Tag: comparing fractions

Questions Related to comparing fractions

State whether true or false


$\cfrac { 2 }{ 5 } $ of $\cfrac { 4 }{ 7 } $  is smaller than $\cfrac { 3 }{ 4 } $ of $\cfrac { 1 }{ 2 } $

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

$\dfrac{2}{5}$ of $\dfrac{4}{7}=\dfrac{2\times 4}{5\times 7}=\dfrac{8}{35}$


$\dfrac{3}{4}$ of $\dfrac{1}{2}=\dfrac{3\times 1}{4\times 2}=\dfrac{3}{8}$


To compare two fractions let us make the denominators same.

LC.M of $8,35=280$

$\therefore \dfrac{8\times 8}{35 \times 8}=\dfrac{64}{280}$

And $\dfrac{3\times 35}{8\times 35}=\dfrac{105}{280}$

We have $\dfrac{105}{280}>\dfrac{64}{280}$

Hence $\dfrac{3}{8}>\dfrac{8}{35}$

Akshit, Rajat, Sanjay and Nikunj each took the same spelling test.
$\bullet$ Akshit spelled $\displaystyle\frac{7}{10}$ of the words correctly.
$\bullet$ Rajat spelled $\displaystyle\frac{3}{4}$ of the words correctly.
$\bullet$ Sanjay spelled $\displaystyle\frac{4}{5}$ of the words correctly.
$\bullet$ Nikunj spelled $\displaystyle\frac{2}{3}$ of the words correctly.
Who spelled the least number of words correctly?

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. Akshit

  2. Rajat

  3. Sanjay

  4. Nikunj

Show answer
Correct Option: D
Explanation:

Descending order of the fraction of words spelled correctly is,

$\Rightarrow$  $\dfrac{4}{5}>\dfrac{3}{4}>\dfrac{7}{10}>\dfrac{2}{3}$

$\Rightarrow$  $Sanjay>Rajat>Akshit>Nikunj$

$\therefore$    $Nikunj$ spelled least number of words correctly.

Simplify : $\frac{(-18\frac{1}{3}\times 2\frac{8}{11})}{|\frac{3}{5}+(\frac{-9}{10})| + |-(\frac{-3}{5})|}$

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. 63$\frac{4}{81}$

  2. -23$\frac{7}{9}$

  3. -67$\frac{7}{9}$

  4. 12$\frac{6}{17}$

Show answer
Correct Option: C
Explanation:

$\cfrac {\left(-18\cfrac{1}{3}\times 2\cfrac {8}{11}\right)}{\left|\cfrac {3}{5}+\left(\cfrac {-9}{10}\right)\right|+\left|-\left(\cfrac{-3}{5}\right)\right|}$

$=\cfrac{-\cfrac{55}{3}\times \cfrac{30}{11}}{\left|\cfrac {6-9}{10}\right|+\cfrac {3}{5}}$
$=\cfrac {\cfrac {-55\times 30}{33}}{\cfrac {3}{10}+\cfrac {3}{5}}$
$=\cfrac {\cfrac {-55\times 30}{33}}{\cfrac{9}{50}}$
$=\cfrac {-55\times 30\times 50}{33\times 9}$
$=\cfrac {-5\times 10\times 50}{9}$
$=-67\cfrac {7}{9}$

Which of the following options is arranged in descending order?

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. $\frac{1}{4},\frac{6}{4},\frac{16}{9},\frac{25}{4}$

  2. $\frac{-3}{6},\frac{-4}{3},\frac{-9}{4},\frac{-13}{4}$

  3. $\frac{-5}{8},\frac{-3}{8},\frac{0}{8},\frac{1}{8}$

  4. $\frac{-7}{4},\frac{-3}{4},\frac{5}{4},\frac{8}{3}$

Show answer
Correct Option: B
Explanation:

To check the order, first make the denominator same of all the fractions, then compare the numerator.

Note- To make the denominator same, multiply both numerator and denominator by HCF of denominator values.
$\cfrac {-3}{6}, \cfrac {-4}{3},\cfrac {-9}{4}, \cfrac {-13}{4}$
Multiply by $12$ both numerator and denominator.
$\cfrac {-36}{12}, \cfrac {-43}{12},\cfrac {-108}{12}, \cfrac {-156}{12}$

The smallest of the fractions given.

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. $9/10$

  2. $11/12$

  3. $23/28$

  4. $32/33$

Show answer
Correct Option: C

Compare the given fractions and specify the correct operator

$\dfrac{9}{16}$ ___ $\dfrac{13}{5}$

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. $\displaystyle = $

  2. $\displaystyle > $

  3. $\displaystyle < $

  4. None of the above

Show answer
Correct Option: C
Explanation:

To compare fractions, make the denominators equal

LCM of denominators $16$ and $5$ is $80$
$\therefore \dfrac{9}{16} \times \dfrac{5}{5}$ $=\dfrac{45}{80}$ and $\dfrac{13}{5} \times  \dfrac {16}{16}$ $=\dfrac{208}{80}$


By making denominators equal, we find that $208$ is greater than $45$ 
$\therefore \dfrac{9}{16} < \dfrac{13}{5} $.

If a, b, c, are positive $\displaystyle \frac{a+c}{b+c}$ is 

maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

  1. always smaller than $\displaystyle \frac{a}{b}$

  2. always greater than $\displaystyle \frac{a}{b}$

  3. greater than $\displaystyle \frac{a}{b}$ only if a > b

  4. greater than $\displaystyle \frac{a}{b}$ only if a < b

Show answer
Correct Option: D
Explanation:

Since we need to compare the fraction $\displaystyle \frac{a+c}{b+c}$ with $\displaystyle \frac{a}{b}$, we cross multiply the terms and check since $a,b,c$ are all given to be positive.
We thus get $b(a + c)$ on the L.H.S. and $a(b + c)$ on R.H.S.
Thus, simplifying we are left with $ab + bc$ on the L.H.S. and $ab + ac$ on the R.H.S.
Now, which side is greater depends on $ac$ and $bc$, which in turn depends upon $a$ & $b.$
L.H.S. is greater if $b > a$, which implies $\frac{a + c}{b + c}$ is greater when $b > a.$