To do: We have to find whether \( 0.3 \) is the multiplicative inverse of \( 3 \frac{1}{3} \).Solution:$3\frac{1}{3} =\frac{3\times3+1}{3}$$=\frac{10}{3}$We know that,The multiplicative inverse of $\frac{a}{b}$ is $\frac{b}{a}$ Therefore,The multiplicative inverse of $\frac{10}{3}$ is $\frac{3}{10}$.$0.3=\frac{3}{10}$Hence, $0.3$ is the multiplicative inverse of $3\frac{1}{3}$.

To do: We have to find whether \( \frac{8}{9} \) is the multiplicative inverse of \( -1 \frac{1}{8} \).Solution:$-1\frac{1}{8} =-(1\frac{1}{8})$$=-(\frac{1\times8+1}{8})$$=-\frac{9}{8}$We know that,The multiplicative inverse of $\frac{a}{b}$ is $\frac{b}{a}$ Therefore,The multiplicative inverse of $\frac{-9}{8}$ is $\frac{8}{-9}=\frac{-8}{9}$ $\frac{-8}{9}≠\frac{8}{9}$Hence, $\frac{8}{9}$ is not the multiplicative inverse of $-1\frac{1}{8}$.

Given: \( \frac{1}{3} \times\left(6 \times \frac{4}{3}\right) \) =\( \left(\frac{1}{3} \times 6\right) \times \frac{4}{3} \)To do: We have to find the property according to which the given equation is true.Solution:Associative property for multiplication:When we multiply two or more whole numbers grouped in any order we get the same result$(a \times b)\times c=a \times (b \times c) $Therefore, Associative property allows us to compute \( \frac{1}{3} \times\left(6 \times \frac{4}{3}\right) \) as \( \left(\frac{1}{3} \times 6\right) \times \frac{4}{3} \).

Given:(i) \( \frac{-4}{5} \times 1=1 \times \frac{-4}{5}=-\frac{4}{5} \)(ii) \( -\frac{13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17} \)(iii) \( \frac{-19}{29} \times \frac{29}{-19}=1 \).To do:We have to name the property under multiplication used in each case.Solution:(i) Multiplicative Identity:One (1) is the multiplicative identity of rational numbers. When we multiply a rational number with 1, the result will always be the same rational number.  Therefore, Multiplicative identity is used in the given expression.(ii) \( -\frac{13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17} \) is commutative property of multiplication.(iii) \( \frac{-19}{29} \times \frac{29}{-19}=1 \) is multiplicative inverse property. Read More

To do:We have to find the multiplicative inverse of the given rational numbers.Solution:The multiplicative inverse is that number which makes the existing number equal to unity on multiplication.Multiplicative inverse of $a$ is $\frac{1}{a}$.Therefore, (i) The multiplicative inverse of $-13=\frac{1}{-13}$ $=\frac{-1}{13}$The multiplicative inverse of $-13$ is $\frac{-1}{13}$.(ii)The multiplicative inverse of $\frac{-13}{19}=\frac{1}{\frac{-13}{19}}$ $=\frac{-19}{13}$ The multiplicative inverse of $\frac{-13}{19}$ is $\frac{-19}{13}$.  (iii) The multiplicative inverse of $\frac{1}{5}=\frac{1}{\frac{1}{5}}$ $=\frac{5}{1}$$=5$ The multiplicative inverse of $\frac{1}{5}$ is $5$.   (iv) $\frac{-5}{8} \times \frac{-3}{7}=\frac{-5\times(-3)}{8\times7}$$=\frac{15}{56}$Therefore, The multiplicative inverse of $\frac{15}{56}=\frac{1}{\frac{15}{56}}$ $=\frac{56}{15}$ The multiplicative inverse of $\frac{-5}{8}\times\frac{-3}{7}$ is $\frac{56}{15}$.    (v) $-1\times\frac{-2}{5}=\frac{-1\times(-2)}{5}$$=\frac{2}{5}$Therefore, The multiplicative inverse of $\frac{2}{5}=\frac{1}{\frac{2}{5}}$ $=\frac{5}{2}$ The multiplicative inverse of $-1\times\frac{-2}{5}$ is $\frac{5}{2}$.(vi) The multiplicative inverse of $-1=\frac{1}{-1}$ $=-1$ The multiplicative inverse of $-1$ is $-1$.      Read More

To do:We have to write the additive inverse of the given rational numbers.Solution:Additive Inverse:The number in the set of real numbers that when added to a given number will give zero. (i) Let the additive inverse of the given rational number be $x$.Therefore, $x+\frac{2}{8}=0$$x=0-(\frac{2}{8})$$=0-\frac{2}{8}$   $=-\frac{2}{8}$The additive inverse of the given rational number is $-\frac{2}{8}$.    (ii) Let the additive inverse of the given rational number be $x$.Therefore, $x+\frac{-5}{9}=0$$x=0-(\frac{-5}{9})$$=0+\frac{5}{9}$   $=\frac{5}{9}$The additive inverse of the given rational number is $\frac{5}{9}$.     (iii) Let the additive inverse of the given rational number be $x$.Therefore, $x+\frac{-6}{-5}=0$$x=0-(\frac{-6}{-5})$$=0-\frac{6}{5}$   $=-\frac{6}{5}$The additive inverse of the given rational number is $-\frac{6}{5}$.      (iv) Let the additive ... Read More

Given:(i) $\frac{-2}{3} \times \frac{3}{5} + \frac{5}{2} - \frac{3}{5} \times \frac{1}{6}$(ii) \( \frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5} \).To do:We have to use appropriate properties and find the values of the given expressions.Solution:Distributive Property:The distributive property of multiplication states that when a factor is multiplied by the sum or difference of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition or subtraction operation.This property is symbolically stated as:$a (b+c) = a\times b + a\times c$$a (b-c) = a\times b - a\times c$Therefore, (i) $\frac{-2}{3} \times \frac{3}{5} + \frac{5}{2} - \frac{3}{5} \times ... Read More

To do:We have to give one example of a situation in which(i) the mean is an appropriate measure of central tendency.(ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.Solution:(i) When the values of data do not change much, then the mean is an appropriate measure of central tendency. For example, Marks of 5 students in Mathematics test(out of 10) are $6, 5, 7, 6, 5$Therefore, Mean marks $=\frac{6+5+7+6+5}{5}$$=\frac{29}{5}$$=5.8$(ii) When the values of data have very high or low values, then the median is an appropriate measure of central tendency. For ... Read More

Given:The mean salary of 60 workers of a factory.To do:We have to find the mean salary of 60 workers.Solution:We know that,$\bar{x}=\frac{\sum{f_ix_i}}{\sum{x_i}}$Salary($x_i$)Number of workers($f_i$)$f_ix_i$300016$3000\times16=48000$400012$4000\times12=48000$500010$5000\times10=50000$60008$6000\times8=48000$70006$7000\times6=42000$80004$8000\times4=32000$90003$9000\times3=27000$100001$10000\times1=10000$Total$\sum{f_i}=60$$\sum{f_ix_i}=305000$Therefore,The mean salary of 60 workers $=\frac{\sum{f_ix_i}}{\sum{x_i}}$$=\frac{305000}{60}$$=Rs.\ 5083.33$Hence, the mean salary of 60 workers is Rs. 5083.33.

To do:We have to find the mode of $14,25,14,28,18,17,18,14,23,22,14,18$.Solution:To find the mode of the given data, we have to arrange the data in ascending order.The given data in ascending order is $14,14,14,14,17,18,18,18,22,23,25,28$In the given data,Frequency of $14$ is $4$Frequency of $17$ is $1$Frequency of $18$ is $3$Frequency of $22$ is $1$Frequency of $23$ is $1$Frequency of $25$ is $1$Frequency of $28$ is $1$We know that,Mode is the value or values in the data set that occur most frequently.Therefore,Mode of the given data is $14$.