Question 11 Mark
Add the following rational numbers.
$0\ \text{and}\ \frac{-2}{5}$
AnswerWe can write $0\ \text{as}\ \frac{0}{1}$
The denominators of the given rational number are $1$ and $4.$
$LCM$ of $1$ and $5$ is $5,$ that is, $(1 × 5)$
Now,
$\frac{0}{1}=\frac{0\times5}{1\times5}$
$=\frac{0}{5}$
and $\frac{-2}{5}=\frac{-2\times1}{5\times1}$
$=\frac{-2}{5}$
$\therefore0+ \frac{(-2)}{5}$
$=\frac{0}{5}+\frac{(-2)}{5}$
$=\frac{0+(-2)}{5}$
$=\frac{0-2}{5}$
$=\frac{-2}{5}$
View full question & answer→Question 21 Mark
Add the following rational numbers. $\frac{5}{8}\ \text{and}\ \frac{-7}{12}$
AnswerThe denominators of the given rational number are $8$ and $12.$
$LCM$ of $8, 12$ is $24$
Now,
$\frac{5}{8}=\frac{5\times3}{8\times3}$
$=\frac{15}{24}$
and $\frac{-7}{12}=\frac{-7\times2}{12\times2}$
$=\frac{-14}{24}$
$\therefore\frac{5}{8}+\frac{-7}{12}$
$=\frac{15}{24}+\frac{-14}{24}$
$=\frac{15+(-14)}{24}$
$=\frac{15-14}{24}$
$=\frac{1}{24}$
View full question & answer→Question 31 Mark
Can we divide $1$ by $0?$
AnswerNo, It is not possible to divide any number by zero.
View full question & answer→Question 41 Mark
Fill in the blank: The reciprocal of $a,$ where $a ≠ 0,$ is _________.
AnswerThe reciprocal of a where $a\ \#\ 0,$ is $\frac{1}{\text{a}}$
View full question & answer→Question 51 Mark
Add the following rational numbers. $\frac{3}{4}\ \text{and}\ \frac{-3}{5}$
AnswerThe denominators of the given rational number are $4$ and $5.$
$LCM$ of $4, 5$ is $20$
Now,
$\frac{3}{4}=\frac{3\times5}{4\times5}$
$=\frac{15}{20}$
and $\frac{-3}{5}=\frac{-3\times4}{5\times4}$
$=\frac{-12}{20}$
$\therefore\frac{3}{4}+\Big(\frac{-3}{5}\Big)$
$=\frac{15}{20}+\frac{-12}{20}$
$=\frac{15+(-12)}{20}$
$=\frac{15-12}{20}$
$=\frac{3}{20}$
View full question & answer→Question 61 Mark
Name the property of multiplication shown by the following statement: $\Big(\frac{-2}{3}\times\frac{7}{8}\Big)\times\frac{-5}{7}=\frac{-2}{3}\times\Big(\frac{7}{8}\times\frac{-5}{7}\Big)$
AnswerAssociative law of multiplication.
View full question & answer→Question 71 Mark
Fill in the blank: Zero has ___________ reciprocal.
Question 81 Mark
Fill in the blanks with the correct symbol out of $>, =$ and <. $0\ ....\ \frac{-3}{-5}$
AnswerBetween $0\ \text{and}\ \frac{-3}{-5}$ It is clear that $0$ is greater than $\frac{-3}{-5}$or $0>\frac{-3}{-5}$
View full question & answer→Question 91 Mark
Name the property of multiplication shown by the following statement:
$\frac{-8}{15}\times1=\frac{-8}{15}$
Answer Existence of multiplicative identity.
View full question & answer→Question 101 Mark
Which of the following statement are true and which are false? Every integer is a rational number.
AnswerTrue.Solution:
As the set of integers is a subset of the set of rational numbers.
View full question & answer→Question 111 Mark
Fill in the blank: Zero is ________ the reciprocal of any number.
AnswerZero is not the reciprocal of any number.
View full question & answer→Question 121 Mark
Add the following rational numbers. $\frac{1}{-12}\ \text{and}\ \frac{2}{-15}$
AnswerWe will first write each of the given numbers with positive denominators.
$\frac{1}{-12}=\frac{1\times(-1)}{-12\times(-1)}$
$=\frac{-1}{12}$
and $\frac{2}{-15}=\frac{2\times(-1)}{-15\times(-1)}$
$=\frac{-2}{15}$
The denominators of the given rational number are $12$ and $15.$
$LCM$ of $12, 15$ is $60$
Now,
$\frac{-1}{12}=\frac{-1\times5}{12\times5}$
$=\frac{-5}{60}$
and $\frac{-2}{15}=\frac{2\times4}{15\times4}$
$=\frac{-8}{60}$
$\therefore\frac{1}{-12}+\frac{2}{-15}$
$=\frac{-5}{60}+\frac{-8}{60}$
$=\frac{-5+(-8)}{60}$
$=\frac{-5-8}{60}$
$=\frac{-13}{60}$
View full question & answer→Question 131 Mark
Add the following rational numbers. $\frac{7}{-18}\ \text{and}\ \frac{8}{27}$
AnswerWe will first write each of the given numbers with positive denominators.
$\frac{7}{-18}=\frac{7\times(-1)}{-18\times(-1)}=\frac{-7}{18}$
The denominators of the given rational number are $18$ and $27.$
$LCM$ of $18, 27$ is $54$
Now,
$\frac{-7}{18}=\frac{-7\times3}{18\times3}$
$=\frac{-21}{54}$
and $\frac{8}{27}=\frac{8\times2}{27\times2}$
$=\frac{16}{54}$
$\therefore\frac{7}{-18}+\frac{8}{27}$
$\frac{-7}{18}+\frac{8}{27}$
$=\frac{-21+16}{54}$
$=\frac{-5}{54}$
View full question & answer→Question 141 Mark
Find the multiplicative inverse (i.e., reciprocal) of:-$16$
AnswerMultiplicative inverse of $-16=\frac{-1}{16}$
View full question & answer→Question 151 Mark
Which of the following statements are true and which are false? $\frac{-12}{7}$ lies to the right of $0$ on the number line.
AnswerAs the numbers right of $0$ are positive and $\frac{-12}{7}$ is negative.
View full question & answer→Question 161 Mark
Name the property of multiplication illustrated of the following statement: $\Big(\frac{-2}{3}\times\frac{7}{9}\Big)\times\frac{-9}{5}=\frac{-2}{3}\times\Big(\frac{7}{9}\times\frac{-9}{5}\Big)$
Answer$\Big(\frac{-2}{3}\times\frac{7}{9}\Big)\times\frac{-9}{5}=\frac{-2}{3}\times\Big(\frac{7}{9}\times\frac{-9}{5}\Big)$ It is associative law of multiplication.
View full question & answer→Question 171 Mark
Fill in the blank: The product of a rational number and its reciprocal is ___________.
AnswerThe product of a rational number and its reciprocal is 1.
View full question & answer→Question 181 Mark
Find the multiplicative inverse (i.e., reciprocal) of: $\Big(\frac{-4}{9}\Big)^{-1}$
Answer$\Big(\frac{-4}{9}\Big)^{-1}=\frac{-9}{4}$
View full question & answer→Question 191 Mark
Fill in the blanks. $\frac{19}{-5}+\Big(\frac{-3}{11}+\frac{-7}{8}\Big)=\Big\{\frac{19}{-5}+(....)\Big\}+\frac{-7}{8}$
Answer$\frac{19}{-5}+\Big(\frac{-3}{11}+\frac{-7}{8}\Big)=\Big\{\frac{19}{-5}+\frac{-3}{11}\Big\}+\frac{-7}{8}$ (By Associative Law of addition)
View full question & answer→Question 201 Mark
Add the following rational numbers.
$2\ \text{and}\ \frac{-5}{4}$
AnswerWe can write $2\ \text{as}\ \frac{2}{1}$
The denominators of the given rational number are $1$ and $4.$
$LCM$ of $1$ and $4$ is $4$
Now,
$\frac{2}{1}=\frac{2\times4}{1\times4}$
$=\frac{8}{4}$
and $\frac{5}{-4}=\frac{-5\times1}{4\times1}$
$=\frac{-5}{4}$
$\therefore2+\frac{(-5)}{4}$
$=\frac{8}{4}+\frac{(-5)}{4}$
$=\frac{8+(-5)}{4}$
$=\frac{8-5}{4}$
$=\frac{3}{4}$
View full question & answer→Question 211 Mark
Fill in the blank: The numbers ________ and ______ are their own reciprocals.
AnswerThe numbers 1 and -1 are their own reciprocal.
View full question & answer→Question 221 Mark
Fill in the blank. $\frac{-8}{9}\times(......)=\frac{-2}{3}$
Answer$\frac{-8}{9}\times\frac{3}{4}=\frac{-2}{3}$
Solution:
Let the blank space be $x$ Now, we have:$\frac{-8}{9}\times\text{x}=\frac{-2}{3}$
$\Rightarrow\text{x}=\frac{-2}{3}\div\frac{-8}{9}$
$\Rightarrow\text{x}=\frac{-2}{3}\times\frac{9}{-8}$
$\Rightarrow\text{x}=\frac{18}{24}$
$\Rightarrow\text{x}=\frac{18\div6}{24\div6}$
$\Rightarrow\text{x}=\frac{3}{4}$
View full question & answer→Question 231 Mark
Fill in the blank. $\frac{2}{3}-(......)=\frac{1}{15}$
Answer$\frac{2}{3}-\frac{3}{5}=\frac{1}{15}$Solution:
Let the blank space be x Now, we have:$\frac{2}{3}-\text{x}=\frac{1}{15}$
$\Rightarrow-\text{x}=\frac{1}{15}-\frac{2}{3}$
$\Rightarrow-\text{x}=\frac{1-10}{15}$
$\Rightarrow-\text{x}=\frac{-9}{15}$
$\Rightarrow\text{x}=\frac{9}{15}$
$\Rightarrow\text{x}=\frac{3}{5}$
View full question & answer→Question 241 Mark
Fill in the blanks with the correct symbol out of $>, =$ and $<.$ $\frac{-2}{3}\ ....\ \frac{5}{-8}$
AnswerBetween $\frac{-2}{3}\ \text{and}\ \frac{5}{-8}$ or $\frac{-2}{3}\ \text{and}\ \frac{-5}{8}$
$LCM$ of $3$ and $8 = 24$
$\therefore\frac{-2}{3}=\frac{-2\times8}{3\times8}=\frac{-16}{24}$ and
$\frac{-5}{8}=\frac{-5\times3}{8\times3}=\frac{-15}{24}$
It is clear that $\frac{-16}{24}$ is less than $\frac{-15}{24}$or $\frac{-2}{3}>\frac{-5}{8}$
View full question & answer→Question 251 Mark
Find the multiplicative inverse (i.e., reciprocal) of: $\frac{-7}{24}$
AnswerMultiplicative inverse of $\frac{-7}{24}=\frac{24}{-7}$
View full question & answer→Question 261 Mark
Find the multiplicative inverse (i.e., reciprocal) of: $\frac{-1}{8}$
AnswerMultiplicative inverse of $\frac{-1}{8}=-8$
View full question & answer→Question 271 Mark
Is addition commutative on rational numbers?
AnswerYes, addition is commutative.
View full question & answer→Question 281 Mark
Fill in the blanks. $\Big(\frac{-3}{17}\Big)+\Big(\frac{-12}{5}\Big)=\Big(\frac{-12}{5}\Big)+\ (......)$
Answer$\Big(\frac{-3}{17}\Big)+\Big(\frac{-12}{5}\Big)=\Big(\frac{-12}{5}\Big)+\Big(\frac{-3}{17}\Big)$ (By commutative Law of addition)
View full question & answer→Question 291 Mark
Find the multiplicative inverse (i.e., reciprocal) of: $\frac{-3}{-5}$
AnswerMultiplicative inverse of $\frac{-3}{-5}=\frac{-5}{-3}$
View full question & answer→Question 301 Mark
Fill in the blanks. $\frac{-16}{7}+\ ...\ =\ ...\ +\frac{-16}{7}=\frac{-16}{7}$
Answer$\frac{-16}{7}+0=0+\frac{-16}{7}=\frac{-16}{7}[$ Existance of Additive Identity $(0)]$
View full question & answer→Question 311 Mark
Add the following rational numbers.
$-1\ \text{and}\ \frac{3}{4}$
AnswerWe can write $-1\ \text{as}\ \frac{-1}{1}$
The denominators of the given rational number are $1$ and $4.$
$LCM$ of $1$ and $4$ is $4$
Now,
$\frac{-1}{1}=\frac{-1\times4}{1\times4}$
$=\frac{-4}{4}$
and $\frac{3}{4}=\frac{3\times1}{4\times1}$
$=\frac{3}{4}$
$\therefore-1+\frac{3}{4}$
$=\frac{-4}{4}+\frac{3}{4}$
$=\frac{-4+3}{4}$
$=\frac{-1}{4}$
View full question & answer→Question 321 Mark
What is the negative of a negative rational number?
Question 331 Mark
Is the difference of two rational numbers a rational number?
AnswerYes, difference of two rational number is also a rational.
View full question & answer→Question 341 Mark
Fill in the blank: $(.....)\div(-3)=\frac{-4}{15}$
AnswerLet required number $= x$ Then, $\text{x}\div(-3)=\frac{-4}{15}$
$\Rightarrow\text{x}=\frac{-4}{15}\div\frac{1}{-3}$
$\Rightarrow\text{x}=\frac{-4}{15}\times\frac{-3}{1}$
$=\frac{12}{15}$
$=\frac{12\div3}{15\div3}$
$=\frac{4}{5}$
$\therefore$ Required number $=\frac{4}{5}$
View full question & answer→Question 351 Mark
Which of the following statements are true and which are false? The rational numbers $\frac{1}{3}$ and $\frac{-5}{2}$ are on opposite sides of 0 on the number line.
AnswerTrue.Solution:
As $\frac{1}{3}$ is positive and $\frac{-5}{2}$ is negative.
View full question & answer→Question 361 Mark
Find the multiplicative inverse (i.e., reciprocal) of:
$-1$
AnswerMultiplicative inverse of $-1 = -1$
View full question & answer→Question 371 Mark
Name the property of multiplication illustrated of the following statements:
$\frac{-16}{9}\times1=1\times\frac{-16}{9}=\frac{-16}{9}$
Answer $\frac{-16}{9}\times1=1\times\frac{-16}{9}=\frac{-16}{9}$
It is existance of multiplicative identify.
View full question & answer→MCQ 381 Mark
Tick $(\checkmark)$ the correct answer the following : A rational number between $\frac{-2}{3}$ and $\frac{1}{4}$ is:
- A
$\frac{5}{12}$
- B
$\frac{-5}{12}$
- C
$\frac{5}{24}$
- ✓
$\frac{-5}{24}$
AnswerCorrect option: D. $\frac{-5}{24}$
A rational number between $=\frac{-2}{3}$
$\frac{1}{4}$ will be $=\frac{1}{2}\Big(\frac{-2}{3}+\frac{1}{4}\Big)$
$=\frac{1}{2}\Big(\frac{-8+3}{12}\Big)$
$=\frac{1}{2}\times\frac{-5}{12}$
$=\frac{-5}{24}$
View full question & answer→Question 391 Mark
Name the property of multiplication shown by the following statement: $\frac{2}{5}\times\Big(\frac{-4}{5}+\frac{-3}{10}\Big)=\Big(\frac{2}{5}\times\frac{-4}{5}\Big)+\Big(\frac{2}{5}\times\frac{-3}{10}\Big)$
AnswerDistributive law of multiplication over addition.
View full question & answer→MCQ 401 Mark
Tick $(\checkmark)$ the correct answer the following:What should be subtracted from $\frac{-3}{5}$ to get $-2?$
- A
$\frac{-7}{5}$
- B
$\frac{-13}{5}$
- C
$\frac{13}{5}$
- ✓
$\frac{7}{5}$
AnswerCorrect option: D. $\frac{7}{5}$
Let $x$ be the subtracted
Then,
$\frac{-3}{5}-\text{x}=-2$
$\Rightarrow\text{x}=-\frac{3}{5}+2$
$\Rightarrow\text{x}=\frac{-3+10}{5}$
$=\frac{7}{5}$
View full question & answer→Question 411 Mark
Name the property of multiplication illustrated of the following statement:
$\frac{-15}{8}\times\frac{-12}{7}=\frac{-12}{7}\times\frac{-15}{8}$
Answer $\frac{-15}{8}\times\frac{-12}{7}=\frac{-12}{7}\times\frac{-15}{8}$
It is commutative law of multiplication.
View full question & answer→Question 421 Mark
Fill in the blanks. $\Big(\frac{-8}{13}+\frac{3}{7}\Big)+\Big(\frac{-13}{4}\Big)=(.....)+\bigg[\frac{3}{7}+\Big(\frac{-13}{4}\Big)\bigg]$
Answer$\Big(\frac{-8}{13}+\frac{3}{7}\Big)+\Big(\frac{-13}{4}\Big)=\Big(\frac{-8}{13}\Big)+\bigg[\frac{3}{7}+\Big(\frac{-13}{4}\Big)\bigg]$ (By Associative Law of addition)
View full question & answer→Question 431 Mark
Which of the following statement are true and which are false? Every whole number is a rational number.
AnswerTrue.Solution:
As the set of whole number is a subset of the set of rational numbers.
View full question & answer→Question 441 Mark
Which rational number is its own additive inverse$?$
Answer$0$ is the rational number.
View full question & answer→Question 451 Mark
Write $‘T’$ for true and $‘F’$ for false for the following: $1\div0=0$
AnswerFalse.Solution:
$\frac{\text{a}}{0}=\infty$
Hence, $\frac{1}{0}\neq0$
View full question & answer→Question 461 Mark
Fill in the blanks: $\frac{-23}{17}\times\frac{18}{35}\times=\frac{18}{35}\times(.....)$
Answer$\frac{-23}{17}\times\frac{18}{35}\times=\frac{18}{35}\times\Big(\frac{-23}{17}\Big)$
View full question & answer→Question 471 Mark
Fill in the blank: $\frac{9}{8}\div(....)=\frac{-3}{2}$
AnswerLet required number $= x$
Then,
$\frac{9}{8}\div\text{x}=\frac{-3}{2}$
$\Rightarrow\frac{9}{8}\times\frac{1}{\text{x}}=\frac{-3}{2}$
$\Rightarrow\frac{1}{\text{x}}=\frac{-3}{2}\div\frac{9}{8}$
$\Rightarrow\frac{-3}{2}\times\frac{8}{9}=\frac{-24}{18}$
$\Rightarrow\text{x}=\frac{18}{-24}$
$\Rightarrow\frac{18\div6}{-24\div6}$
$=\frac{3}{-4}$
$=\frac{-3}{4}$
$\therefore$ Required number $=\frac{-3}{4}$
View full question & answer→Question 481 Mark
Name the property of multiplication illustrated of the following statement: $\frac{-3}{4}\times\Big(\frac{-5}{6}+\frac{7}{8}\Big)=\Big(\frac{-3}{4}\times\frac{-5}{6}\Big)+\Big(\frac{-3}{4}\times\frac{7}{8}\Big)$
Answer$\frac{-3}{4}\times\Big(\frac{-5}{6}+\frac{7}{8}\Big)=\Big(\frac{-3}{4}\times\frac{-5}{6}\Big)+\Big(\frac{-3}{4}\times\frac{7}{8}\Big)$ It is distributive law of multiplication over addition.
View full question & answer→Question 491 Mark
Fill in the blank: The reciprocal of a positive rational rational number is ____________.
AnswerThe reciprocal of a positive rational number is positive.
View full question & answer→Question 501 Mark
Add the following rational numbers. $\frac{-7}{3}\ \text{and}\ \frac{1}{3}$
Answer$\frac{-7}{3}+\frac{1}{3}$
$=\frac{-7+1}{3}$
$=\frac{-6}{3}$
$=\frac{-6\div3}{3\div3}=\frac{-2}{1}$
$=-2$
View full question & answer→