Question 1011 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{-13}{9}\times\frac{27}{-26}$
Answer$\frac{-13}{9}\times\frac{27}{-26}=\frac{-13\times27}{9\times(-26)}$
$=\frac{-1\times3}{-\times(-2)}=\frac{-3}{-2}=\frac{3}{2}$
View full question & answer→Question 1021 Mark
Simplify:
$0+\frac{-3}{5}$
Answer$0+\frac{-3}{5}$
$=\frac{-3}{5}$
View full question & answer→Question 1031 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{7}{4}\times\Big(\frac{-8}{3}+\frac{-13}{12}\Big)=\frac{7}{4}\times\frac{-8}{3}+\frac{7}{4}+\frac{-13}{12}$
Answer$\frac{7}{4} \times\left(\frac{-8}{3}+\frac{-13}{12}\right)$
$=\frac{7}{4}\times\frac{-8}{3}+\frac{7}{4}+\frac{-13}{12}$
View full question & answer→Question 1041 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-5}{9}\times\Big(\frac{4}{15}\times\frac{-9}{8}\Big)=\Big(\frac{-5}{9}\times\frac{4}{15}\Big)\times\frac{-9}{8}$
Answer$\frac{-5}{9}\times\Big(\frac{4}{15}\times\frac{-9}{8}\Big)$
$=\Big(\frac{-5}{9}\times\frac{4}{15}\Big)\times\frac{-9}{8
It is associativem property.
View full question & answer→Question 1051 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-5}{16}\times\frac{8}{15}=\frac{8}{15}\times\frac{-5}{16}$
Answer$\frac{-5}{16}\times\frac{8}{15}=\frac{8}{15}\times\frac{-5}{16}$
It is commutative property.
View full question & answer→Question 1061 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-3}{2}\times\frac{5}{4}+\frac{-3}{2}\times\frac{-7}{6}=\frac{-3}{2}\times\Big(\frac{5}{4}+\frac{-7}{6}\Big)$
Answer$\frac{-3}{2}\times\frac{5}{4}+\frac{-3}{2}\times\frac{-7}{6}$
$=\frac{-3}{2}\times\Big(\frac{5}{4}+\frac{-7}{6}\Big)$
It is destributive law of multiplication over addition.
View full question & answer→Question 1071 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{2}{13}\times0=0=0\times\frac{2}{13}$
Answer$\frac{2}{13}\times0=0=0\times\frac{2}{13}$
It is zero property of multiplication.
View full question & answer→Question 1081 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-17}{5}\times9=9\times\frac{-17}{5}$
Answer$\frac{-17}{5}\times9=9\times\frac{-17}{5}$
It is commutative property.
View full question & answer→Question 1091 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{13}{-17}\times1=\frac{13}{-17}=1\times\frac{13}{-17}$
Answer$\frac{13}{-17}\times1=\frac{13}{-17}$
$=1\times\frac{13}{-17}$
It is multiplicative identity.
View full question & answer→Question 1101 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-11}{16}\times\frac{16}{-11}=1$
Answer$\frac{-11}{16}\times\frac{16}{-11}=1$
It is existanceof multiplicative inverse.
View full question & answer→Question 1111 Mark
Multiply: $\frac{9}{-7}\ \text{by}\ \frac{36}{-11}$
Answer$\frac{9}{-7}\ \text{by}\ \frac{36}{-11}=\frac{9\times36}{(-7)\times(-11)}=\frac{324}{77}$
View full question & answer→Question 1121 Mark
Multiply: $\frac{-8}{9}\ \text{by}\ \frac{3}{64}$
Answer$\frac{-8}{9}\ \text{by}\ \frac{3}{64}$
$=\frac{-8\times3}{9\times64}=\frac{-1\times1}{3\times8}=\frac{-1}{24}$
View full question & answer→Question 1131 Mark
Multiply: $\frac{-8}{25}\ \text{by}\ \frac{-5}{16}$
Answer$\frac{-8}{25}\ \text{by}\ \frac{-5}{16}=\frac{(-8)\times(-5)}{25\times16}$
$=\frac{(-1)\times(-1)}{5\times2}=\frac{1}{10}$
View full question & answer→Question 1141 Mark
Multiply: $\frac{7}{11}\ \text{by}\ \frac{5}{4}$
Answer$\frac{7}{11}\ \text{by}\ \frac{5}{4}=\frac{7\times5}{11\times4}=\frac{35}{44}$
View full question & answer→Question 1151 Mark
Multiply: $\frac{6}{7}\ \text{by}\ \frac{-49}{36}$
Answer$\frac{6}{7}\ \text{by}\ \frac{-49}{36}=\frac{6}{7}\times\frac{-49}{36}$
$=\frac{6\times(-49)}{7\times36}=\frac{1\times(-7)}{1\times6}=\frac{-7}{6}$
View full question & answer→Question 1161 Mark
Multiply: $\frac{5}{7}\ \text{by}\ \frac{-3}{4}$
Answer$\frac{5}{7}\ \text{by}\ \frac{-3}{4}=\frac{5\times(-3)}{7\times4}=\frac{-15}{28}$
View full question & answer→Question 1171 Mark
Multiply: $-\frac{3}{5}\ \text{by}\ -\frac{4}{7}$
Answer$-\frac{3}{5}\ \text{by}\ -\frac{4}{7}=\frac{-3\times(-4}{5\times7}=\frac{12}{35}$
View full question & answer→Question 1181 Mark
Multiply: $\frac{-3}{17}\ \text{by}\ \frac{-5}{-4}$
Answer$\frac{-3}{17}\ \text{by}\ \frac{-5}{-4}=\frac{-3\times(-5)}{17\times(-4)}=\frac{15}{-68}$
View full question & answer→Question 1191 Mark
Multiply: $\frac{-2}{9}\ \text{by}\ \frac{5}{11}$
Answer$\frac{-2}{9}\ \text{by}\ \frac{5}{11}=\frac{-2\times5}{9\times11}=\frac{-10}{99}$
View full question & answer→Question 1201 Mark
Multiply: $-\frac{15}{11}\ \text{by}\ 7$
Answer$-\frac{15}{11}\ \text{by}\ 7=\frac{-15\times7}{11}=\frac{-105}{11}$
View full question & answer→Question 1211 Mark
Multiply: $\frac{-11}{13}\ \text{by}\ \frac{-21}{7}$
Answer$\frac{-11}{13}\ \text{by}\ \frac{-21}{7}=\frac{(-11)\times(-21)}{13\times7}$
$=\frac{231}{91}=\frac{231\div7}{91\div7}=\frac{33}{13}$
View full question & answer→Question 1221 Mark
If 24 trousers of equal size can be prepared in 54 metres of cloth, what length of cloth is required for each trouser?
AnswerCloth required for 24 trousers = 54m
$\therefore$Cloth required for 1 trouser$=(54\div24)\text{m}$
$=\frac{54}{24}=\frac{9}{4}=2\frac{1}{4}\text{m}$
View full question & answer→Question 1231 Mark
Find the value and express as a rational number in standard form: $\frac{-36}{126}\div\frac{-3}{75}$
Answer$\frac{-36}{126}\div\frac{-3}{75}=\frac{-36}{125}\times\frac{75}{-3}$ $=\frac{-36\times75}{125\times(-3)}=\frac{-12\times3}{5\times(-1)}$ $=\frac{-36}{-5}=\frac{36}{5}$
View full question & answer→Question 1241 Mark
Find the value and express as a rational number in standard form: $\frac{2}{5}\div\frac{26}{15}$
Answer$\frac{2}{5}\div\frac{26}{15}=\frac{2}{5}\times\frac{15}{26}=\frac{2\times15}{5\times26}$ $=\frac{1\times3}{1\times13}=\frac{3}{13}$
View full question & answer→Question 1251 Mark
Find the value and express as a rational number in standard form: $\frac{-22}{27}\div\frac{-110}{18}$
Answer$\frac{-22}{27}\div\frac{-110}{18}=\frac{-22}{27}\times\frac{18}{-110}$ $=\frac{-22\times18}{27\times(-110)}=\frac{-1\times2}{34\times(-5)}$ $=\frac{-2}{-15}=\frac{2}{15}$
View full question & answer→Question 1261 Mark
Find the value and express as a rational number in standard form: $\frac{10}{3}\div\frac{-35}{12}$
Answer$\frac{10}{3}\div\frac{-35}{12}=\frac{10}{3}\times\frac{12}{-35}$ $=\frac{10\times12}{3\times(-35)}$ $=\frac{2\times4}{1\times(-7)}=\frac{8}{-7}$ $=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
View full question & answer→Question 1271 Mark
Find the value and express as a rational number in standard form:
$\frac{-40}{99}\div(-20)$
Answer$\frac{-40}{99}\div(-20)=\frac{-40}{99}\times\frac{1}{-20}$ $=\frac{-2\times1}{99\times(-1)}=\frac{-2}{99}=\frac{2}{99}$
View full question & answer→Question 1281 Mark
Find the value and express as a rational number in standard form: $-6\div\frac{-8}{17}$
Answer$-6\div\frac{-8}{17}=-6\times\frac{17}{-8}$ $=\frac{-3\times17}{-4}$ $=\frac{-51}{4}=\frac{51}{4}$
View full question & answer→Question 1291 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{-7}{9}$
AnswerMultiplicative inverse of$\frac{-7}{9}=\frac{9}{-7}$
View full question & answer→Question 1301 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{-3}{-5}$
AnswerMultiplicative inverse of$=\frac{-5}{-3}=\frac{5}{3}$
View full question & answer→Question 1311 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{2}{3}\times\frac{9}{4}$
AnswerMultiplicative inverse of$\frac{2}{3}\times\frac{9}{4}$ $=\frac{3}{2}\times\frac{4}{9}$ $\frac{3\times4}{2\times9}=\frac{1\times2}{1\times3}$ $=\frac{2}{3}$
View full question & answer→Question 1321 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{12}{5}$
AnswerMultiplicative inverse of$\frac{12}{5}=\frac{5}{12}$
View full question & answer→Question 1331 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{0}{3}$
AnswerMultiplicative inverse of $0=$Does not exist as division by 0 is not admissible.
View full question & answer→Question 1341 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$-7$
AnswerMultiplicative inverse of$-7=\frac{1}{-7}$
View full question & answer→Question 1351 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $9$
AnswerMultiplicative inverse of$9=\frac{1}{9}$![]()
View full question & answer→Question 1361 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $-2\times\frac{-3}{5}$
AnswerMultiplicative inverse of $-2\times\frac{-3}{5}$ $=\frac{1}{-2}\times\frac{5}{-3}=\frac{1\times5}{(-2)\times(-3)}$ $=\frac{5}{6}$
View full question & answer→Question 1371 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $1$
AnswerMultiplicative inverse of$1=1$
View full question & answer→Question 1381 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $-1$
AnswerMultiplicative inverse of $-1=-1$
View full question & answer→Question 1391 Mark
Divide:
$\frac{-3}{4}\ \text{by}\ -6$
Answer$\frac{-3}{4}\ \text{by}\ -6=\frac{-3}{4}\div\frac{-6}{1}=\frac{-3}{1}\times\frac{1}{-6}$
$=\frac{-1\times1}{4\times(-2)}=\frac{-1}{-8}=\frac{1}{8}$
View full question & answer→Question 1401 Mark
Divide:
$\frac{-3}{13}\ \text{by}\ \frac{-4}{65}$
Answer$\frac{-3}{13}\ \text{by}\ \frac{-4}{65}$
$=\frac{-3}{13}\div\frac{-4}{65}=\frac{-3}{13}\times\frac{65}{-4}$
$=\frac{-3\times5}{1\times(-4)}=\frac{-15}{-4}=\frac{15}{4}$
View full question & answer→Question 1411 Mark
Divide:
$\frac{2}{3}\ \text{by}\ \frac{-7}{12}$
Answer$\frac{2}{3}\ \text{by}\ \frac{-7}{12}$
$=\frac{2}{3}\div\frac{-7}{12}=\frac{2}{3}\times\frac{12}{-7}$
$=\frac{2\times4}{1\times(-7)}=\frac{8}{-7}$
$=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
View full question & answer→Question 1421 Mark
Divide:
$-4\ \text{by}\ \frac{-3}{5}$
Answer$-4\ \text{by}\ \frac{-3}{5}$
$=-4\div\frac{-3}{5}$
$=-4\times\frac{5}{-3}$
$=\frac{-4\times5}{-3}$
$=\frac{-20}{-3}=\frac{20}{3}$
$=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
View full question & answer→Question 1431 Mark
Divide:
$1\ \text{by}\ \frac{1}{2}$
Answer$1\ \text{by}\ \frac{1}{2}=1\div\frac{1}{2}=1\times\frac{2}{1}=2$
View full question & answer→Question 1441 Mark
Divide:
$0\ \text{by}\ \frac{-7}{5}$
Answer$0\ \text{by}\ \frac{-7}{5}=0\div\frac{-7}{5}=0\times\frac{5}{-7}=0$
View full question & answer→Question 1451 Mark
Add the following ration numbers:
$\frac{-8}{11}$ and $\frac{-4}{11}$
Answer$\frac{-8}{11}+\frac{-4}{11}=\frac{-8-4}{11}=\frac{-12}{11}$
View full question & answer→Question 1461 Mark
Add the following ration numbers:
$\frac{6}{13}$ and $\frac{-9}{13}$
Answer$\frac{6}{13}+\frac{-9}{13}=\frac{6-9}{13}=\frac{-3}{13}$
View full question & answer→Question 1471 Mark
Add the following ration numbers:
$\frac{-5}{7}$ and $\frac{3}{7}$
Answer$\frac{-5}{7}+\frac{3}{7}=\frac{-5+3}{7}=\frac{-2}{7}$
View full question & answer→Question 1481 Mark
Add the following ration numbers:
$\frac{-15}{4}$ and $\frac{7}{4}$
Answer$\frac{-15}{7}+\frac{7}{4}=\frac{-15+7}{4}=\frac{-8}{4}=-2$
View full question & answer→