Question 12 Marks
Find six rational numbers between $\frac{-4}{8}\text{ and }\frac{3}{8}$
AnswerWe know that: $- 4, -3, -2, -1, 0, 1, 2, 3$
Therefore $\frac{-4}{8},\frac{-3}{8},\frac{-2}{8},\frac{-1}{8},\frac{0}{8},\frac{1}{8},\frac{2}{8},\frac{3}{8}$
Hence $6$ rational numbers between $\frac{-4}{8}$ and $\frac{3}{8}$ are $\frac{-3}{8},\frac{-2}{8},\frac{-1}{8},\frac{0}{8},\frac{1}{8},\frac{2}{8}$
View full question & answer→Question 22 Marks
Find the value and express as a rational number in standard form:
$\frac{10}{3}\div\frac{-35}{12}$
Answer $\frac{10}{3}\div\frac{-35}{12}$
$=\frac{10}{3}\times\frac{-12}{35}$
$=\frac{-40}{35}$
$=\frac{-8}{7}$
View full question & answer→Question 32 Marks
Multiply: $\frac{5}{7}\text{ by }\Big(\frac{-3}{4}\Big)$
Answer$\frac{5}{7}\text{ by }\frac{-3}{4}$ $=\frac{5}{7}\times\frac{-3}{4}=\frac{-15}{28}$
View full question & answer→Question 42 Marks
Find the value and express as a rational number in standard form: $-6\div\frac{-8}{17}$
Answer$-6\div\frac{-8}{17}$ $=-6\times\frac{-17}{8}$ $=\frac{102}{8}$ $=\frac{51}{4}$
View full question & answer→Question 52 Marks
Multiply: $\frac{-5}{17}\text{ by }\frac{51}{-60}$
Answer$\frac{-5}{17}\text{ by }\frac{51}{-60}$ $\frac{-5}{7}\times\frac{51}{-60}$ $=\frac{-255}{-1020}$ $=\frac{255}{1020}$ $=\frac{1}{4}$
View full question & answer→Question 62 Marks
Simplify the following and express the result as a rational number in standard form: $\frac{-13}{9}\times\frac{27}{26}$
Answer$\frac{-13}{9}\times\frac{27}{26}$ $\frac{-13}{9}\times\frac{27}{-26}$ $=\frac{3}{2}$
View full question & answer→Question 72 Marks
By what number should$\frac{-3}{4}$ so that the product may be $\frac{2}{3}?$
AnswerLet $x$ be the number by which we should multiply $\frac{-3}{4}$ to get $\frac{2}{3}$
$\frac{-3}{4}\times\text{x}=\frac{2}{3}$
$\Rightarrow\text{x}=\frac{2}{3}\times\frac{4}{-3}=\frac{-8}{9}$
View full question & answer→Question 82 Marks
Divide: $\frac{2}{3}\text{ by} \frac{-7}{12}$
Answer$\frac{2}{3}\text{ by} \frac{-7}{12}$ $\frac{2}{3}\div \frac{-7}{12}$ $\frac{2}{3}\times\frac{-12}{7}$ $=\frac{-8}{7}$
View full question & answer→Question 92 Marks
Divide: $5\text{ by }\frac{-5}{7}$
Answer$5\text{ by }\frac{-5}{7}$ $5\div\frac{-5}{7}$ $=5\times\frac{-7}{5}$ $=-7$
View full question & answer→Question 102 Marks
Multiply: $\frac{-6}{11}\text{ by }\frac{-55}{36}$
Answer$\frac{-6}{11}\text{ by }\frac{-55}{36}$ $\frac{-6}{11}\times\frac{-55}{36}$ $=\frac{-6}{11}\times\frac{-5\times11}{6\times6}$ $=\frac{5}{6}$
View full question & answer→Question 112 Marks
Find the value and express as a rational number in standard form:
$\frac{40}{98}\div-20$
Answer $\frac{40}{98}\div-20$
$=\frac{-2}{98}$
$=\frac{-1}{49}$
View full question & answer→Question 122 Marks
Subtract the first rational number from the second of the following: $-\frac{2}{11},\frac{-9}{11}$
Answer$\frac{-2}{11}+\frac{-9}{11}=\frac{-9}{11}+\frac{2}{11}$ $=\frac{-9+2}{11}$ $=-\frac{7}{11}$
View full question & answer→Question 132 Marks
Simplify the following and express the result as a rational number in standard form: $\frac{-19}{36}\times{16}$
Answer$\frac{-19}{36}\times{16}$ $=\frac{-304}{36}$ $=\frac{-76}{9}$
View full question & answer→Question 142 Marks
Divide: $\frac{-3}{4}\text{ by }\frac{9}{-16}$
Answer$\frac{-3}{4}\text{ by }\frac{9}{-16}$$\frac{-3}{4}\div\frac{9}{-16}$
$=\frac{-3}{4}\times\frac{-16}{9}$
$=\frac{-4}{-3}$
$=\frac{4}{3}$
View full question & answer→Question 152 Marks
Subtract the first rational number from the second of the following: $\frac{11}{13},\frac{-4}{13}$
Answer$\frac{11}{13},\frac{-4}{13}$ $\frac{-4}{13}-\frac{11}{13}=\frac{-4-11}{13}$ $=\frac{-15}{13}$
View full question & answer→Question 162 Marks
Divide: $\frac{-3}{4}\text{ by} -6$
Answer$\frac{-3}{4}\text{ by} -6$ $\frac{-3}{4}\div-6$ $\frac{-3}{4}\times\frac{-1}{6}$ $=\frac{1}{8}$
View full question & answer→Question 172 Marks
Divide: $\frac{-7}{8}\text{ by }\frac{-21}{16}$
Answer$\frac{-7}{8}\text{ by }\frac{-21}{16}$$\frac{-7}{8}\div\frac{-21}{16}$
$=\frac{-7}{8}\times\frac{-16}{21}$
$=\frac{2}{3}$
View full question & answer→Question 182 Marks
The product of two rational numbers is $15$. If one of the numbers is $-10$, find the other.
AnswerLet the first rational number $= x$. $\text{x}\times-10=15$
$\text{x}=\frac{15}{-10}$
$\text{x}=\frac{3}{-2}$
$\text{x}=\frac{-3}{2}$
Hence the number is $\text{x}=\frac{-3}{2}$
View full question & answer→Question 192 Marks
Simplify the following and express the result as a rational number in standard form: $\frac{7}{6}\times\frac{-3}{28}$
Answer$\frac{7}{6}\times\frac{-3}{28}$ $\frac{7}{6}\times\frac{-3}{28}$ $=\frac{-1}{8}$
View full question & answer→Question 202 Marks
Multiply: $\frac{6}{7}\text{ by }\frac{-49}{36}$
Answer$\frac{6}{7}\text{ by }\frac{-49}{36}$ $\frac{6}{7}\times\frac{-49}{36}$ $=\frac{-7}{6}$
View full question & answer→Question 212 Marks
Subtract the first rational number from the second of the following: $\frac{3}{8},\frac{5}{8}$
Answer$\frac{5}{8}-\frac{3}{8}=\frac{5-3}{8}$ $=\frac{2}{8}$
View full question & answer→Question 222 Marks
Divide: $\frac{7}{-4}\text{ by }\frac{63}{64}$
Answer$\frac{7}{-4}\text{ by }\frac{63}{64}$ $\frac{7}{-4}\div\frac{63}{64}$ $=\frac{7}{-4}\times\frac{64}{63}$ $=\frac{-16}{9}$
View full question & answer→Question 232 Marks
Divide: $0\text{ by }\frac{-7}{5}$
Answer$0\text{ by }\frac{-7}{5}$ $0\div\frac{-7}{5}$ $0\div\frac{-5}{7}$ $=0$
View full question & answer→Question 242 Marks
If 24 trousers of equal size can be prepared in $54$ metres of cloth, what length of cloth is required for each trouser?
AnswerLegnth of cloth required for each trouser $=\frac{\text{Total legnth of cloth}}{\text{number of trousers}}$
$=\frac{54}{24}$
$=\frac{9}{4}\text{ meters}$
$\frac{9}{4}$ meters of cloth is reiquired to make each trouser.
View full question & answer→Question 252 Marks
Find $10$ rational numbers between $\frac{7}{13}$ and $\frac{-4}{13}$
AnswerWe know that $7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, –4$
Therefore $\frac{7}{13},\frac{6}{13},\frac{5}{13},\frac{4}{13},\frac{3}{13},\frac{2}{13},\frac{1}{13},\frac{0}{13},\frac{-1}{13},\frac{-2}{13},\frac{-3}{13},\frac{-4}{13}$
Hence the $10$ rational numbers berween $\frac{7}{13}$and $\frac{-4}{13}$ are: $\frac{-3}{13},\frac{-2}{13},\frac{-1}{13},\frac{0}{13},\frac{1}{13},\frac{2}{13},\frac{3}{13},\frac{4}{13},\frac{5}{13},\frac{6}{13},\frac{7}{13}$
View full question & answer→Question 262 Marks
Add the following rational numbers: $\frac{-15}{4}\text{ and }\frac{7}{4}$
AnswerWe have: $\frac{-15}{4}+\frac{7}{4}$ $=\frac{-15+7}{4}$ $=\frac{-8}{4}$ $=-2$
View full question & answer→Question 272 Marks
Simplify the following and express the result as a rational number in standard form: $\frac{-16}{21}\times\frac{14}{5}$
Answer$\frac{-16}{21}\times\frac{14}{5}$ $=\frac{-224}{105}$ $=\frac{-35}{15}$
View full question & answer→Question 282 Marks
Add the following rational numbers:
$\frac{-8}{11}\text{ and }\frac{-4}{11}$
Answer $\frac{-8}{11}+\frac{-4}{11}$
$=\frac{-8-4}{11}$
$=\frac{-12}{11}$
View full question & answer→Question 292 Marks
Multiply: $\frac{-3}{17}\text{ by }\Big(\frac{-5}{-4}\Big)$
Answer$\frac{-3}{17}\text{ by }\Big(\frac{-5}{-4}\Big)$ $=\frac{-3}{17}\times\frac{-5}{-4}$ $=\frac{15}{-68}$ $=\frac{-15}{68}$
View full question & answer→Question 302 Marks
Find the value and express as a rational number in standard form: $\frac{2}{5}\div\frac{26}{15}$
Answer$\frac{2}{5}\div\frac{26}{15}$ $=\frac{2}{5}\times\frac{15}{26}$ $=\frac{3}{13}$
View full question & answer→Question 312 Marks
By what number should $\frac{-33}{16}$ be divided to get $\frac{-11}{4}?$
Answer$\frac{-33}{16}\div\text{x}=\frac{-11}{4}$
$\Rightarrow\text{x}=\frac{-33}{16}\div\frac{-11}{4}$
$\Rightarrow\text{x}=-\frac{33}{16}\times\frac{4}{-11}$
$\text{x}=\frac{3}{4}$
The number is $\text{x}=\frac{3}{4}$
View full question & answer→Question 322 Marks
Multiply: $\frac{7}{11}\text{ by }\frac{5}{4}$
Answer$\frac{7}{11}\times\frac{5}{4}$ $=\frac{7\times5}{11\times4}=\frac{35}{44}$
View full question & answer→Question 332 Marks
Add the following rational numbers: $\frac{-5}{7}\text{ and }\frac{3}{7}$
Answer$\frac{-5}{7}+\frac{3}{7}$ $=\frac{-5+3}{7}$ $=\frac{-2}{7}$
View full question & answer→Question 342 Marks
Subtract the first rational number from the second of the following: $-\frac{7}{9},\frac{4}{9}$
Answer$-\frac{7}{9}+\frac{4}{9}=\frac{4}{9}-\frac{-7}{9}$ $=\frac{4+7}{9}$ $=\frac{11}9{}$
View full question & answer→Question 352 Marks
Multiply: $\frac{-8}{25}\text{ by }\frac{-5}{16}$
Answer$\frac{-8}{25}\text{ by }\frac{-5}{16}$ $\frac{-8}{5\times5}\times\frac{-5}{8\times2}$ $=\frac{1}{10}$
View full question & answer→Question 362 Marks
The sum of the two numbers is $\frac{5}{9},$ $r$ one of me numbers is $\frac{1}{3}$ find the other.
AnswerRequired number $=\frac{5}{9}-\frac{1}{3}$
$LCM$ of $3$ and $9$ is $9$ $\frac{1}{3}=\frac{1\times3}{3\times3}=\frac{3}{9}$
Therefore required number $=\frac{5}{9}-\frac{3}9{}$
$=\frac{2}{9}$
View full question & answer→Question 372 Marks
Multiply: $\frac{(-2)}{9}\text{ by }\Big(\frac{5}{11}\Big)$
Answer$\frac{(-2)}{9}\text{ by }\Big(\frac{5}{11}\Big)$ $=\frac{-2}{9}\times\frac{5}{11}$ $=\frac{-10}{99}$
View full question & answer→Question 382 Marks
By what number should $\frac{-3}{4}$ be multiplied in order to produce $\frac{2}{3}$ ?
View full question & answer→Question 392 Marks
By what number should we multiply $\frac{-8}{13}$ so that the product may be 24 ?
View full question & answer→Question 402 Marks
By what number should we multiply $\frac{-15}{28}$ so that the product may be $\frac{-5}{7}$ ?
View full question & answer→Question 412 Marks
By what number should we multiply $\frac{-1}{6}$ so that the product may be $\frac{-23}{9}$ ?
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.
View full question & answer→Question 432 Marks
The product of two rational numbers is 15 . If one of the numbers is -10 , find the other.
Question 442 Marks
Find the value and express as a rational number in standard form:
$\frac{40}{98} \div(-20)$
View full question & answer→Question 452 Marks
Find the value and express as a rational number in standard form:
$-6 \div\left(\frac{-8}{17}\right)$
View full question & answer→Question 462 Marks
Find the value and express as a rational number in standard form:
$\frac{10}{3} \div \frac{-35}{12}$
View full question & answer→Question 472 Marks
Find the value and express as a rational number in standard form:
$\frac{2}{5} \div \frac{26}{15}$
View full question & answer→Question 482 Marks
By what number should $\frac{-33}{16}$ be divided to get $\frac{-11}{4}$ ?
View full question & answer→Question 492 Marks
Simplify:
$\left(\frac{-9}{4} \times \frac{5}{3}\right)+\left(\frac{13}{2} \times \frac{5}{6}\right)$
View full question & answer→Question 502 Marks
Simplify:
$\left(-5 \times \frac{2}{15}\right)-\left(-6 \times \frac{2}{9}\right)$
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