Question 12 Marks
Subtract the first rational number from the second in the following:
$\frac{-7}{9},\frac{4}{9}$
Answer$\frac{-7}{9},\frac{4}{9}$
$\frac{-7}{9}$ from $\frac{4}{9}=\frac{4}{9}-\Big(\frac{-7}{9}\Big)$
$=\frac{4}{9}+\frac{7}{9}=\frac{4+7}{9}$
$=\frac{11}{9}$
View full question & answer→Question 22 Marks
Simplify:
$1+\frac{-4}{5}$
Answer$1+\frac{-4}{5}$
The LCM of the denominator 1 and 5 is 5.
Now,
We need to express $\frac{1}{1}$ in the form in which it takes denominator as 5.
$\frac{1}{1}=\frac{1\times5}{1\times5}=\frac{5}{5}$
So,
$\frac{5}{5}+\frac{-4}{5}$
$=\frac{5-4}{5}=\frac{1}{5}$
View full question & answer→Question 32 Marks
Find ten rational number between $\frac{-2}{5}$ and $\frac{1}{2}$.
Answer$\therefore \frac{-2}{5}=\frac{-2\times4}{5\times4}=\frac{-8}{20}$
and $\frac{1}{2}=\frac{1\times10}{2\times10}=\frac{10}{20}$
Now number lying between -8, 10 will be
-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4,.............9
$\therefore$ The rational number will be
$\frac{-7}{20},\frac{-6}{20},\frac{-5}{20},\frac{-4}{20},.........\frac{8}{2},\frac{9}{20}$
View full question & answer→Question 42 Marks
The sum of two numbers is $\frac{-4}3{}.$ If one of the numbers is $-5,$ find the other.
AnswerSum of two number $=\frac{-4}{3}$
One number $=-5$
$\therefore$ Second number $=\frac{-4}{3}-(-5)$
$=\frac{-4}{3}+\frac{5}{1}$
$=\frac{-4+15}{3}=\frac{11}{3}$
View full question & answer→Question 52 Marks
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$\frac{-5}{8}\times\frac{16}{15}$
AnswerMultiplicative inverse of $=\frac{-5}{8}\times\frac{16}{15}$
$=\frac{8}{-5}\times\frac{15}{16}=\frac{8\times15}{-5\times16}$
$=\frac{1\times3}{-1\times2}=\frac{3}{-2}$
$=\frac{3\times(-1)}{-2\times(-1)}=\frac{-3}{2}$
View full question & answer→Question 62 Marks
By what number should we multiply $\frac{-15}{28}$ so that the product may be $\frac{-5}{7}$?
AnswerProduct of two number $=\frac{-5}{7}$
One number $=\frac{-15}{28}$
$\therefore$ Required number $=\frac{-5}{7}\times\frac{28}{-15}=\frac{-1\times4}{1\times(-3)}$
$=\frac{-5}{7}\times\frac{28}{-15}=\frac{-1\times4}{1\times(-3)}$
$=\frac{-4}{-3}=\frac{4}{3}$
View full question & answer→Question 72 Marks
Add the following rational number:
$\frac{5}{36}$ and $\frac{-7}{12}$
Answer$\frac{5}{36}+\frac{-7}{12}$
The LCM of the denminater 12 and 36.
Now,
We will express $\frac{-7}{12}$in the form in which it taken denominator as 36.
$\frac{-7}{12}=\frac{-7\times3}{12\times3}=\frac{-12}{36}$
So,
$\frac{-21}{36}+\frac{5}{36}$
$=\frac{-21+5}{36}=\frac{-16}{36}=\frac{-4}{9}$
View full question & answer→Question 82 Marks
Simplify the following and express the result as a rational number in standard form:
$\frac{-11}{9}\times\frac{-81}{-88}$
Answer$\frac{-11}{9}\times\frac{-81}{-88}=\frac{(-11)\times(-81)}{9\times(-88)}$
$=\frac{(-1)\times(-9)}{1\times(-8)}=\frac{9}{-8}$
$=\frac{9\times(-1)}{(-8)\times(-1)}=\frac{-9}{8}$
View full question & answer→Question 92 Marks
Use the distributivity of multiplication of rational numbers over their addition to simplify:$\frac{2}{7}\times\Big(\frac{7}{16}-\frac{21}{4}\Big)$
Answer$\frac{2}{7}\times\Big(\frac{7}{16}-\frac{21}{4}\Big)$
$=\frac{2}{7}\times\frac{7}{16}-\frac{2}{7}\times\frac{21}{4}$
$=\frac{2\times7}{7\times16}-\frac{2\times21}{7\times4}$
$=\frac{1\times1}{1\times8}-\frac{1\times3}{1\times2}$
$=\frac{1}{8}-\frac{3}2{}$
$=\frac{1-12}{8}=\frac{-11}{8}$
View full question & answer→Question 102 Marks
Evaluate the following:$\frac{-6}{13}-\frac{-7}{13}$
Answer$\frac{-6}{13}-\frac{-7}{13}$
$\frac{-6}{13}-\frac{-7}{13}=\frac{-6}{13}+\frac{7}{13}=\frac{-6+7}{13}$
$=\frac{1}{13}$
View full question & answer→Question 112 Marks
Subtract the first rational number from the second in the following:
$\frac{11}{13},\frac{-4}{13}$
Answer$\frac{11}{13},\frac{-4}{13}$
$\frac{11}{13}$ from $\frac{-4}{13}=\frac{-4}{13}-\frac{11}{13}$
$=\frac{-4-11}{13}=\frac{-15}{13}$
View full question & answer→Question 122 Marks
Evaluate the following:$\frac{-5}{14}-\frac{-2}{7}$
Answer$\frac{-5}{14}-\frac{-2}{7}$
$\frac{-5}{14}-\frac{-2}{7}=\frac{-5}{14}+\frac{2}{7}$
$=\frac{-5+4}{14}$ (LCM of 14, 7 = 14)
$=\frac{-1}{14}$
View full question & answer→Question 132 Marks
Add the following rational number:
$\frac{31}{-4}$ and $\frac{-5}{8}$
Answer$\frac{31}{-4}+\frac{-5}{8}$
$=\frac{31}{-4}=\frac{-31}{4}$
The LCM of the denominators 4 and 8 is 8.
Now,
We will express $\frac{31}{-4}$ in the form in which it taken denominator as 8.
$\frac{-31}{4}=\frac{-31\times2}{4\times2}=\frac{-62}{8}$
So,
$\frac{-62}{8}+\frac{-5}{8}$
$=\frac{-62-5}{8}=\frac{-67}{8}$
View full question & answer→Question 142 Marks
Use the distributivity of multiplication of rational numbers over their addition to simplify:$\frac{3}{4}\times\Big(\frac{8}{9}-40\Big)$
Answer$\frac{3}{4}\times\Big(\frac{8}{9}-40\Big)$
$\frac{3}{4}\times\frac{8}{9}-\frac{3}{4}\times\frac{40}{1}$
$=\frac{3\times8}{4\times9}-\frac{3\times40}{4\times1}$
$=\frac{1\times2}{1\times3}-\frac{3\times10}{1\times1}$
$=\frac{2}{3}-\frac{30}{1}$
$=\frac{2-90}{3}=\frac{-88}{5}$
View full question & answer→Question 152 Marks
Evaluate the following:$\frac{-4}{7}-\frac{2}{-3}$
Answer$\frac{-4}{7}-\frac{2}{-3}$
$\frac{-4}{7}-\frac{2}{-3}=\frac{-4}{7}+\frac{2}{3}$
$=\frac{-12+14}{21}$ (LCM of 7, 3 = 21)
$=\frac{2}{21}$
View full question & answer→Question 162 Marks
What should be added to $\Big(\frac{2}3{}+\frac{3}{5}\Big)$ to get $\frac{-12}{15}?$
AnswerThe required number $=\frac{-2}{15}-\Big(\frac{2}{3}+\frac{3}{5}\Big)$
$=\frac{-2}{15}-\frac{19}{15}=\frac{-2-19}{15}$
$=\frac{-21}{15}=\frac{-21\div3}{15\div3}=\frac{-7}{5}$
View full question & answer→Question 172 Marks
By what number should $\frac{-33}{16}$ be divided to get $\frac{-11}{4}$?
AnswerLet x be divide, then
$\frac{-33}{16}\div\text{x}=\frac{-11}{4}$
$\Rightarrow\frac{-33}{16}\times\frac{1}{\text{x}}=\frac{-11}{4}$
$\Rightarrow\text{x}=\frac{-33}{16}\times\frac{4}{-11}=\frac{3\times1}{4\times1}=\frac{3}{4}$
$\therefore$ Required number $=\frac{3}{4}$
View full question & answer→Question 182 Marks
Simplify:
$\frac{5}{3}-\frac{7}{6}+\frac{-2}{3}$
Answer$\frac{5}{3}-\frac{7}{6}+\frac{-2}{3}$
Taking the LCM of the denominators:
$\frac{10}{6}-\frac{7}{6}+\frac{-4}{6}$
$=\frac{10-7+(-4)}{6}$
$=\frac{10-7-4}{6}$
$=\frac{-1}{6}$
View full question & answer→Question 192 Marks
Subtract the first rational number from the second in the following:
$\frac{3}{8},\frac{5}{8}$
Answer$\frac{3}{8},\frac{5}{8}$
$\frac{3}{8}$ from $\frac{5}{8}$ $=\frac{5}{8}-\frac{3}{8}=\frac{5-3}{8}$
$=\frac{2}{8}=\frac{2\div2}{8\div2}=\frac{1}{4}$
View full question & answer→Question 202 Marks
Fill in blanks:$\frac{-7}{9}+ \ ........ \ =3$
Answer$\frac{-7}{9}+\frac{34}{9} =3$Solution:
Required number $=3-\Big(\frac{-7}{9}\Big)$ $=\frac{3}{1}+\frac{7}{9}$ $=\frac{27+7}{9}$ $=\frac{34}{9}$
View full question & answer→Question 212 Marks
Simplify:
$\frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7}$
Answer$\frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7}$
Taking the LCM of the denominators:
$\frac{-28}{70}-\frac{-21}{70}-\frac{-40}{70}$
$=\frac{(-28)-(-21)-(-40)}{70}$
$=\frac{-28+21+40}{70}$
$=\frac{33}{70}$
View full question & answer→Question 222 Marks
Find a rational number between -3 and 1.
AnswerWe know that a number between two rational
numbers a, b $=\frac{\text{a}+\text{b}}{2}$
$\therefore$ RAtional number between -3 and 1 $=\frac{-3+1}{2}$
$=\frac{-2}{2}=-1$
View full question & answer→Question 232 Marks
Fill in blanks:$\frac{-4}{13}-\frac{-3}{26}= \ ...........$
Answer$\frac{-4}{13}-\frac{-3}{26}=\frac{-5}{26}$Solution:
Required number $=\frac{-4}{13}+\frac{-3}{26}=\frac{-4}{13}+\frac{3}{26}$ $=\frac{-8+3}{26}=\frac{-5}{26}$ $\therefore\frac{-4}{13}-\frac{-3}{26}=\frac{-5}{26}$
View full question & answer→Question 242 Marks
Evaluate the following:$\frac{-3}{-8}-\frac{-2}{7}$
Answer$\frac{-3}{-8}-\frac{-2}{7}$
$\frac{-3}{-8}-\frac{-2}{7}=\frac{3}{8}+\frac{2}{7}$
$=\frac{21+16}{56}$ (LCM of 8, 7 = 56)
$=\frac{37}{56}$
View full question & answer→Question 252 Marks
Simplify the following and write as a rational number of the form $\frac{\text{p}}{\text{q}}:$
$\frac{-4}{5}+\frac{-7}{10}+\frac{-8}{15}$
Answer$\frac{-4}{5}+\frac{-7}{10}+\frac{-8}{15}$
$=\frac{-24}{30}+\frac{-21}{30}+\frac{-16}{30}$
$=\frac{(-24)+(-21)+(-16)}{30}$
$=\frac{-24-21-16}{30}$
$=\frac{-61}{30}$
View full question & answer→Question 262 Marks
What should be added to so as to $\frac{-7}{8}$ get $\frac{5}{9}?$
AnswerThe required nuber $=\frac{5}{9}-\Big(\frac{-7}{8}\Big)$
$=\frac{5}{9}+\frac{7}{8}$
$=\frac{40+63}{72}$ (LCM of 9, 8 = 72)
$=\frac{103}{72}$
View full question & answer→Question 272 Marks
Evaluate the following:$\frac{-4}{13}-\frac{-5}{26}$
Answer$\frac{-4}{13}-\frac{-5}{26}$
$\frac{-4}{13}-\frac{-5}{26}=\frac{-4}{13}+\frac{5}{26}$
$=\frac{-8+5}{26}$ (LCMof 13, 26 = 26)
$=\frac{-3}{26}$
View full question & answer→Question 282 Marks
Add the following rational number:
$\frac{5}{-9}$ and $\frac{7}{3}$
Answer$\frac{5}{-9}+\frac{7}{3}$
$=\frac{-5}{9}+\frac{7}{3}$
The LCM of the denominators 9 and 3 is 9.
Now,
We wil express $\frac{7}{3}$ in the from in which it taken denominator as 9.
$\frac{7\times3}{3\times3}=\frac{21}{9}$
So,
$\frac{-5}{9}+\frac{21}{9}$
$=\frac{-5+21}{9}=\frac{16}{9}$
View full question & answer→Question 292 Marks
Subtract the first rational number from the second in the following:
$\frac{1}{4},\frac{-3}{8}$
Answer$\frac{1}{4},\frac{-3}{8}$
$\frac{1}{4}$ from $\frac{-3}{8}=\frac{-3}{8}-\Big(\frac{1}{4}\Big)$
$=\frac{-3}{8}-\frac{1}{4}$
$=\frac{-3-2}{8}$ (LCM 8, 4 = 8)
$=\frac{-5}{8}$
View full question & answer→Question 302 Marks
Evaluate the following:$\frac{4}7{}-\frac{-5}{-7}$
Answer$\frac{4}{7}-\frac{-5}{-7}$
$\frac{4}{7}-\frac{-5}{-7}=\frac{4}{7}-\frac{5}{7}$
$=\frac{4-5}{7}=\frac{-1}{7}$
View full question & answer→Question 312 Marks
Simplify the following and write as a rational number of the form $\frac{\text{p}}{\text{q}}:$
$\frac{-9}{10}+\frac{22}{15}+\frac{13}{-20}$
Answer$\frac{-9}{10}+\frac{22}{15}+\frac{13}{-20}$
$=\frac{-54}{60}+\frac{88}{60}+\frac{-39}{60}$
$=\frac{(-54)+88+(-39)}{60}$
$=\frac{-54+88-39}{60}$
$=\frac{-5}{60}$
$=\frac{-1}{12}$
View full question & answer→Question 322 Marks
Express the following as a rational number of the form $\frac{\text{p}}{\text{q}}:$
$\frac{6}{7}+1+\frac{-7}{9}+\frac{19}{21}+\frac{-12}{7}$
Answer$\frac{6}{7}+1+\frac{-7}{9}+\frac{19}{21}+\frac{-12}{7}$
$=\frac{54}{63}+\frac{63}{63}+\frac{-49}{63}+\frac{57}{63}+\frac{-108}{63}$
$=\frac{54+63+(-49)+57+(-108)}{63}$
$=\frac{54+63-49+57-108}{63}$
$=\frac{17}{63}$
View full question & answer→Question 332 Marks
Subtract the first rational number from the second in the following:
$\frac{-8}{33},\frac{-7}{22}$
Answer$\frac{-8}{33},\frac{-7}{22}$
$\frac{-8}{33}$ from $\frac{-7}{22}=\frac{-7}{22}-\Big(\frac{-8}{33}\Big)$
$=\frac{-21+16}{66}=\frac{-5}{66}$
View full question & answer→Question 342 Marks
What number should be added to $\frac{-5}{7}$ so as to get $\frac{-2}{3}?$
AnswerThe required number $=\frac{-2}{3}-\Big(\frac{-5}{7}\Big)$
$=\frac{-2}{3}+\frac{5}{7}$
$=\frac{-14+15}{21}$ (LCM of 3, 7 = 21)
$=\frac{1}{21}$
View full question & answer→Question 352 Marks
Add the following rational number:
$\frac{3}{4}$ and $\frac{-5}{8}$
AnswerClearly, denominators of the given number are positive.
The LCM of the denominators 4 and 8 is 8.
Now, will express 34 in the form in which it taken the denominatore as 8.
$\frac{3\times2}{4\times2}=\frac{6}{8}=\frac{3}{4}$
Now,
$\frac{-5}{8}+\frac{6}{8}$
$=\frac{-5+6}{8}=\frac{1}{8}$
View full question & answer→Question 362 Marks
Simplify:
$\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}$
Answer$\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}$
Taking the LCM of the denominators:
$\frac{15}{12}-\frac{14}{12}-\frac{-8}{12}$
$=\frac{15-14-(-18)}{12}$
$=\frac{15-14+8}{12}$
$=\frac{9}{12}$
$=\frac{3}{4}$
View full question & answer→Question 372 Marks
The sum of two numbers is $\frac{5}{9}.$ If one of the numbers is $\frac{1}{3},$ find the other.
AnswerSum of two number $=\frac{5}{9}$
One number $=\frac{1}{3}$
$\therefore$ Second number $=\frac{5}{9}-\frac{1}{3}$
$=\frac{5-3}{9}$ (LCM of 9, 3 = 9)
$=\frac{2}{9}$
View full question & answer→Question 382 Marks
Evaluate the following:$\frac{13}{15}-\frac{12}{25}$
Answer$\frac{13}{15}-\frac{12}{25}$
$\frac{65-36}{75}$ (LCM of 15, 25 = 75)
$=\frac{29}{75}$
View full question & answer→Question 392 Marks
Simplify the following and write as a rational number of the form $\frac{\text{p}}{\text{q}}:$
$\frac{-11}{2}+\frac{7}{6}+\frac{-5}{8}$
Answer$\frac{-11}{2}+\frac{7}{6}+\frac{-5}{8}$
$=\frac{-132}{24}+\frac{28}{24}+\frac{-15}{24}$
$=\frac{(-132)+28+(-15)}{24}$
$=\frac{-132+28-15}{24}$
$=\frac{-119}{24}$
View full question & answer→Question 402 Marks
Multiply:
$\frac{-6}{11}\ \text{by}\ \frac{-55}{36}$
Answer$\frac{-6}{11}\ \text{by}\ \frac{-55}{36}=\frac{-6}{11}\times\frac{-55}{36}$
$=\frac{(-6)\times(-55)}{36}$
$=\frac{(-1)\times(-5)}{1\times6}=\frac{5}{6}$
View full question & answer→Question 412 Marks
The sum of two numbers is $\frac{-1}3{}.$ If one of the numbers is $\frac{-12}{3},$ find the other.
AnswerSum of two number $=\frac{-1}{3}$
One number $=\frac{-12}{3}$
$\therefore$ Second number $=\frac{-1}{3}-\Big(\frac{-12}{3}\Big)$
$=\frac{-1}{3}+\frac{12}{3}$
$=\frac{-1+12}{3}=\frac{11}{3}$
View full question & answer→Question 422 Marks
The product of two rational numbers is $\frac{-8}{9}$ If one of the numbers is $\frac{-4}{15},$ find the other.
AnswerProduct of twon numbers $=\frac{-8}{9}$One number $=\frac{-4}{15}$
$\therefore$ Second number $=\frac{-8}{9}+\frac{-4}{15}$
$=\frac{-8}{9}\times\frac{15}{-4}=\frac{-2\times5}{3\times(-1)}$
$=\frac{-10}{-3}=\frac{10}{3}$
View full question & answer→Question 432 Marks
Simplify the following and write as a rational number of the form $\frac{\text{p}}{\text{q}}:$
$\frac{5}{3}+\frac{3}{-2}+\frac{-7}{3}+3$
Answer$\frac{5}{3}+\frac{2}{-3}+\frac{-7}{3}+3$
$=\frac{10}{6}+\frac{-9}{6}+\frac{-14}{6}+\frac{18}{6}$
$=\frac{10(-9)+(-14)+18}{6}$
$=\frac{10-9-14+18}{6}$
$=\frac{5}{6}$
View full question & answer→Question 442 Marks
Use the distributivity of multiplication of rational numbers over their addition to simplify:$\frac{3}{5}\times \Big(\frac{35}{24}+\frac{10}{1}\Big)$
Answer$\frac{3}{5}\times \Big(\frac{35}{24}+\frac{10}{1}\Big)$
$=\frac{3}{5}\times\frac{35}{24}+\frac{3}{5}\times\frac{10}{1}$
$=\frac{3\times35}{5\times24}+\frac{3\times10}{5\times1}$
$=\frac{1\times7}{1\times8}+\frac{3\times2}{1\times1}=\frac{7}{8}+6$
$=\frac{7}{8}+\frac{48}{1}$
$=\frac{7+48}{8}=\frac{55}{8}$
View full question & answer→Question 452 Marks
Evaluate the following:$\frac{5}{63}-\frac{-8}{21}$
Answer$\frac{5}{63}-\frac{-8}{21}$
$\frac{5}{63}-\frac{-8}{21}=\frac{5}{63}+\frac{8}{21}$
$=\frac{5+24}{63}$ (LCM of 63, 21 = 63)
$=\frac{29}{63}$
View full question & answer→Question 462 Marks
Find two number betwen $\frac{1}{5}$ and $\frac{1}{2}$.
AnswerRational' number between $\frac{1}{5}$ and $\frac{1}{2}=\frac{\Big(\frac{1}{5}+\frac{1}{2}\Big)}{2}=\frac{\frac{2+5}{10}}{2}=\frac{7}{20}$
Rational number between $\frac{1}{5}$ and $\frac{7}{20}=\frac{\Big(\frac{1}{5}+\frac{1}{2}\Big)}{2}=\frac{\frac{4+7}{20}}{2}=\frac{11}{40}$
Therefore, two rational number between $\frac{1}{5}$ and $\frac{1}{2}$ are $\frac{7}{20}$ and $\frac{11}{40}.$
View full question & answer→Question 472 Marks
What number should be added to $\frac{-5}{11}$ so as to get $\frac{26}{3}?$
AnswerThe required number $=\frac{26}{33}-\Big(\frac{-5}{11}\Big)$
$=\frac{26}{33}+\frac{5}{11}$ (LCM of 33, 11 = 33)
$=\frac{26+15}{33}=\frac{41}{33}$
View full question & answer→Question 482 Marks
Use the distributivity of multiplication of rational numbers over their addition to simplify:$\frac{-5}{4}\times\Big(\frac{8}{5}+\frac{16}{5}\Big)$
Answer$\frac{-5}{4}\times\Big(\frac{8}{5}+\frac{16}{5}\Big)$
$=\frac{-5}{4}\times\frac{8}{5}+\frac{-5}{4}\times\frac{16}{5}$
$=\frac{-5\times8}{4\times5}+\frac{-5\times16}{4\times5}$
$=\frac{-1\times2}{1\times1}+\frac{-1\times4}{1\times1}$
$=-2-4=-6$
View full question & answer→Question 492 Marks
What should be subtracted from $\Big(\frac{3}{4}-\frac{2}{3}\Big)$ to get $\frac{-1}{6}?$
AnswerThe required number $=\Big(\frac{3}{4}-\frac{2}{3}\Big)-\Big(\frac{-1}{6}\Big)$
$=\frac{3}{4}-\frac{2}{3}+\frac{1}{6}$
$=\frac{9-8+2}{12}$ (LCM of 4, 3, 6 = 12)
$=\frac{11-8}{12}=\frac{3}{12}$
$=\frac{3\div3}{12\div3}=\frac{1}{4}$
View full question & answer→Question 502 Marks
Find four rational number between $\frac{-2}{9}$ and $\frac{5}{9}.$
Answer$\because -1,0,1,2,3,4$ lie between -2 and 5
$\therefore$four rational numbers between $\frac{-2}{9}$ and $\frac{5}{9}$
can be $\frac{-1}{9},0,\frac{1}{9},\frac{2}{9}.....$
View full question & answer→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$\frac{77}{23}+\frac{15}{32}=4$Solution:
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$\frac{-9}{14}+\frac{-5}{14}= -1$Solution:
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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