Question 512 Marks
Multiply: $\frac{-12}{5}\text{ by }\frac{10}{-3}$
Answer$\frac{-12}{5}\text{ by }\frac{10}{-3}$ $=\frac{-12}{5}\times\frac{10}{-3}$ $=\frac{-12\times10}{5\times(-3)}$ $=\frac{-4\times2}{1\times(-1)}$ $=\frac{-8}{-1}=8$
View full question & answer→Question 522 Marks
Write the following rational numbers in standard form: $\frac{-14}{-49}$
Answer$\frac{-14}{-49}=\frac{-14\div(-7)}{-49\div(-7)}$
$(HCL$ of $-14$ and $-49 = -7)$
$=\frac{2}{7}$
View full question & answer→Question 532 Marks
Simplify: $-32\times\frac{-7}{36}$
Answer$-32\times\frac{-7}{36}$ $=\frac{(-32)\times(-7)}{36}$ $=\frac{(-8)\times(-7)}{9}$ $=\frac{56}{9}$
View full question & answer→Question 542 Marks
Express $\frac{-8}{11}$ as a rational number with denominator $-55$
AnswerRational number $=\frac{-8}{11}$
$-55=11\times(-5)$
$\therefore\frac{-8}{11}=\frac{-8\times(-5)}{1\times(-5)}=\frac{40}{-55}$
View full question & answer→Question 552 Marks
What should be subtracted from $\frac{-2}{3}$ to get $\frac{-5}{6}?$
AnswerThe required number $=\frac{-2}{3}-\Big(\frac{-5}{6}\Big)$
$(LCM$ of $3, 6 = 6)$
$=\frac{-2}{3}+\frac{5}{6}$
$=\frac{-4+5}{6}$$=\frac{1}{6}$
View full question & answer→Question 562 Marks
Evaluate: $\frac{-3}{5}+\frac{7}{5}+\frac{-1}{5}$
Answer$\frac{-3}{5}+\frac{7}{5}+\frac{-1}{5}$ $=\frac{-3+7+(-1)}{5}$ $=\frac{-3+7-1}{5}$ $=\frac{7-4}{5}=\frac{3}{5}$
View full question & answer→Question 572 Marks
Represent the following rational numbers on the number line: $\frac{36}{-5}$
AnswerDraw a number line and locate a point $O$ on it. Let it represent $0.$ The number $\frac{36}{-5}$ has been represented on it as given below: $\frac{36}{-5}=\frac{-36}{5}=-7\frac{1}{5}$
View full question & answer→Question 582 Marks
Represent the following rational numbers on the number line:
$\frac{-3}{4}$
AnswerDraw a number line and locate a point $O$ on it. Let it represent $0.$ The number $\frac{-3}{4}$ has been represented on it is as given below:
View full question & answer→Question 592 Marks
Express $\frac{14}{-5}$ as a rational number with numerator $-70$
AnswerRational number $=\frac{14}{-5}$ $-70=14\times(-5)$ $\therefore\frac{14}{-5}=\frac{14\times(-5)}{-5\times(5)}=\frac{-70}{25}$
View full question & answer→Question 602 Marks
Find x such that: $\frac{13}{6}=\frac{-65}{\text{x}}$
Answer$\frac{13}{6}=\frac{-65}{\text{x}}$$\Rightarrow13\times\text{x}=-65\times6$
$\Rightarrow-\text{x}=\frac{-65\times6}{13}$
$=-5\times6=-30$
$\therefore\text{x}=-30$
View full question & answer→Question 612 Marks
Express $\frac{-36}{24}$ as a rational number with numerator $6$
AnswerRational number $=\frac{-36}{24}$
$6=-36\div(-6)$
$\therefore\frac{-36}{24}=\frac{-36\div(-6)}{24\div(-6)}=\frac{6}{-4}$
View full question & answer→Question 622 Marks
Express $\frac{13}{-8}$ as a rational number with denominator $32$
AnswerRational number $=\frac{13}{-8}$
$32=-8\times(-4)$
$\therefore\frac{13}{-8}=\frac{13\times(-4)}{-8\times5}=\frac{-52}{32}$
View full question & answer→Question 632 Marks
By what number should $-4\frac{3}{8}$ be divided to obtain $-3\frac{1}{2}?$
AnswerLet the required number be $x -4\frac{3}{8}\div\text{x}=-3\frac{1}{2}$
$\Rightarrow\text{x}=\frac{-35}{8}\times\frac{2}{-7}$
$=\frac{5}{4}$
Hence, the require numbers is $\frac{5}{4}$
View full question & answer→Question 642 Marks
Write the following rational numbers in standard form: $\frac{-68}{119}$
Answer$\frac{-68}{119}=\frac{-68\div17}{119\div17}$
$(HCL$ of $68$ and $119 = 17)$
$=\frac{-4}{7}$
View full question & answer→Question 652 Marks
Find x such that: $\frac{3}{5}=\frac{\text{x}}{-25}$
Answer$\frac{3}{5}=\frac{\text{x}}{-25}$$\Rightarrow5\times\text{x}=3\times(-25)$
$\Rightarrow-\text{x}=\frac{3(-25)}{5}$
$=3\times(-5)=-15$
$\therefore\text{x}=-15$
View full question & answer→Question 662 Marks
Find the multiplicative inverse, or reciprocal of the following: $-16$
AnswerReciprocal of $-16=\frac{1}{-16}$ $=\frac{1\times(-1)}{-16\times(-1)}=\frac{-1}{16}$
View full question & answer→Question 672 Marks
Find five rational numbers between $-1$ and $1.$
AnswerWe can write $-1=\frac{-3}{3}\text{ and }1\frac{3}{3}$
$\frac{-3}{3}<\frac{-2}{3}<\frac{-1}{3}<\frac{0}{3}<\frac{1}{3}<\frac{2}{3}<\frac{3}{3}$
$\therefore$ Five rational between $-1$ and $1$ are
$\frac{-2}{3}<\frac{-1}{3}<\frac{0}{3}<\frac{1}{3}<\frac{2}{3}$
View full question & answer→Question 682 Marks
Simplify:
$\frac{-9}{8}\times\frac{-16}{3}$
Answer $\frac{-9}{8}\times\frac{-16}{3}$
$=\frac{(-9)\times(-16)}{8\times3}$
$=\frac{(-3)\times(-2)}{1\times1}$
$=\frac{6}{1}=6$
View full question & answer→Question 692 Marks
Find the additive inverse of:
$\frac{15}{-4}$
Answer $\frac{15}{-4}=\frac{15\times(-1)}{-4\times(-1)}=\frac{-15}{4}$
$\therefore$ Additive inverse of $\frac{-15}{4}=-\Big(\frac{-15}{4}\Big)$
$=\frac{15}{4}$
View full question & answer→Question 702 Marks
Add the following rational numbers: $\frac{-17}{9}\text{ and }\frac{-11}{9}$
Answer$\frac{-17}{9}\text{ and }\frac{-11}{9}$ $=\frac{-17}{9}+\frac{-11}{9}$ $=\frac{-17-11}{9}$ $=\frac{-28}{9}$
View full question & answer→Question 712 Marks
Represent the following rational numbers on the number line: $\frac{2}{7}$
AnswerDraw a number line and locate a point $O$ on it. Let it represent $0.$ The number $\frac{2}{7}$ has been represented on the number line given below:
View full question & answer→Question 722 Marks
Simplify: $-13\times\frac{17}{26}$
Answer$-13\times\frac{17}{26}$$=\frac{-13}{1}\times\frac{17}{26}$
$=\frac{-1\times17}{1\times2}$
$=\frac{-17}{2}$
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Express $\frac{84}{-147}$ as a rational number with denominator $7$
AnswerDenominator of $\frac{84}{-147}\text{ is }-147$$\therefore-147\div(-21)=7$
Dividing both the numerator and the denominator by $-21$
$\frac{84\div(-21)}{-147\div(-21)}=\frac{-4}{7}$
$=\frac{8}{-147}=\frac{-4}{7}$
View full question & answer→Question 742 Marks
Express $\frac{4}{7}$ as a rational number with denominator $21$
AnswerRational number $=\frac{4}{7}$ $21=7\times3$ $\therefore\frac{4}{7}=\frac{4\times3}{7\times3}=\frac{12}{21}$
View full question & answer→Question 752 Marks
Find the multiplicative inverse, or reciprocal of the following: $\frac{-3}{-5}$
AnswerReciprocal of $\frac{-3}{-5}=\frac{-5}{-3}$ $=\frac{-5\times(-1)}{-3\times(-1)}=\frac{5}{3}$
View full question & answer→Question 762 Marks
Find the multiplicative inverse, or reciprocal of the following: $\frac{-17}{12}$
AnswerReciprocal of $\frac{-17}{12}=\frac{12}{-17}$ $=\frac{12\times(-1)}{-17\times(-1)}=\frac{-12}{17}$
View full question & answer→Question 772 Marks
Find x such that:
$\frac{16}{\text{x}}-4$
Answer $\frac{16}{\text{x}}-4$ $\Rightarrow-4\times\text{x}=16$
$\Rightarrow-\text{x}=\frac{16}{-4}=-4$
$\therefore\text{x}=-4$
View full question & answer→Question 782 Marks
Simplify: $\frac{-13}{5}\times-10$
Answer$\frac{-13}{5}\times-10$$=\frac{-13}{5}\times\frac{-10}{1}$
$=\frac{(-13)\times(-10)}{5\times1}$
$=\frac{(-13)\times(-2)}{1\times1}$ $=26$
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Simplify: $\frac{-19}{36}\times16$
Answer$\frac{-19}{36}\times16$$=\frac{-19}{36}\times\frac{16}{1}$
$=\frac{-19\times16}{36\times1}$
$=\frac{-19\times4}{9\times1}=\frac{-76}{9}$
View full question & answer→Question 802 Marks
Find the multiplicative inverse, or reciprocal of the following: $\frac{-6}{19}$
AnswerReciprocal of $\frac{-6}{19}=\frac{19}{-6}$ $=\frac{19\times(-1)}{-6\times(-1)}=\frac{-19}{6}$
View full question & answer→Question 812 Marks
Express $\frac{14}{-5}$ as a rational number with numerator $56$
AnswerRational number $=\frac{14}{-5}$
$56=14\times4$
$\therefore\frac{14}{-5}=\frac{14\times4}{-5\times4}=\frac{56}{20}$
View full question & answer→Question 822 Marks
Write the following rational numbers in standard form: $\frac{299}{-161}$
Answer$\frac{299}{-161}=\frac{299\div23}{161\div23}$
$(HCL$ of $299$ and $161 = 23)$
$=\frac{13}{-7}$
View full question & answer→Question 832 Marks
Express $\frac{-12}{13}$ as a rational number with numerator $-48$
AnswerRational number $=\frac{-12}{13}$
$-48=-12\times4$
$\therefore\frac{-12}{13}=\frac{-12\times4}{13\times4}=\frac{-48}{52}$
View full question & answer→Question 842 Marks
Represent the following rational numbers on the number line: $\frac{22}{7}$
AnswerDraw a number line and locate a point $O$ on it. Let it represent $0. $ The number $\frac{22}{7}$ has been represented on it as given below:
View full question & answer→Question 852 Marks
Fill in the blank: $\frac{-6}{11}=\frac{-18}{\dots}=\frac{\dots}{-18}$
Answer$\frac{-6}{11}=\frac{-18}{\dots}=\frac{\dots}{44}$ $-18=-6\times3$ $\therefore\frac{-6}{11}=\frac{-6\times3}{11\times3}=\frac{-18}{33}$ $\therefore\frac{-6}{11}=\frac{-6\times3}{11\times3}=\frac{-18}{33}$ $44=11\times4$ $\therefore\frac{-6}{11}=\frac{-6\times4}{11\times4}=\frac{-24}{44}$ $\therefore\frac{-6}{11}=\frac{-18}{33}=\frac{-24}{44}$
View full question & answer→Question 862 Marks
Represent the following rational numbers on the number line:
$\frac{1}{3}$
AnswerDraw a number line and locate a point $O$ on it. Let it represent $0$ Now $\frac{1}{3}$ has been presented on the number line given below.
View full question & answer→Question 872 Marks
Somplify: $\frac{-12}{7}\div(-18)$
Answer$\frac{-12}{7}\div(-18)$ $=\frac{12}{7}\times\Big(\frac{-1}{18}\Big)$ $=\frac{2}{21}$
View full question & answer→Question 882 Marks
What should be subtracted from $\frac{-3}{4}$ to get $\frac{5}{6}?$
AnswerThe required number $=\frac{-3}{4}-\frac{5}{6}$
$(LCM$ of $4, 6 = 12)$
$=\frac{-9-10}{12}$
$=-\frac{19}{12}$
View full question & answer→Question 892 Marks
Somplify: $-8\div\Big(\frac{-5}{16}\Big)$
Answer$-8\div\Big(\frac{-5}{16}\Big)$ $=-8\times\frac{-16}{5}$ $=\frac{128}{5}$
View full question & answer→Question 902 Marks
Which of the following are pairs of equivalent rational number? $\frac{-13}{7},\frac{39}{-21}$
Answer$\frac{-13}{7},\frac{39}{-21}$
$\frac{39}{-21}=\frac{39\div3}{-21\div3}=\frac{13}{-7}$
$=\frac{13\times(1)}{-7\times(-1)}=\frac{-13}{7}$
$(HCF$ of $39$ and $21 = 3)$
$\therefore\frac{-13}{7}\text{ and }\frac{29}{-21}$ are equivalent rational numbers.
View full question & answer→Question 912 Marks
Represent the following rational numbers on the number line: $\frac{-43}{9}$
AnswerDraw a number line and locate is point $O$ on it. Let is represent $0.$ The number $\frac{-43}{9}$ has been represented on it as given below: $\frac{-43}{9}=-4\frac{7}{9}$
View full question & answer→Question 922 Marks
What should be added to $\frac{2}{9}$ to get $-1?$
AnswerThe required number $=\frac{-1}{1}-\frac{2}{9}$
$=\frac{-9-2}{9}$
$=\frac{-11}{9}$
View full question & answer→Question 932 Marks
Find the additive inverse of: $\frac{-18}{-13}$
Answer$\frac{-18}{-13}=\frac{-18\times(-1)}{-13\times(-1)}=\frac{18}{13}$ $\therefore$ Additive inverse of $\frac{18}{13}=-\Big(\frac{18}{13}\Big)$ $=\frac{-18}{13}$
View full question & answer→Question 942 Marks
Simplify:
$\frac{3}{20}\times\frac{4}{5}$
Answer $\frac{3}{20}\times\frac{4}{5}$
$=\frac{3\times4}{20\times5}$
$=\frac{3\times1}{5\times5}$
$=\frac{3}{25}$
View full question & answer→Question 952 Marks
Simplify:
$\frac{7}{24}\times-48$
Answer $\frac{7}{24}\times-48$
$=\frac{7}{24}\times\frac{(-48)}{1}$
$=\frac{7\times(-48)}{24\times1}$
$=\frac{7\times(-2)}{1\times1}=-14$
View full question & answer→Question 962 Marks
Express $\frac{-36}{24}$ as a rational number with numerator $-9$
AnswerRational number $=\frac{-36}{24}$ $-9=-36\div4$ $\therefore\frac{-36}{24}=\frac{-36\div4}{24\div4}=\frac{-9}{6}$
View full question & answer→Question 972 Marks
Add the following rational numbers:
$\frac{9}{-13}\text{ and }\frac{-11}{-13}$
Answer $\frac{9}{-13}\text{ and }\frac{-11}{-13}$
$\frac{9}{-13}=\frac{9\times(-1)}{-13\times(-1)}=\frac{-9}{13}$
$\frac{-11}{-13}=\frac{-11\times(-1)}{-13\times(-1)}=\frac{11}{13}$
$\therefore\frac{-9}{13}+\frac{11}{13}=\frac{-9+11}{13}$
$=\frac{2}{13}$
View full question & answer→Question 982 Marks
Which of the two rational numbers is greater in the following pairs? $\frac{-6}{11}\text{ or }\frac{-5}{11}$
Answer$\frac{-6}{11}\text{ or }\frac{-5}{11}$
$\Rightarrow\frac{-6}{11}\text{ or }\frac{5\times(-1)}{-11\times(-1)}$ (Making denominator positive)
$\Rightarrow\frac{-6}{11}\text{ or }\frac{-5}{11}$
$\frac{-5}{11}$ is greater as $(-5)$ is greater than $(-6)$
$\therefore\frac{5}{-11}>\frac{-6}{11}$
View full question & answer→Question 992 Marks
Simplify: $\frac{-7}{30}\times\frac{5}{15}$
Answer$\frac{-7}{30}\times\frac{5}{15}$ $=\frac{-7\times5}{30\times14}$ $=\frac{-1\times1}{6\times2}$ $=\frac{-1}{2}$
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