBSE STD 7 (CBSE - English Medium). 71 questions.

Questions · Page 2 of 2

3 Marks Question

Question 513 Marks
Which of the two rational numbers is greater in the following pairs? $\frac{7}{-9}\text{ or }\frac{-5}{8}$
Answer
$\frac{7}{-9}\text{ or }\frac{-5}{8}$
$\Rightarrow\frac{7\times(-1)}{-9\times(-1)}\text{ or }\frac{-5}{8}$
$\Rightarrow\frac{-7}{9}\text{ or }\frac{-5}{8}$ (Making denominator positive)
$LCM$ of $9$ and $8 = 72$
$\therefore\frac{-7}{9}=\frac{-7\times8}{9\times8}=\frac{-56}{72}$
$\frac{-5}{8}=\frac{-5\times9}{8\times9}=\frac{-45}{72}$
It is clear that $\frac{-45}{72}\text{ or }\frac{-5}{8}$ is greater.
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Question 523 Marks
By what number should $\frac{-8}{15}$ be multiplied to get $24$?
Answer
The required number $=24\div\Big(\frac{-8}{15}\Big)$
$=24\times\frac{15}{-8}$
$=24\times\frac{15\times(-1)}{-8\times(-1)}$
$=24\times\frac{(-15)}{-8}$
$=3\times(-15)$
$=-45$
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Question 533 Marks
What should be added to $\frac{-3}{8}$ to get $\frac{5}{12}?$
Answer
Required number $=\frac{5}{12}-\Big(\frac{-3}{8}\Big)$
$=\frac{5}{12}+\frac{3}{8}=\frac{10+9}{24}$ $(LCM$ of $12, 8 = 24)$ $=\frac{19}{24}$
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Question 543 Marks
Subtract: $\frac{-18}{11}\text{ from }1$
Answer
$\frac{-18}{11}\text{ from }1$$\frac{1}{1}=\frac{1\times11}{1\times11}=\frac{11}{11}$
$\therefore1-\Big(\frac{-18}{11}\Big)=1+\frac{18}{11}$
$\frac{11}{11}+\frac{18}{11}=\frac{11+18}{11}=\frac{29}{11}$
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Question 553 Marks
Which of the two rational numbers is greater in the following pairs? $\frac{-12}{5}\text{ or }-3$
Answer
$\frac{-12}{5}\text{ or }-3$
$\frac{-12}{5}\text{ or }\frac{-12}{5}$
$LCM$ of $5$ and $1 = 5$
$\frac{-3}{1}=\frac{-3\times5}{1\times5}=\frac{-15}{5}$
It is clear that $\frac{-12}{5}$ is greater.
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Question 563 Marks
The cost of $2\frac{1}{2}\text{ metres}$ of cloth is $\text{Rs. }78\frac{3}{4}.$ Find the cost of cloth per metre.
Answer
Cost of $2\frac{1}{2}\text{m or }\frac{5}{2}\text{m}$ of Cloth $\text{Rs. }78\frac{3}{4}$
$=\text{Rs. }\frac{315}{4}$
$\therefore$ Cost of one metre of cloth $=\text{Rs. }\frac{315}{4}\div\frac{5}{2}$
$=\text{Rs. }\frac{315}{4}\times\frac{2}{5}$
$=\text{Rs. }\frac{63}{2}$
$=\text{Rs. }31\frac{1}{2}$
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Question 573 Marks
Which of the two rational numbers is greater in the following pairs? $\frac{4}{-5}\text{ or }\frac{-7}{8}$
Answer
$\frac{4}{-5}\text{ or }\frac{-7}{8}$
$\Rightarrow\frac{4\times(-1)}{-5\times(-1)}\text{ or }\frac{-7}{8}$
$\Rightarrow\frac{-4}{5}\text{ or }\frac{-7}{8}$ (Making denominator positive) $LCM$ of $5$ and $8 = 40$
$\therefore\frac{-4}{5}=\frac{-4\times8}{5\times8}=\frac{-32}{40}$ and $\frac{-4}{5}=\frac{-7\times5}{5\times8}=\frac{-32}{40}$
It is clear that $\frac{-32}{40}\text{ or }\frac{4}{-5}\text{ or }\frac{4}{-5}$ is greater.
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Question 583 Marks
Evaluate:
$\frac{14}{15}-\frac{13}{20}$
Answer
$\frac{14}{15}-\frac{13}{20}$
$LCM$ of $15$ and $20 = 60$
$\therefore\frac{14}{15}=\frac{14\times4}{15\times4}=\frac{56}{60}$
$\frac{13}{20}=\frac{13\times3}{20\times3}=\frac{39}{60}$
$\therefore\frac{14}{15}-\frac{13}{20}$
$=\frac{56}{60}-\frac{39}{60}$
$=\frac{56-39}{60}$
$=\frac{17}{60}$
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Question 593 Marks
The sum of two rational numbers is $-4$. If one of them is $\frac{-11}{6}$, find other.
Answer
Let the required number be $x$ $\text{x}+\Big(\frac{-11}{6}\Big)=-4$
$\Rightarrow\text{x}=(-4)-\Big(\frac{-11}{6}\Big)$
$=-4+\frac{11}{6}$
$=\frac{-24+11}{6}$
$=\frac{-13}{6}$
Hence, the other number is $\frac{-13}{6}$
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Question 603 Marks
Evaluate: $\frac{-5}{14}-\frac{-2}{7}$
Answer
$\frac{-5}{14}-\frac{-2}{7}$
$LCM$ of $14$ and $7 = 14$
​​​​​​​ $\therefore\frac{-2}{7}=\frac{-2\times2}{7\times2}=\frac{-4}{14}$
$\therefore\frac{-5}{14}-\frac{-2}{7}$
$=\frac{-5}{14}-\Big(\frac{-4}{14}\Big)$
$=\frac{-5}{14}+\frac{4}{14}$
$=\frac{-5+4}{14}$
$=\frac{-1}{14}$
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Question 613 Marks
The product of two rational numbers is $-9$. If one of the numbers is $-12$, find the other.
Answer
Product of two rational numbers $= -9$
One number $= -12$
Second number $= (-9) ÷ (-12)$
$=-9\times\frac{-1}{12}\Big\{\because\frac{1}{-12}=\frac{1\times(-1)}{-12\times(-1)}=\frac{-1}{12}\Big\}$
$=\frac{3}{4}$
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Question 623 Marks
If $24$ pairs of trousers of equal size can be prepared with $54m$ of cloth, what length of cloth is required for each pair of trousers?
Answer
Cloth required for $24$ pairs of trousers $= 54m$
Cloth required for one pair $= (54 ÷ 24)m$ $=54\times\frac{1}{24}=\frac{9}{4}\text{m}$ $=2\frac{1}{4}\text{m}$
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Question 633 Marks
Add the following rational numbers:
$\frac{-5}{9}\text{ and }\frac{2}{3}$
Answer
$\frac{-5}{9}\text{ and }\frac{2}{3}$
$\frac{2}{3}=\frac{2\times3}{3\times3}=\frac{6}{9}$
$\therefore\frac{-5}{9}+\frac{2}{3}=\frac{-5}{9}+\frac{6}{9}$
$=\frac{-5+6}{9}=\frac{1}{9}$
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Question 643 Marks
Simplify: $\frac{-9}{11}+\frac{2}{3}+\frac{-3}{4}$
Answer
$\frac{-9}{11}+\frac{2}{3}+\frac{-3}{4}$
$LCM$ of $11, 3, 4 = 11 \times 3 \times 4 = 132$
$\therefore\frac{-9}{11}=\frac{-9\times12}{11\times12}=\frac{-108}{132}$
$\frac{2}{3}=\frac{2\times44}{3\times44}=\frac{88}{132}$
$\frac{-3}{4}=\frac{-3\times33}{4\times33}=\frac{-99}{132}$
$\therefore\frac{-9}{11}+\frac{2}{3}+\frac{-3}{4}$
$=\frac{-108}{132}+\frac{88}{132}+\frac{-99}{132}$
$=\frac{-108+88+(-99)}{132}$
$=\frac{-108+88-99}{132}$
$=\frac{-207+88}{132}$$=\frac{-119}{132}$
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Question 653 Marks
The product of two rational numbers is $10$. If one of the numbers is $-8$, find the other.
Answer
Product of two number $= 10$ One number $= -8$
Second number $= 10 ÷ (-8)$ $=10\times\frac{1\times(-1)}{-8}$
$=10\times\frac{1\times(-1)}{8}$
$=\frac{-10}{8}-\frac{-5}{4}$
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Question 663 Marks
Express the following rational numbers in standard form:
$\frac{84}{-147}$
Answer
$\frac{84}{-147}$Converting the number to a positive denominator:
$=\frac{84\times(-1)}{-147\times(-1)}=\frac{-84}{147}$
$H.C.F.$ of $84$ and $147$ is $21$
 Dividing both the numerator and the denominator by $21$
$=\frac{-84\div(21)}{147\div(21)}$
$=\frac{-4}{7}$
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Question 673 Marks
Add the following rational numbers: $\frac{-7}{27}\text{ and }\frac{5}{18}$
Answer
$\frac{-7}{27}\text{ and }\frac{5}{18}$
$\frac{-7}{27}=\frac{-7\times2}{27\times2}=\frac{-14}{54}$
$(\because\text{LCM }\text{of }27,18=54)$
$\frac{5}{18}=\frac{5\times3}{18\times3}=\frac{15}{54}$
$\therefore\frac{-7}{27}+\frac{5}{8}=\frac{-14}{54}+\frac{15}{54}$
$=\frac{-14+15}{54}=\frac{1}{54}$
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Question 683 Marks
Add the following rational numbers: $\frac{1}{9}\text{ and }\frac{4}{-27}$
Answer
$\frac{1}{9}\text{ and }\frac{4}{-27}$
$\frac{-1}{9}=\frac{1\times(-1)}{-9\times(-1)}=\frac{-1}{9}$
$=\frac{-1\times3}{9\times3}=\frac{-3}{27}$
$\frac{4}{-27}=\frac{4\times(-1)}{-27\times(-1)}=\frac{-4}{27}$
$=\frac{-3+(-4)}{27}=\frac{-3-4}{27}$
$=\frac{-7}{27}$
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Question 693 Marks
What are rational numbers? Give examples of five positive and five negative rational numbers. Is there any rational number which is neither positive nor negative? Name it.
Answer
$i.$ Rational numbers: The numbers of the form $\frac{\text{p}}{\text{q}}$ where $p$ and $q$ are integers and $\text{q}\neq0$ are called rational numbers.
$ii.$ Positive rational numbers: $\frac{3}{4},\frac{7}{8},\frac{15}{11}$$\frac{-3}{-5},\frac{-9}{-4}$
$iii.$ Negative rational numbers: $\frac{-5}{7},\frac{-3}{8}$ $\frac{11}{-5},\frac{13}{-7},\frac{-8}{3}$
Yes, there is one rational number $(0)$ which is neither positive nor negative.
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Question 703 Marks
The sum of two rational numbers is $-3$ If one of them is $\frac{-15}{6}$ find the other.
Answer
Sum of two numbers $= -3$ One number $=\frac{-15}{7}$
$\therefore$ second number $=-3-\Big(\frac{-15}{7}\Big)$
$=\frac{-3}{1}+\frac{15}{7}$
$=\frac{-21+15}{7}=\frac{-6}{7}$
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Question 713 Marks
Divide the sum $\frac{65}{12}$ and $\frac{8}{3}$ by their difference.
Answer
Sum $=\frac{65}{12}+\frac{8}{3}=\frac{65+32}{12}=\frac{97}{12}$Difference $=\frac{65}{12}-\frac{8}{3}=\frac{65-32}{12}=\frac{33}{12}$
$=\frac{97}{12}\div=\frac{33}{12}$
$=\frac{97}{12}\times=\frac{12}{33}$
$=\frac{97}{33}$
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