Tag: fraction

Quizzes (7) Questions (84)

Questions Related to fraction

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

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?

  1. Rs. $0.50$
  2. Rs. $0.80$
  3. Rs. $1.25$
  4. Rs. $2.00$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.
Multiple choice maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

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

  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. $10^{r} . 10^{2s}D = PQ.QQQ...$
Reveal answer Fill a bubble to check yourself
D Correct answer
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
$10^{r + s}D - 10^{r}D = PQ - P. \therefore 10^{r}(10^{s} - 1)D = P(Q - 1)$.

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

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

  1. $\dfrac {42}{11}$
  2. $\dfrac {40}{11}$
  3. $\dfrac {39}{25}$
  4. $\dfrac {16}{25}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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} $


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

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

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) $\displaystyle \frac{14588}{625}=23.3408$

  1. $a,b,c,d$
  2. $a,c,d$
  3. $a,b,c$
  4. $a,b,d$
Reveal answer Fill a bubble to check yourself
A Correct answer
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) $\displaystyle \frac{14588}{625} = \frac{2^2 \times 7 \times 521}{5^4} = \frac{2^6 \times 7 \times 521}{2^4 \times 5^4}$
$\displaystyle =\frac{233408}{10^4}=23.3408$

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

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

  1. $40$
  2. $\dfrac{433}{24}$
  3. $24$
  4. $\dfrac{437}{24}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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,

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

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