Question 12 Marks
Define:
Fractions.
Give two examples.
AnswerA number of the form $\frac{\text{a}}{\text{b}},$ where a and b are rational numbers, is called a natural number.
Here, a is the numerator and b is the denominator.
- $\frac{2}{3}$ is a fraction with 2 as the numerator and 3 as the denominator.
- $\frac{12}{5}$ is a fraction with 12 as the numerator and 5 as the denominator.
View full question & answer→Question 22 Marks
What should be added to $7\frac{3}{5}$ to get 18?
AnswerFor finding the required fraction, we have to subtract $7\frac{3}{5}$ from 18
$\therefore$ Required number $=18-7\frac{3}{5}=\frac{18}{1}-\frac{38}{5}$
$=\frac{90}{5}-\frac{38}{5}=\frac{90-38}{5}$
$=\frac{52}{5}=10\frac{2}{5}$
$\therefore10\frac{2}{5}$ should be added.
View full question & answer→Question 32 Marks
Compare the fractions:
$\frac{5}{9}\text{ and }\frac{11}{15}$
Answer$\frac{5}{9}\text{ and }\frac{11}{15}$
$\Rightarrow5\times15=75$
$11\times9=99$
$\because75<99$
$\therefore\frac{5}{9}<\frac{11}{15}$
View full question & answer→Question 42 Marks
Simplify:$24\div\frac{6}{7}$
Answer$24\div\frac{6}{7}=\frac{24}{1}\times\frac{7}{6}=\frac{4\times7}{1}=28$
View full question & answer→Question 52 Marks
Simplify:$\frac{10}{27}\times\frac{28}{65}\times\frac{39}{56}$
Answer$\frac{10}{27}\times\frac{28}{65}\times\frac{39}{56}$
$\frac{10}{27}\times\frac{28}{65}\times\frac{39}{56}$
$=\frac{10\times28\times39}{27\times65\times56}$
$=\frac{2\times1\times3}{27\times1\times2}=\frac{1}{9}$
View full question & answer→Question 62 Marks
Simplify:
$\frac{4}{7}\div\frac{9}{14}$
Answer$\frac{4}{7}\div\frac{9}{14}=\frac{4}{7}\times\frac{14}{9}=\frac{4\times2}{9}=\frac{8}{9}$
View full question & answer→Question 72 Marks
Divide:$\frac{11}{24}$ by $\frac{7}{8}$
Answer$\frac{11}{24}\div\frac{7}{8}$$=\frac{11}{24}\times\frac{7}{8}$ $\big[\because\text{Reciprocal of }\frac{7}{8}=\frac{8}{7}\big]$
$=\frac{11}{21}$
View full question & answer→Question 82 Marks
Simplify:$5\frac{5}{9}\div3\frac{1}{3}$
AnswerWe have,$5\frac{5}{9}\div3\frac{1}{3}$
$=\frac{50}{9}\times\frac{10}{3}$
$\Big[\because\text{ Reciprocal of }\frac{10}{3}=\frac{3}{10}\Big]$
$=\frac{5\times1}{3\times1}=\frac{5}{3}=1\frac{2}{3}$
View full question & answer→Question 92 Marks
Simplify:$3\frac{3}{5}\div\frac{4}{5}$
Answer$3\frac{3}{5}\div\frac{4}{5}=\frac{18}{5}\div\frac{4}{5}=\frac{18}{5}\times\frac{5}{4}=\frac{9\times{1}}{1\times2}=4\frac{1}{2}$
View full question & answer→Question 102 Marks
Simplify:$9\div\frac{1}{3}$
Answer$9\div\frac{1}{3}=9\times\frac{3}{1}=27$
View full question & answer→Question 112 Marks
Define:
Vulgar fractions.
Give two examples.
AnswerA fraction whose denominator is a whole number other than 10, 100, 1000, etc., is called a vulgar faction.
Example:
View full question & answer→Question 122 Marks
Simplify:$\frac{8}{9}\div16$
Answer$\frac{8}{9}\div16=\frac{8}{9}\times\frac{1}{16}=\frac{1\times1}{9\times2}=\frac{1}{18}$
View full question & answer→Question 132 Marks
Divide:$45$ by $1\frac{4}{5}$
Answer$45$ by $1\frac{4}{5}=45\div\frac{9}{5}$$=45\times\frac{5}{9}=\frac{5\times5}{1}=25$
View full question & answer→Question 142 Marks
Find:$\frac{3}{5}$ of a hour.
Answer$\frac{3}{5}$ of 1 hour
$=\frac{3}{5}\text{ of } 60\text{min}$
$=\Big(60\times\frac{3}{5}\Big)\text{min}=(12\times3)\text{min}$
$=36\text{min}$
View full question & answer→Question 152 Marks
Divide:$32$ by $1\frac{3}{5}$
Answer$32$ by $1\frac{3}{5}=32\div\frac{8}{5}$$=32\times\frac{5}{8}=\frac{4\times5}{1}=20$
View full question & answer→Question 162 Marks
Divide:$63$ by $2\frac{1}{4}$
Answer$63$ by $2\frac{1}{4}=63\div\frac{9}{4}$$=63\times\frac{4}{9}=\frac{7\times4}{1}=28$
View full question & answer→Question 172 Marks
Find:$\frac{12}{25}$ of a litre.
Answer$\frac{12}{25}\text{ of 1 litre}=\frac{12}{25}\text{ of }1000\text{ml}$
$=\Big(1000\times\frac{12}{25}\Big)\text{ml}=(40\times12)\text{ml}$
$=480\text{ml}$
View full question & answer→Question 182 Marks
What should be added to $7\frac{4}{15}$ to get $8\frac{2}{5}?$
AnswerFor finding the required fraction, we have to subtract $7\frac{4}{15}$ from $8\frac{2}{5}$
$\therefore$ Required number $=8\frac{2}{5}-7\frac{4}{15}$
$=\frac{42}{5}-\frac{109}{15}$
$=\frac{126-109}{15}$ (LCM of 5, 15 = 15)
$=\frac{17}{15}=1\frac{2}{15}$
View full question & answer→Question 192 Marks
Divide:$6\frac{7}{8}$ by $\frac{11}{16}$
Answer$6\frac{7}{8}\div\frac{11}{16}=\frac{55}{8}\div\frac{11}{16}$$=\frac{55}{8}\times\frac{16}{11}$ $\big[\because\text{Reciprocal of } \frac{11}{16}=\frac{16}{11}\big]$
$=5\times2=10$
View full question & answer→Question 202 Marks
A piece of wire $3\frac{3}{4}\text{m}$ long broke into two pieces one piece is $1\frac{1}{2}\text{m}$ long. How long is the other piece?
AnswerTotal length of wire $3\frac{3}{4}\text{m}=\frac{15}{4}\text{m}$
One piece $1\frac{1}{2}\text{m}=\frac{3}{2}\text{m}$
$\therefore$ other piece $=\frac{15}{4}-\frac{3}{2}$
$=\frac{15-6}{4}$ (LCM of 4, 2 = 4)
$=\frac{9}{4}=2\frac{1}{4}\text{m}$
View full question & answer→Question 212 Marks
Define:
Improper fractions.
Give two examples.
AnswerA fraction whose numerator is greater than or equal to its denominator is called an improper fraction.
Example:
View full question & answer→Question 222 Marks
Compare the fractions:
$\frac{11}{12}\text{ and }\frac{15}{16}$
Answer$\frac{11}{12}\text{ and }\frac{15}{16}$
$\Rightarrow11\times16=176$
$15\times12=180$
$\because176<180$
$\therefore\frac{11}{12}<\frac{15}{16}$
View full question & answer→Question 232 Marks
Simplify:$3\frac{2}{16}\times7\frac{3}{7}\times1\frac{25}{39}$
Answer$3\frac{2}{16}\times7\frac{3}{7}\times1\frac{25}{39}$
$=\frac{49}{16}\times\frac{52}{7}\times\frac{64}{39}$
$=\frac{49\times52\times64}{16\times7\times39}=\frac{7\times4\times4}{1\times1\times3}$
$=\frac{112}{3}=37\frac{1}{3}$
View full question & answer→Question 242 Marks
Simplify:$2\frac{2}{17}\times7\frac{2}{9}\times1\frac{33}{52}$
Answer$2\frac{2}{17}\times7\frac{2}{9}\times1\frac{33}{52}$
$=\frac{36}{17}\times\frac{65}{9}\times\frac{85}{52}$
$=\frac{36=\times65\times85}{17\times9\times52}$
$=5\times5=25$
View full question & answer→Question 252 Marks
Simplify:$5\frac{4}{7}\div1\frac{3}{10}$
Answer$15\frac{3}{7}\div1\frac{3}{10}=\frac{39}{7}\div\frac{13}{10}=\frac{39}{7}\times\frac{10}{13}$$=\frac{3\times{10}}{7\times1}=\frac{30}{7}=4\frac{2}{7}$
View full question & answer→Question 262 Marks
Simplify:$15\frac{3}{7}\div1\frac{23}{49}$
Answer$15\frac{3}{7}\div1\frac{23}{49}=\frac{108}{7}\div\frac{72}{49}=\frac{108}{7}\times\frac{49}{72}$$=\frac{3\times{7}}{1\times2}=\frac{21}{2}=10\frac{1}{2}$
View full question & answer→Question 272 Marks
Divide:$5\frac{5}{9}$ by $3\frac{1}{3}$
Answer$5\frac{5}{9}\div3\frac{1}{3}=\frac{50}{9}\div\frac{10}{3}$$=\frac{50}{9}\times\frac{3}{10}$ $\big[\because\text{Reciprocal of } \frac{10}{3}=\frac{3}{10}\big]$
$=\frac{5}{3}=1\frac{2}{3}$
View full question & answer→Question 282 Marks
Compare the fractions:
$\frac{5}{8}\text{ and }\frac{7}{12}$
Answer$\frac{5}{8}\text{ and }\frac{7}{12}$
$\Rightarrow5\times12=60$
$7\times8=56$
$\because60>56$
$\therefore\frac{5}{8}>\frac{7}{12}$
View full question & answer→Question 292 Marks
Simplify:
$\frac{7}{10}\div\frac{3}{5}$
Answer$\frac{7}{10}\div\frac{3}{5}=\frac{7}{10}\times\frac{5}{3}=\frac{7\times1}{2\times3}=\frac{7}{6}=1\frac{1}{6}$
View full question & answer→Question 302 Marks
24 litres of milk was distributed equally among all the students of a hostel. If each student got $\frac{2}{5}$ litre of milk, how many students are there in the hostel?
AnswerTotal quantity of milk = 24 liters
and quantity of milk got by one student $=\frac{2}{5}\text{litres}$
$\therefore$ Number of students $=\Big(24\div\frac{2}{5}\Big)$
$=24\times\frac{2}{5}=60$
View full question & answer→Question 312 Marks
Simplify:$\frac{2}{3}\times\frac{5}{44}\times\frac{33}{35}$
Answer$\frac{2}{3}\times\frac{5}{44}\times\frac{33}{35}=\frac{2\times5\times33}{3\times44\times35}$
$=\frac{10\times33}{3\times44\times35}=\frac{2\times11}{44\times7}$
$=\frac{1}{2\times7}=\frac{1}{14}$
View full question & answer→Question 322 Marks
Simplify:$1\frac{4}{7}\times1\frac{13}{22}\times1\frac{1}{15}$
Answer$1\frac{4}{7}\times1\frac{13}{22}\times1\frac{1}{15}$
$=\frac{11}{7}\times\frac{35}{22}\times\frac{16}{15}$
$=\frac{11\times35\times16}{7\times22\times15}=\frac{1\times5\times16}{1\times2\times15}$
$=\frac{8}{3}=2\frac{2}{3}$
View full question & answer→Question 332 Marks
Find:$\frac{5}{8}$ of a kilogram.
Answer$\frac{5}{8}$ of 1 kilogram
$=\frac{5}{8}\text{ of }1000\text{g}$
$=\Big(1000\times\frac{5}{8}\Big)\text{g}$
$=(125\times5)\text{g}=625\text{g}.$
View full question & answer→Question 342 Marks
A picture is $7\frac{3}{5}\text{cm}$ wide. How much should it be trimmed to fit in a frame $7\frac{3}{10}\text{cm}$ wide?
AnswerWidht of picture $=7\frac{3}{5}=\frac{38}{5}\text{cm}$
and width of frame $=7\frac{3}{10}\text{cm}=\frac{73}{10}\text{cm}$
$\therefore$ width trimmed to fit in the frame
$=\frac{38}{5}-\frac{73}{10}$
$=\frac{76-73}{10}=\frac{3}{10}\text{cm}$
View full question & answer→Question 352 Marks
Simplify:$3\frac{3}{7}\div\frac{8}{21}$
Answer$3\frac{3}{7}\div\frac{8}{21}=\frac{24}{7}\times\frac{8}{21}=\frac{24}{7}\times\frac{21}{8}=\frac{3\times{3}}{1\times1}=9$
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