Tag: fraction

Questions Related to fraction

Prem went to a craft fair where he spent a total of Rs. $16.00$. He spent Rs. $6.00$ on admission and went to $8$ tables. He spent the same amount of money(m) at each table. The given expression can be used to find how much money he spend at each table.
$16=6+8m$
How much money did Prem spent at each table?

maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

  1. Rs. $0.50$

  2. Rs. $0.80$

  3. Rs. $1.25$

  4. Rs. $2.00$

Show answer
Correct Option: C
Explanation:
We have, $16=6+8$m
$\Rightarrow 8m=16-6=10$
$\Rightarrow \displaystyle m=\frac{10}{8}=1.25$
So, Prem spent Rs. $1.25$ at each table.

State true or false.
$10cm$ in kilometre is $0.0001km$

maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

As we know,


$1$ m $= 100$ m


$1$ km $= 1000$ m

Given, $10$ cm

So, $10$ cm $= \dfrac{10}{100}$ m$= 0.1$ m

$0.1$ m = $\dfrac{0.1}{1000}$ km $= 0.0001$ km

So, $10$ cm $= 0.0001$ km

State true or false.

$9$ paise is equal to Rs.$0.09$.

maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

As we know,

1 Rs = 100 paisa

Given, 9 paisa
So, 9 paisa = $\frac{9}{100}$ Rs
= 0.09 Rs

Fill in the banks: 
$1765$ grams $=................... kg$

maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

  1. $1.765$

  2. $1.65$

  3. $1.55$

  4. $1.25$

Show answer
Correct Option: A
Explanation:

$1$ kg $= 1000$ gm


So, $1765$ grams $= \dfrac{1765}{1000}$ kg


$= 1.765$ kg 

Let $D$ represent a repeating decimal. If $P$ denotes the $r$ figures of $D$ which do not repeat themselves, and $Q$ denotes the $s$ figures which do repeat themselves, then the incorrect expression is

maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

  1. $D = P.QQQ....$

  2. $10^{r}D = P.QQQ...$

  3. $10^{r + s}D = PQ .QQQ .....$

  4. $10^{r}(10^{s} - 1)D = Q(P - 1)$

  5. $10^{r} . 10^{2s}D = PQ.QQQ...$

Show answer
Correct Option: D
Explanation:

$D = .PQQQ .... = .a _{1} ...a _{r}b _{1} ...b _{x}b _{1} ...b _{s} ...$ So $(a), (b), (c)$ and $(e)$ are all correct choices. To check that $(d)$ is incorrect, we have
$10^{r + s}D - 10^{r}D = PQ - P. \therefore 10^{r}(10^{s} - 1)D = P(Q - 1)$.

$2+\dfrac {1}{2}$ In the decimal form

maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

  1. $2.5$

  2. $1.5$

  3. $3.5$

  4. $2$

Show answer
Correct Option: A
Explanation:

$2+\dfrac{1}{2}$

As $\dfrac{1}{2}=0.5$
So $2+0.5=2.5$

Simplify: $\dfrac{{4 + \sqrt 5 }}{{4 - \sqrt 5 }} + \dfrac{{4 - \sqrt 5 }}{{4 + \sqrt 5 }}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\dfrac {42}{11}$

  2. $\dfrac {40}{11}$

  3. $\dfrac {39}{25}$

  4. $\dfrac {16}{25}$

Show answer
Correct Option: A
Explanation:

$\dfrac{4+\sqrt5}{4-\sqrt5} = \dfrac{(4+\sqrt5)}{(4-\sqrt5)} \dfrac{(4+\sqrt5)}{(4+\sqrt5)}$    ...... rationalizing numerator and the denominator


$= \dfrac{(4+\sqrt5)^2}{16-5} = \dfrac{(4+\sqrt5)^2}{11} $

$\dfrac{4-\sqrt5}{4+\sqrt5} = \dfrac{(4-\sqrt5)}{(4+\sqrt5)} \dfrac{(4-\sqrt5)}{(4-\sqrt5)}$    ...... rationalizing numerator and the denominator, 

$= \dfrac{(4-\sqrt5)^2}{16-5} = \dfrac{(4-\sqrt5)^2}{11} $


$\dfrac{4+\sqrt5}{4-\sqrt5} +\dfrac{4-\sqrt5}{4+\sqrt5} = \dfrac{(4+\sqrt5)^2 +(4-\sqrt5)^2}{11} =\dfrac{16+5+16+5}{11} = \dfrac{42}{11}$

What fraction of a day is $16$ hours?

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $\dfrac{3}{2}$

  2. $\dfrac{1}{24}$

  3. $\dfrac{2}{3}$

  4. $\dfrac{16}{60}$

Show answer
Correct Option: C
Explanation:

A complete day has $24$ hours so

$Required\>ratio\>=\>\dfrac{16}{24}\>=\>\dfrac23$

Hence option $'C'$ is the answer.

Which of the following are true?

(a) $\displaystyle \frac{35}{16}=2.1875$
(b) $\displaystyle \frac{17}{8}=2.125$
(c) $\displaystyle \frac{327}{500}=0.654$
(d) $\displaystyle \frac{14588}{625}=23.3408$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $a,b,c,d$

  2. $a,c,d$

  3. $a,b,c$

  4. $a,b,d$

Show answer
Correct Option: A
Explanation:

(i) $\displaystyle \frac{35}{16} = \frac{35 \times 5^4}{2 \times 5^4}= \frac{35 \times 625}{(10)^4}= \frac{21875}{10000}=2.1875$
(ii) $\displaystyle \frac{17}{8} = \frac{17 \times 5^3}{2^3 \times 5^3} = \frac{17 \times 125}{(10)^3}=\frac{2125}{1000}=2.125$
(iii) $\displaystyle \frac{327}{500} = \frac{327}{5\times 5 \times 5 \times 2 \times 2}$
$=\displaystyle \frac{327}{5^3 \times 2^2} = \frac{327}{5^3 \times 2^3}= \frac{654}{(10)^3} = 0.654$
(iv) $\displaystyle \frac{14588}{625} = \frac{2^2 \times 7 \times 521}{5^4} = \frac{2^6 \times 7 \times 521}{2^4 \times 5^4}$
$\displaystyle =\frac{233408}{10^4}=23.3408$

Solve: $8\dfrac{2}{3}+9\dfrac{3}{8}$

maths fraction lowest form of a fraction simplest ratio lowest form of fractions

  1. $40$

  2. $\dfrac{433}{24}$

  3. $24$

  4. $\dfrac{437}{24}$

Show answer
Correct Option: B
Explanation:

Given, $\displaystyle 8\frac{2}{3} + 9\frac{3}{8}$


Could be written as,


$\displaystyle \frac{26}{3} + \frac{75}{8}$

LCM of 3 and 8 is 24,

= $\displaystyle \dfrac{208}{24} + \dfrac{225}{24}$

= $\displaystyle\dfrac{433}{24}$