Fractions And Decimals(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

FRACTIONS AND DECIMALS MCQs

Fractions, Decimals

Total Questions : 227 | Page 19 of 23 pages

Question 181.

Which of the given option is the simplest form of $\frac{13860}{18480}$ ?

$\frac{1}{2}$
$\frac{3}{4}$
$\frac{1}{4}$
$\frac{3}{2}$

Discuss Question

Answer: Option B. ->

\frac{3}{4}

:
B

In order to reduce a fraction to its lowest terms, divide both numerator and denominator by their common factor.

$\frac{\frac{13860}{10}}{\frac{18480}{10}} = \frac{1386}{1848}$

$\frac{\frac{1386}{3}}{\frac{1848}{3}} = \frac{462}{616}$

$\frac{\frac{462}{11}}{\frac{616}{11}} = \frac{42}{56}$

$\frac{\frac{42}{7}}{\frac{56}{7}} = \frac{6}{8} = \frac{3}{4}$

Question 182.

Convert $\frac{6}{12}$ , $\frac{1}{4}$ and $\frac{6}{3}$ into like fractions.

$\frac{5}{12}$ , $\frac{3}{12}$ , $\frac{24}{12}$
$\frac{6}{12}$ , $\frac{2}{12}$ , $\frac{24}{12}$
$\frac{6}{12}$ , $\frac{3}{12}$ , $\frac{20}{12}$
$\frac{6}{12}$ , $\frac{3}{12}$ , $\frac{24}{12}$

Discuss Question

Answer: Option D. ->

\frac{6}{12}

\frac{3}{12}

\frac{24}{12}

:
D
In order to convert the fractions into like fractions, find the L.C.M of denominators of given fractions.
Then convert each fraction into an equivalent fraction having denominator as the L.C.M of the denominators of the given fractions.

L.C.M of [12, 4, 3] = 12

\frac{6}{12} = \frac{6 \times 1}{12 \times 1} = \frac{6}{12}

\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}

\frac{6}{3} = \frac{6 \times 4}{3 \times 4} = \frac{24}{12}

Question 183.

Find the value of a if,

$3 \frac{a}{4} = \frac{15}{4}$

Discuss Question

Answer: Option A. ->

3

:
A

$3 \frac{a}{4}$ is a mixed fraction.

$3 \frac{a}{4} =$ $\frac{(3 \times 4) + a}{4} =$ $\frac{12 + a}{4}$

Given, $\frac{(12 + a)}{4}$ = $\frac{15}{4}$

Comparing the numerator gives, (12 + a) =15

Therefore, a = (15 - 12) = 3

Question 184.

Arrange the following fractions in ascending order,
fractions: $\frac{12}{16}$ , $\frac{4}{9}$ and $\frac{6}{10}$

$\frac{6}{10}$ , $\frac{4}{9}$ , $\frac{12}{16}$
$\frac{4}{9}$ , $\frac{6}{10}$ , $\frac{12}{16}$
$\frac{12}{16}$ , $\frac{6}{10}$ , $\frac{4}{9}$
$\frac{12}{16}$ , $\frac{4}{9}$ , $\frac{6}{10}$

Discuss Question

Answer: Option B. ->

\frac{4}{9}

\frac{6}{10}

\frac{12}{16}

:
B
To compare the fractions, make the denominators equal.
For that, we have to find LCM of denominators

16, 9, 10

16 = 2 \times 2 \times 2 \times 2

9 = 3 \times 3

10 = 2 \times 5

LCM of [16, 9, 10] =

2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 = 720

\frac{12}{16} = \frac{12 \times 45}{16 \times 45} = \frac{540}{720}

\frac{4}{9} = \frac{4 \times 80}{9 \times 80} = \frac{320}{720}

\frac{6}{10} = \frac{6 \times 72}{10 \times 72} = \frac{432}{720}

Comparing numerators,

\frac{320}{720} < \frac{432}{720} < \frac{540}{720}

∴ \frac{4}{9} < \frac{6}{10} < \frac{12}{16}

Question 185.

_____ is a fraction between $\frac{2}{9}$ and $\frac{6}{19}$

$\frac{12}{24}$
$\frac{6}{10}$
$\frac{8}{28}$
$\frac{32}{40}$

Discuss Question

Answer: Option C. ->

\frac{8}{28}

:
C

One fraction exisiting between $\frac{a}{b}$ and $\frac{c}{d}$ is $\frac{a + c}{b + d}$ .

Here, we have to insert a fraction between $\frac{2}{9}$ and $\frac{6}{19}$ .

$a = 2, b = 9, c = 6 and d = 19$

One fraction exisiting between them is: $\frac{2 + 6}{9 + 19}$ = $\frac{8}{28}$

Question 186.

Which of the following is a pair of like decimals?

$0.2010$ , $0.21159$
$4.260$ , $4.9125$
$4.19$ , $4.625$
$9865.4946$ , $28.4900$

Discuss Question

Answer: Option D. ->

9865.4946

28.4900

:
D

Decimal numbers having the same number of decimal places, i.e. decimals having the same number of digits on the right of the decimal point, are known as like decimals.

In the option with the numbers 9865.4946 and 28.4900, both decimal numbers have 4 digits in the decimal place.

Therefore, they are like decimals.
The rest of the options do not have same number of decimal places.

Question 187.

Which of the following decimals are equal?

$10.0101$ , $10.01010$
$10.101010$ , $01.010010$
$0.1010$ , $0.1010000$
$11.011011$ , $11.0101$

Discuss Question

Answer: Option A. ->

10.0101

10.01010

:
A and C

A very important property of decimals is that adding zeros after the last digit of the decimal part of any decimal number does not change the value of the decimal.

Hence,
$10.0101$ , $10.01010$ and
$0.1010$ , $0.1010000$ are the right options