Question 512 Marks
Simplify the following and write as a rational number of the form $\frac{\text{p}}{\text{q}}:$ $\frac{2}{3} + \frac{-5}{6} + \frac{-7}{9}$
Answer$\frac{2}{3}+\frac{-5}{6}+\frac{-7}{9}$
$=\frac{12}{18}+\frac{-15}{18}+\frac{-14}{18}$
$=\frac{12+(-15)+(-14)}{18}$
$=\frac{12-15-14}{18}$
$=\frac{-17}{18}$
View full question & answer→Question 522 Marks
Divide: $\frac{-7}{8}\ \text{by}\ \frac{-21}{16}$
Answer$\frac{-7}{8}\ \text{by}\ \frac{-21}{16}=\frac{-7}{8}\div\frac{-21}{16}$
$=\frac{-7}{8}\times\frac{16}{-21}=\frac{-1\times2}{1\times(-3)}$
$=\frac{-2}{-3}=\frac{2}{3}$
View full question & answer→Question 532 Marks
By what number should we multiply $\frac{-1}{6}$ so that the product may be $\frac{-23}{9}$?
Answerproduct $=\frac{-23}{9}$ and given nummber $=\frac{-1}{6}$
$\therefore$ Required number $=\frac{-23}{9}\div\frac{-1}{6}$
$=\frac{-23}{9}\times\frac{6}{-1}=\frac{-23\times2}{3\times(-1)}$
$=\frac{-46}{-3}=\frac{46}{3}$
View full question & answer→Question 542 Marks
Simplify: $\frac{-3}{2}+\frac{5}{4}-\frac{7}{4}$
Answer$\frac{-3}{2}+\frac{5}{4}-\frac{7}{4}$
Taking the $LCM$ of the denominators: $\frac{-6}{4}+\frac{5}{4}-\frac{7}{4}$
$=\frac{-6+5-7}{4}$
$=\frac{-8}{4}$
$=-2$
View full question & answer→Question 552 Marks
Divide: $5\ \text{by}\ \frac{-5}{7}$
Answer$5\ \text{by}\ \frac{-5}{7}=5\div\frac{-5}{7}=5\times\frac{7}{-5}$
$=\frac{7\times(-1)}{-5\times(-1)}=\frac{-7}{5}$
$=\frac{7\times(-5)}{-5(-1)}=\frac{-35}{5}$
$=-7$
View full question & answer→Question 562 Marks
Subtract the first rational number from the second in the following: $\frac{-2}{3},\frac{5}{6}$
Answer$\frac{-2}{3},\frac{5}{6}$ $\frac{-2}{3}$ from $\frac{5}{6}=\frac{5}{6}-\Big(\frac{-2}{3}\Big)$ $=\frac{5}{6}+\frac{2}{3}$ $=\frac{5+4}{6}=\frac{9}{6}=\frac{9\div3}{6\div3}=\frac{3}{2}$
View full question & answer→Question 572 Marks
$\Big(\frac{1}{2}\times\frac{1}{4}\Big)+\Big(\frac{1}{2}\times6\Big)$
Answer$\Big(\frac{1}{2}\times\frac{1}{4}\Big)+\Big(\frac{1}{2}\times6\Big)$
$=\frac{1\times1}{2\times4}+\frac{1}{2}\times\frac{6}{1}=\frac{1}{8}+\frac{3}{1}$
$=\frac{1+24}{8}=\frac{25}{8}$
View full question & answer→Question 582 Marks
Fill in blanks:$........ \ +\frac{15}{23}=4$
Answer$\frac{77}{23}+\frac{15}{32}=4$
Required number $=\frac{4}{1}-\frac{15}{23}$
$=\frac{92-15}{23}=\frac{77}{23}$
View full question & answer→Question 592 Marks
Simplify: $\frac{3}{8}-\frac{-2}{9}+\frac{-5}{36}$
Answer$\frac{3}{8}-\frac{-2}{9}+\frac{-5}{36}$
Taking the $LCM$ of the denominators: $\frac{27}{72}-\frac{-16}{72}+\frac{-10}{72}$
$=\frac{27-(-16)+(-10)}{72}$
$=\frac{27+16-10}{72}$
$=\frac{33}{72}$
$=\frac{11}{24}$
View full question & answer→Question 602 Marks
Fill in blanks:$\frac{-9}{14}+ \ ........ \ =-1$
Answer$\frac{-9}{14}+\frac{-5}{14}= -1$
Required number $=-1-\Big(\frac{-9}{14}\Big)$
$=-1+\frac{9}{14}$
$=\frac{-14+9}{14}=\frac{-5}{14}$
View full question & answer→Question 612 Marks
Find any five rational number less than $1$.
Answer$\because1=\frac{5}{5}$ and number $0, 1, 2, 3, 4$ are less than $5$ Five number less than $1$ can be $0,\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5}$
View full question & answer→Question 622 Marks
Express the following as a rational number of the form $\frac{\text{p}}{\text{q}}:$ $\frac{-7}{4}+0+\frac{-9}{5}+\frac{19}{10}+\frac{11}{14}$
Answer$\frac{-7}{4}+0+\frac{-9}{5}+\frac{19}{10}+\frac{11}{14}$
$=\frac{-245}{140}+\frac{-252}{140}+\frac{266}{140}+\frac{110}{140}$
$=\frac{(-245)+(-252)+266+110}{140}$
$=\frac{-245-252+266+110}{140}$
$=\frac{-121}{140}$
View full question & answer→Question 632 Marks
The product of two rational numbers is $15$. If one of the numbers is $−10$, find the other.
AnswerProduct of twon numbers $=15$
One number $ = -10$
$\therefore$ Second number $= 15 + (-10) = 15\times\frac{1}{-10}$
$=\frac{3\times1}{-2}=\frac{3}{-2}$
$=\frac{3\times(-1)}{(-2)\times(-1)}=\frac{-3}{2}$
View full question & answer→Question 642 Marks
Divide: $\frac{7}{-4}\ \text{by}\ \frac{63}{34}$
Answer$\frac{7}{-4}\ \text{by}\ \frac{63}{34}=\frac{7}{-4}\div\frac{63}{64}=\frac{7}{-4}\times\frac{64}{63}$
$=\frac{1\times16}{-1\times9}=\frac{16}{-9}=\frac{16\times(-1)}{-9\times(-1)}$
$=\frac{-16}{9}$
View full question & answer→Question 652 Marks
Multiply: $\frac{8}{-9}\ \text{by}\ \frac{-7}{-16}$
Answer$\frac{8}{-9}\ \text{by}\ \frac{-7}{-16}=\frac{8}{-9}\times\frac{-7}{-16}$
$=\frac{8\times(-7)}{(-9)\times(-16)}$
$=\frac{1\times(-70}{(-9)\times(-2)}=\frac{-7}{18}$
View full question & answer→Question 662 Marks
Express the following as a rational number of the form $\frac{\text{p}}{\text{q}}:$ $\frac{-7}{4}+\frac{5}{3}+\frac{-1}{2}+\frac{-5}{6}+2$
Answer$\frac{-7}{4}+\frac{5}{3}+\frac{-1}{2}+\frac{-5}{6}+2$
$=\frac{-21}{12}+\frac{20}{12}+\frac{-6}{12}+\frac{-10}{12}+\frac{24}{12}$
$=\frac{(-21)+20+(-6)+(-10)+24}{12}$
$=\frac{-21+20-6-10+24}{12}$
$=\frac{7}{12}$
View full question & answer→Question 672 Marks
Simplify: $3+\frac{5}{-7}$
Answer$3+\frac{5}{-7}$ $\frac{5}{-7}=\frac{-5}{7}$
The $LCM$ of the denominator $1$ and $7$ is $7$.
Now, We will expresss $\frac{3}{1}$ in the form in which it taken denominator as $7$.
$\frac{3}{1}=\frac{3\times7}{1\times7}=\frac{21}{7}$ So, $\frac{21}{7}+\frac{-5}{7}$
$=\frac{21-5}{7}=\frac{16}{7}$
View full question & answer→Question 682 Marks
What should be added to $\Big(\frac{1}{2}+\frac{1}{3}+\frac{1}{5}\Big)$ to get $3?$
AnswerThe required number $=3-\Big(\frac{1}{2}+\frac{1}{3}+\frac{1}{5}\Big)$
$=\frac{3}{1}-\frac{15+10+6}{30}$ $(LCM$ of $2, 3, 5 = 30)$ $=\frac{3}{1}-\frac{31}{30}$
$=\frac{90-31}{30}=\frac{59}{30}$
View full question & answer→Question 692 Marks
The sum of two numbers is $-8.$ If one of the numbers is $\frac{-15}{7}$ find the other.
AnswerSum of two rational number $=-8$
One number $=\frac{-15}{7}$
$\therefore$ Second number $=-8-\Big(\frac{-15}{7}\Big)$
$=\frac{-8}{1}+\frac{15}{7}$
$=\frac{-56+15}{7}=\frac{-41}{7}$
View full question & answer→Question 702 Marks
What number should be subtracted from $\frac{-5}{3}$ to get $\frac{5}{6}?$
AnswerThe required number $=\frac{-5}{3}-\frac{5}{6}$
$=\frac{-10-5}{6}$ $(LCM$ of $3, 6 = 6)$
$=\frac{-15}{6}=\frac{-15\div3}{6\div3}=\frac{-5}{2}$
View full question & answer→Question 712 Marks
$\Big(\frac{25}{5}\times\frac{2}{5}\Big)-\Big(\frac{3}{5}\times\frac{-10}{9}\Big)$
Answer$\Big(\frac{25}{5}\times\frac{2}{5}\Big)-\Big(\frac{3}{5}\times\frac{-10}{9}\Big)$
$=\frac{25\times2}{8\times5}-\frac{3\times(-10)}{5\times9}$
$=\frac{5\times1}{4\times1}=\frac{1\times(-2)}{1\times3}=\frac{5}{4}-\frac{-2}{3}$
$=\frac{15+8}{12}=\frac{23}{12}$
View full question & answer→Question 722 Marks
$\Big(\frac{-9}{4}\times\frac{5}{3}\Big)+\Big(\frac{13}{2}\times\frac{5}{6}\Big)$
Answer$\Big(\frac{-9}{4}\times\frac{5}{3}\Big)+\Big(\frac{13}{2}\times\frac{5}{6}\Big)$
$=\frac{-9\times5}{4\times3}+\frac{13\times5}{2\times6}$
$=\frac{-3\times5}{4\times1}+\frac{65}{12}$
$=\frac{-15}{4}+\frac{65}{12}$
$=\frac{-45+65}{12}=\frac{20}{12}=\frac{20\div4}{12\div4}=\frac{5}{3}$
View full question & answer→Question 732 Marks
Subtract the first rational number from the second in the following:
$\frac{-6}{7},\frac{-13}{14}$
Answer $\frac{-6}{7},\frac{-13}{14}$
$\frac{-6}{7}$ from $\frac{-13}{14}=\frac{-13}{14}-\Big(\frac{-6}{7}\Big)$
$=\frac{-13}{14}+\frac{6}{7}$
$=\frac{-13+12}{14}=\frac{-1}{14}$
View full question & answer→Question 742 Marks
Evaluate the following:$\frac{7}{24}-\frac{19}{36}$
Answer$\frac{7}{24}-\frac{19}{36}$
$LCM$ of $24, 36 = 72$ $=\frac{7}{24}-\frac{19}{36}$
$=\frac{21-38}{72}=\frac{-17}{72}$
View full question & answer→Question 752 Marks
Multiply:
$\frac{-5}{17}\ \text{by}\ \frac{51}{-60}$
Answer $\frac{-5}{17}\ \text{by}\ \frac{51}{-60}$
$\frac{-5}{17}\times\frac{-51}{60}$
$\Big(\frac{51}{-60}=\frac{51\times(-1)}{-60\times(-1)}=\frac{-51}{60}\Big)$
$=\frac{(-5)\times(-51)}{17\times60}=\frac{255}{1020}=\frac{255\div255}{1020\div255}$
$=\frac{1}{4}$
View full question & answer→Question 762 Marks
$\Big(-5\times\frac{2}{15}\Big)-\Big(-6\times\frac{2}{9}\Big)$
Answer$\Big(-5\times\frac{2}{15}\Big)-\Big(-6\times\frac{2}{9}\Big)$
$=\frac{-5\times2}{15}-\Big(\frac{-6\times2}{9}\Big)$
$=\frac{-1\times2}{3}-\frac{-2\times2}{3}=\frac{-2}{3}-\frac{-4}{3}$
$=\frac{-2+4}{3}=\frac{2}{3}$
View full question & answer→Question 772 Marks
What number should be subtracted from $\frac{3}{7}$ to get $\frac{5}{4}?$
AnswerLet, $x$ be subtracted.
$\therefore\frac{3}{7}=-\text{x}=\frac{5}{4}$
$\Rightarrow\text{x}=\frac{3}{7}-\frac{5}{4}$ $\Rightarrow\text{x}=\frac{12}{28}-\frac{35}{28}$
$\Rightarrow\text{x}=\frac{12-35}{28}=\frac{-23}{28}$
View full question & answer→Question 782 Marks
Divide: $\frac{-3}{4}\ \text{by}\ \frac{9}{-16}$
Answer$\frac{-3}{4}\ \text{by}\ \frac{9}{-16}=\frac{-3}{4}\div\frac{9}{-16}$
$=\frac{-3}{4}\times\frac{-16}{9}=\frac{-3\times(-16)}{4\times9}$
$=\frac{-1\times(-4)}{1\times3}=\frac{4}{3}$
View full question & answer→Question 792 Marks
Simplify the following and write as a rational number of the form $\frac{\text{p}}{\text{q}}:$ $\frac{3}{4} + \frac{5}{6} + \frac{-7}{8}$
Answer$=\frac{3}{4}+\frac{5}{6}+\frac{-7}{8}$
$=\frac{18}{24}+\frac{20}{24}+\frac{-21}{24}$
$=\frac{18+20(-21)}{24}$
$=\frac{18+20-21}{24}$
$=\frac{17}{24}$
View full question & answer→Question 802 Marks
Evaluate the following:$-2-\frac{5}{9}$
Answer$\frac{-2}{1}-\frac{5}{9}$ $=\frac{-18-5}{9}=\frac{-23}{9}$
View full question & answer→Question 812 Marks
Subtract the first rational number from the second in the following: $\frac{-2}{11},\frac{-9}{11}$
Answer$\frac{-2}{11},\frac{-9}{11}$
$\frac{-2}{11}$ from $\frac{-9}{11}=\frac{-9}{11}-\Big(\frac{-2}{11}\Big)$
$\frac{-9}{11}+\frac{2}{11}=\frac{-9+2}{11}$
$=\frac{-7}{11}$
View full question & answer→Question 822 Marks
Simplify: $\frac{5}{6}+\frac{-2}{5}-\frac{-2}{15}$
Answer$\frac{5}{6}+\frac{-2}{5}-\frac{-2}{15}$
Taking the $LCM$ of the denominators:
$\frac{25}{30}+\frac{-12}{30}-\frac{-4}{30}$
$=\frac{25+(-12)-(-4)}{30}$
$=\frac{25-12+4}{30}$
$=\frac{17}{30}$
View full question & answer→Question 832 Marks
Evaluate the following:$\frac{2}{3}-\frac{3}5{}$
Answer$\frac{2}{3}-\frac{3}{5}$
$=\frac{10-9}{15}$$(LCM$ of $3, 5 = 15)$ $=\frac{1}{15}$
View full question & answer→Question 842 Marks
Add the following rational number: $-3$ and $\frac{3}{5}$
Answer$-3$ and $\frac{3}{5}$ $=\frac{-3}{1}+\frac{3}{5}$
The $LCM$ of the denominators $1$ and $5$ is $5$.
Now, we will express $\frac{-3}{1}$ in the form in which it taken denominator as $5$.
$\frac{-3}{1}=\frac{-3\times5}{1\times5}=\frac{-15}{5}$
So, $\frac{15}{5}+\frac{3}{5}$ $=\frac{-15+3}{5}=\frac{-12}{5}$
View full question & answer→Question 852 Marks
Express the following as a rational number of the form $\frac{\text{p}}{\text{q}}:$ $\frac{15}{2}+\frac{9}{8}+\frac{-11}{3}+6+\frac{-7}{6}$
Answer$\frac{15}{2}+\frac{9}{8}+\frac{-11}{3}+6+\frac{-7}{6}$
$=\frac{180}{24}+\frac{27}{24}+\frac{-88}{24}+\frac{144}{24}+\frac{-28}{24}$
$=\frac{180+27+(-88)+144+(-28)}{24}$
$=\frac{180+27-88+144-28}{24}$
$=\frac{235}{24}$
View full question & answer→Question 862 Marks
By what number should we multiply $\frac{-8}{13}$ so that the product may be $24$?
AnswerProduct of two numbr $= 24$ One number $=\frac{-8}{13}$
$\therefore$ Required number $=24\div\frac{-8}{13}$
$=24\times\frac{13}{-8}=\frac{3\times13}{-1}=\frac{39}{-1}$
$=\frac{39\times(-1)}{-1\times(-1)}=\frac{-39}{1}=-39$
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