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→