Word problems and solutions on fraction for grade 6, 7, 8

Q1. Mr. Kumar is getting his house renovated 1/5th of the work has been

completed in 2 months. How much time will it take for the entire work to be

competed?

ANSWER

The whole work is divided into 5 parts

for completing 1/5th of the work =2months

so, for completing full work = 5* 1/5

=5*2 months

=10 months.

QUESTION

In February 2021 a school was working only three-fourths of the total

number of days in the month and the remaining number of days given as

holidays. How many days did the school work in the month of February?

ANSWER

The year 2021

2021

is a non-leap year.

We know that a non-leap has $28$ days in February month.

So, the total number of days

Given, the school was working only three-fourths

of the total number of days in the month.

therefore, The number of days school working in February month $= \frac{3}{4}$

=21 days

Hence, the school working for $21$ days in the month of February for the year $2021$ .

QUESTION

In a of 50 students 3/5 are girls. How many boys are there in the class?

ANSWER

Total no. of students in a class room = 50

No. of girls = 3/5 of 50

=30

Therefore no. of boys = 50-30

= 20

QUESTION

An oil container contains $7 \frac{1}{2}$ litres of oil which are poured into $2 \frac{1}{2}$ liters

bottles. How many bottles are needed to fill $7 \frac{1}{2}$ litres of oil?

ANSWER

Given, a container holds total oil of

7 \frac{1}{2}

litres,

total amount held by each bottle is $2 \frac{1}{2}$ litres.

Let the number of bottles required is $x$

Total oil in the container = product of oil in each bottle and the number

of bottles required.
$\Rightarrow 7 \frac{1}{2} = x \times 2 \frac{1}{2}$

$\Rightarrow 7 \frac{1}{2} = x \times 2 \frac{1}{2}$ 712=x*212

x =712/212

Therefore, $3$ bottles are required to fill the total oil in the container.

QUESTION

A square garden has the area of 3625 cm^2 $\frac{36}{25} sq.ft$

Find the side of the square garden.

ANSWER

Given the area of the square garden is 3625 cm

\frac{36}{25} sq.ft

^2

We know that area of the square =side*side

= s i d e \times s i d e = a^{2}

side*side =3625

a^2 =3625

a = $\Rightarrow a = \sqrt{\frac{36}{25}} = \frac{\sqrt{36}}{\sqrt{25}} = \frac{6}{5}$

a =65

Hence, the length of the side of the square garden is $\frac{6}{5}$ feet

QUESTION

At a party, total $280$ ice-creams are prepared.

Four-seventh of them is eaten by the children. Find the ice- creams

eaten by the children.?

ANSWER

Total ice-creams prepared =280

= 280

Number of ice-creams eaten by children

=4/7 of 280

=4*40

=160
$280 = \frac{4}{7} \times 280 = 160$

Hence, children ate 160 $160$ ice-creams.

QUESTION

A recipe requires 3/4 cup of sugar to make 12 cookies. How much sugar is needed to make 18 cookies?

ANSWER

To find the amount of sugar needed for 18 cookies, we need to set up a proportion. Since the number of cookies is directly proportional to the amount of sugar, we can write:

12 cookies / 3/4 cup = 18 cookies / x cups

Cross-multiplying, we get: 12 * x = 18 * 3/4 12x = 54/4 12x = 13.5

Dividing both sides by 12, we find: x = 13.5 / 12 x = 1.125

Therefore, you would need 1.125 cups of sugar to make 18 cookies.

QUESTION

A pizza is divided into 8 equal slices. If Sarah ate 3/8 of the pizza, how many slices did she eat?

ANSWER

To find the number of slices Sarah ate, we multiply the total number of slices by the fraction representing the portion she ate:

8 slices * 3/8 = (8 * 3) / 8 = 3 slices

Therefore, Sarah ate 3 slices of pizza.

QUESTION

Julia spent 2/5 of her monthly allowance on a book and 1/4 of it on stationery. What fraction of her allowance did she spend altogether?

ANSWER

To find the fraction of her allowance spent altogether, we need to add the fractions representing the amounts spent on the book and stationery:

2/5 + 1/4

To add these fractions, we need to find a common denominator, which in this case is 20:

2/5 * 4/4 = 8/20 1/4 * 5/5 = 5/20

Now we can add the fractions:

8/20 + 5/20 = 13/20

Therefore, Julia spent 13/20 of her allowance altogether.

QUESTION

Mary had a bag of marbles. She gave 3/5 of the marbles to her friend and kept 1/4 of them for herself. If she gave away 12 marbles, how many marbles did she have at first?

ANSWER

Let's represent the total number of marbles Mary had at first as 'x'. According to the problem, she gave away 3/5 of the marbles, which is equivalent to 12 marbles. We can set up the equation:

(3/5) * x = 12

To solve for 'x', we can multiply both sides of the equation by 5/3:

x = 12 * (5/3)

x = 20

Therefore, Mary had 20 marbles at first.

QUESTION

A rectangle has a length of 5/8 units and a width of 3/4 units. What is the area of the rectangle?

ANSWER

To find the area of a rectangle, we multiply its length by its width. In this case, the length is 5/8 units and the width is 3/4 units:

Area = (5/8) * (3/4)

Area = (5 * 3) / (8 * 4)

Area = 15/32

Therefore, the area of the rectangle is 15/32 units.

QUESTION

John solved 3/5 of a math test correctly, and Sarah solved 4/7 of the same test correctly. Who solved a greater fraction of the test?

ANSWER

To compare the fractions solved correctly, we need to find a common denominator. The least common multiple (LCM) of 5 and 7 is 35. Now, we can convert both fractions to have a denominator of 35:

(3/5) * (7/7) = 21/35

(4/7) * (5/5) = 20/35

Since 21/35 is greater than 20/35, John solved a greater fraction of the test.

SUMMARY

In mathematics, a fraction is used to represent a part of whole. It depicts the

whole’s equal pieces. The numerator and denominator are the two elements

of a fraction. The Upper part of a fraction is called Numerator , while lower

part of the fraction is called denominator. The numerator specifies the number

of equal parts taken, whereas the denominator specifies the total number of

equal parts in the total.

Types of Fraction

There are different types of fractions

a) proper fraction;

proper fractions are the fraction in which denominator is greater than the

numerator.

examples; 2/5, 1/2, 5/7

b)Improper fractions;

Improper fractions are the fraction in which numerator is greater than the

denominator.

examples; 11/7 , 22/3 ,84/45

c) Equivalent Fractions;

Equivalent fractions are the fractions that represents the same value after

simplification. We can multiply or divide both numerator and denominator of the

fraction with same number

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