Maharashtra Board Class 4 Maths Part Two Chapter 10 Fractions PDF Download

Fractions

The Meaning Of Fractions. Reading And Writing Fractions:

Half

One bhakari has to be divided equally between two people. When it is divided into two equal parts, each of the parts is one half of the whole bhakari.

When any object is divided into two equal parts, then each of the parts is one half of that object. One half of the whole is shown by the fraction \(\frac{1}{2}\).

Quarters

One bhakari has to be divided equally between four people. When it is divided into four equal parts, and one part is given to each person, each share is a quarter of the whole bhakari.

When any object is divided into four equal parts, each of those parts is a quarter of the whole.

One quarter is shown by the fraction \(\frac{1}{4}\).

Numbers such as \(\frac{1}{2}, \frac{1}{4}\) are called fractions. In a fraction, the number written above the line is the numerator and the number written below the line is the denominator. In the fraction \(\frac{1}{2}\), the numerator is 1 and the denominator is 2.

\(\frac{1}{2}\) is read as 'one half' or 'one upon two.'

\(\frac{1}{4}\) is read as 'one fourth' or 'one quarter' or 'one upon four'.

Teacher's Note

When you share one roti between two people, each person gets half a roti. This is \(\frac{1}{2}\). When you share one roti between four people, each gets \(\frac{1}{4}\).

Exam Trick

Remember: Top number = numerator (how many parts taken), Bottom number = denominator (how many parts total). Think of it like a pizza slice - \(\frac{1}{4}\) means 1 slice out of 4 slices.

Points to Remember

A fraction has a numerator on top and a denominator on bottom.
\(\frac{1}{2}\) means one part out of two equal parts.
\(\frac{1}{4}\) means one part out of four equal parts.
The denominator tells how many equal parts the whole is divided into.
The numerator tells how many of those parts we are taking.

Three Quarters

Three children bought a cake and asked their grandfather to divide it equally among the four of them including himself. Grandfather divided the cake into four equal pieces. Each piece is one quarter of the cake. Grandfather gave Raju, Rani and Pinky one quarter each and kept the last quarter for himself. Grandfather gave his two granddaughters, quarter + quarter, that is, half of the cake. He gave his three grandchildren quarter + quarter + quarter, three quarters of the cake. One half and one quarter also make three quarters of the whole.

When an object is divided into 4 equal parts, 3 of its parts taken together are called three quarters. This is shown by the fraction \(\frac{3}{4}\).

\(\frac{3}{4}\) is read as 'three fourths' or 'three upon four.'

Some More Fractions

Here, a circular disc is divided into 5 equal parts and 3 of its parts are coloured. The coloured part of the disc is shown as \(\frac{3}{5}\).

\(\frac{1}{5} + \frac{1}{5} + \frac{1}{5}\) together make \(\frac{3}{5}\). That is, \(\frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{3}{5}\)

When an object is divided into 5 equal parts and three of them are taken, that part is shown as \(\frac{3}{5}\). Here, the denominator 5 shows how many equal parts are made of the whole, and the numerator 3 shows how many of those are taken.

This strip has been divided into 7 equal parts and 2 parts are coloured, which means \(\frac{2}{7}\) of the strip is coloured. Here, the number 7 gives the total number of equal parts made, and 2 gives the number of parts taken. In the fraction \(\frac{2}{7}\), 2 is the numerator and 7 is the denominator.

You can work out the meanings of fractions such as \(\frac{8}{11}\) or \(\frac{7}{13}\) just like the fractions \(\frac{3}{4}, \frac{3}{5}\) and \(\frac{2}{7}\).

Teacher's Note

Look at your school lunch. If you divide a roti into 5 equal parts and eat 3 parts, you have eaten \(\frac{3}{5}\) of the roti. The bottom number 5 says how many parts total, and the top number 3 says how many you ate.

Exam Trick

To read any fraction easily, say the top number first, then say the bottom number as "upon". For example, \(\frac{3}{5}\) = "three upon five". Always count the total parts for the denominator and the coloured parts for the numerator.

Points to Remember

Any fraction has a numerator on top and denominator on bottom.
The denominator shows total number of equal parts.
The numerator shows how many parts are taken.
You can make fractions with any numbers, like \(\frac{3}{5}, \frac{8}{11}, \frac{7}{13}\).
Each fraction means a part of something whole.

Different Meanings Of Fractions

Amita was given two parts out of three equal parts of a bhakari.

Two bhakaris of the same size as Amita's have to be divided equally between three girls, Sadhana, Anushka and Preeti.

The two bhakaris were divided into three equal parts each. One part of each bhakari was given to Sadhana, Anushka and Preeti.

Sadhana's share: \(\frac{1}{3} + \frac{1}{3}\)

Anushka's share: \(\frac{1}{3} + \frac{1}{3}\)

Preeti's share: \(\frac{1}{3} + \frac{1}{3}\)

Each girl was given a \(\frac{1}{3}\) part twice.

That is, each got \(\frac{1}{3} + \frac{1}{3}\).

However, Amita's share and that of each of the other three girls is the same.

Hence, we can see that \(\frac{2}{3} = \frac{1}{3} + \frac{1}{3}\)

Note that when two bhakaris are divided between three girls, each girl gets \(\frac{2}{3}\) bhakaris.

It means that \(\frac{2}{3}\) can be explained in three different ways.

2 parts out of 3 equal parts of an object.

\(\frac{1}{3}\) twice; which means \(\frac{1}{3} + \frac{1}{3}\); which also means \(2 \times \frac{1}{3}\); or two times \(\frac{1}{3}\).

Equal division of two objects between three people.

Teacher's Note

The fraction \(\frac{2}{3}\) can mean three things. In India, we see this when sharing food - 2 rotis divided equally among 3 people means each person gets \(\frac{2}{3}\) of a roti.

Exam Trick

Remember that \(\frac{2}{3}\) = \(\frac{1}{3} + \frac{1}{3}\) = \(2 \times \frac{1}{3}\). A fraction can be a part of one thing OR sharing multiple things among people.

Points to Remember

\(\frac{2}{3}\) means 2 parts out of 3 equal parts of one object.
\(\frac{2}{3}\) also means \(\frac{1}{3}\) taken two times, written as \(\frac{1}{3} + \frac{1}{3}\).
\(\frac{2}{3}\) also means dividing 2 objects equally among 3 people.
All three meanings give the same answer.
A fraction can be understood in many different ways.

This is a preview of the first 3 pages. To get the complete book, click below.