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 18 of 23 pages

The value of $\frac{(\frac{1}{2}) \times (\frac{1}{2}) + (\frac{1}{2})}{(\frac{2}{1}) \times (\frac{1}{2}) \times (\frac{3}{4})}$ is ___.

Discuss Question

Answer: Option A. ->
:

$\frac{(\frac{1}{2}) \times (\frac{1}{2}) + (\frac{1}{2})}{(\frac{1}{2}) + (\frac{1}{2}) \times (\frac{3}{4})}$ = $\frac{(\frac{1}{4}) + (\frac{1}{2})}{1 \times (\frac{3}{4})}$ = $\frac{(\frac{3}{4})}{(\frac{3}{4})} = 1$

Question 172.

$[5 \frac{1}{4} - \frac{2}{5} \times 5 \frac{5}{9} + (\frac{1}{2} + \frac{3}{4})]$ is equal to:

$\frac{9}{16}$
$\frac{77}{18}$
$\frac{24}{12}$
$\frac{12}{24}$

Discuss Question

Answer: Option B. ->

\frac{77}{18}

:
B

Given $[5 \frac{1}{4} - \frac{2}{5} \times 5 \frac{5}{9} + (\frac{1}{2} + \frac{3}{4})]$
Apply BODMAS rule to solve

= $[\frac{21}{4} - (\frac{2}{5} \times \frac{50}{9}) + \frac{5}{4}]$

= $[\frac{21}{4} - (\frac{20}{9}) + \frac{5}{4}]$

Taking LCM of denominators, we have

$\frac{189 - 80 + 45}{36} = \frac{154}{36} = \frac{77}{18}$
$[5 \frac{1}{4} - \frac{2}{5} \times 5 \frac{5}{9} + (\frac{1}{2} + \frac{3}{4})] = \frac{77}{18}$

Question 173.

A person bought $3 \frac{1}{2} k g$ of apples, $2 \frac{2}{3} k g$ of grapes and $1 \frac{1}{3} k g$ of oranges. He wants to divide them among $4$ people. Find the amount of fruits(in kg) that each person will receive.

$1 \frac{3}{8} k g$
$1 \frac{5}{8} k g$
$1 \frac{7}{8} k g$
$2 \frac{7}{8} k g$

Discuss Question

Answer: Option C. ->

1 \frac{7}{8} k g

:
C

First, let us do the conversion of mixed fractions into improper fractions.
i.e $3 \frac{1}{2} = \frac{(2 \times 3) + 1}{2} = \frac{7}{2}$

$2 \frac{2}{3} = \frac{(3 \times 2) + 2}{3} = \frac{8}{3}$ , and

$1 \frac{1}{3} = \frac{(3 \times 1) + 1}{3} = \frac{4}{3}$
$Total quantity of fruits = (\frac{7}{2} + \frac{8}{3} + \frac{4}{3}) k g$

$= \frac{7}{2} + 4$
$= \frac{7}{2} + \frac{8}{2}$ kg

$= \frac{15}{2}$ kg

When $\frac{15}{2} k g$ is divided among 4 people,

each person's share $= \frac{\frac{15}{2}}{4} k g$

$= (\frac{15}{2} \times \frac{1}{4}) k g$
$= \frac{15}{8} k g$
$= 1 \frac{7}{8} k g$
Hence, each person gets $(1 \frac{7}{8}) k g$ of fruits.

Question 174.

$\frac{2 \frac{1}{2} + 2 \frac{1}{3} + 2 \frac{1}{4}}{\frac{1}{10} \times \frac{2}{5} \times \frac{125}{6}} is equals to:$

$5.5$
$6.5$
$7.5$
$8.5$

Discuss Question

Answer: Option D. ->

8.5

:
D

$\frac{\frac{5}{2} + \frac{7}{3} + \frac{9}{4}}{\frac{1}{10} \times \frac{2}{5} \times \frac{125}{6}}$
$= \frac{\frac{85}{12}}{\frac{5}{6}}$

$= \frac{85}{12} \times \frac{6}{5}$
$= \frac{17}{2} = 8.5$

Question 175.

Varun travelled $\frac{1}{8}$ th of the journey which is equal to $56 k m$ on a scooter . What is the remaining distance he has to cover?

$342 k m$
$392 k m$
$352 k m$
$442 k m$

Discuss Question

Answer: Option B. ->

392 k m

:
B

Let the total distance to be covered $= d k m$
Then, $\frac{1}{8} \times d$ = $56 k m$

$d = (56 \times 8)km = 448km$

$Remaining distance = (448 - 56)km = 392km$

Question 176.

The product of two fractions is $20$ . If one of the fractions is $\frac{1}{4}$ , then the other fraction is ___.

Discuss Question

Answer: Option B. ->

392 k m

:
Let the other fraction be

x

Then,

x \times \frac{1}{4} = 20

x = 20 \times 4 = 80

Question 177.

Simplify the following expression and choose the correct answer:

$\frac{0 \times (\frac{5}{9} \times \frac{2}{3}) + \frac{5}{6} \times 9 \times 0}{(\frac{4}{5} + \frac{3}{5} + \frac{1}{2})}$

$\frac{9}{10}$
$\frac{4}{9}$
$1$
$0$

Discuss Question

Answer: Option D. ->

0

:
D

Concentrate on numerator. The expression has ' $0$ ' multiplied to it, and any number multiplied by ' $0$ ' is ' $0$ '.
And 0 divided by any number always ' $0$ '.
Hence the answer is ' $0$ '.

Question 178.

A fraction is ______.

the ratio of the total number of parts to the number of parts considered.
the ratio of the number of parts considered to the total number of parts.
never a whole part
always a whole part

Discuss Question

Answer: Option B. -> the ratio of the number of parts considered to the total number of parts.
:
B

Consider the following example.
Suppose you have a pizza.
Divide the whole pizza into $4$ parts.
Now, take $3$ parts out of the $4$ parts.
These $3$ parts represent the fraction $3$ out of $4$ , i.e., $\frac{3}{4}$ .
i.e., a fraction is the ratio of the number of divisions considered to the total number of divisions.

Question 179.

a $\frac{b}{c}$ is called a/an ____ and is equal to ____.

proper fraction, $\frac{b}{c}$
improper fraction, $a \div \frac{b}{c}$
mixed fraction, $a \times \frac{b}{c}$
mixed fraction, $a + \frac{b}{c}$

Discuss Question

Answer: Option D. -> mixed fraction,

a + \frac{b}{c}

:
D

$a \frac{b}{c}$ is called a mixed fraction.
Here, 'a' is whole number part and $\frac{b}{c}$ is the fractional part.
e.g. $2 \frac{3}{4}$ , $5 \frac{1}{6}$

$a \frac{b}{c} = a + \frac{b}{c}$
e.g: $2 \frac{3}{4} =$ $2 + \frac{3}{4}$

Question 180.

Which of the following is correct about improper fractions?

In an improper fraction, the numerator is less than denominator and numerator is greater than 0.
In an improper fraction, the numerator is always greater than the denominator.
In an improper fraction, the numerator is greater than the denominator and denominator should not be equal to zero.
In an improper fraction, the numerator is always equal to the denominator.

Discuss Question

Answer: Option C. -> In an improper fraction, the numerator is greater than the denominator and denominator should not be equal to zero.
:
C

In an improper fraction, the numerator is greater than the denominator and denominator should not be equal to zero.

e.g. $\frac{61}{5}$ , $\frac{7}{6}$ , $\frac{9}{4}$ , $\frac{66}{21}$ etc