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Halves and Quarters - Introduction to Fractions

Grade 4CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A fraction represents a part of a whole or a part of a collection. Imagine a whole chapati being divided into equal pieces; each piece is a fraction of that chapati.

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When a whole object is divided into two equal parts, each part is called a half. It is written as 12\frac{1}{2}. Visually, if you draw a line straight through the middle of a circle, you create two identical semi-circles, each being 12\frac{1}{2} of the whole.

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When a whole is divided into four equal parts, each part is called a quarter or one-fourth. It is written as 14\frac{1}{4}. If you take a square and draw two lines (one horizontal and one vertical) through the center, you get four smaller equal squares, each representing 14\frac{1}{4} of the original square.

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In a fraction ab\frac{a}{b}, the top number 'aa' is called the Numerator, which indicates how many parts are being considered. The bottom number 'bb' is the Denominator, which shows the total number of equal parts the whole is divided into.

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Two quarters combined make a half. Mathematically, 14+14=24\frac{1}{4} + \frac{1}{4} = \frac{2}{4}, which is the same as 12\frac{1}{2}. Visually, if you have a chocolate bar with four equal squares and you eat two, you have eaten half the bar.

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A 'Whole' is represented when all equal parts are taken together. For example, 22=1\frac{2}{2} = 1 and 44=1\frac{4}{4} = 1. If you color all four quarters of a circle, the entire circle is shaded.

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Fractions can also be applied to a collection of objects. If there are 8 marbles and you take half of them, you are taking 12\frac{1}{2} of 8, which is 4 marbles. Visually, this is like splitting a group of items into equal sets.

📐Formulae

Fraction=Number of parts being consideredTotal number of equal parts\text{Fraction} = \frac{\text{Number of parts being considered}}{\text{Total number of equal parts}}

One Half=12\text{One Half} = \frac{1}{2}

One Quarter=14\text{One Quarter} = \frac{1}{4}

14+14=24=12\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}

12+12=22=1\frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1

14+14+14+14=44=1\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{4}{4} = 1

Finding a fraction of a number=(Total Number÷Denominator)×Numerator\text{Finding a fraction of a number} = (\text{Total Number} \div \text{Denominator}) \times \text{Numerator}

💡Examples

Problem 1:

Rohan has 12 pencils. He gives 14\frac{1}{4} of his pencils to his sister. How many pencils does his sister get?

Solution:

Total pencils = 1212. Fraction given to sister = 14\frac{1}{4}. To find the number of pencils, we divide the total by the denominator: 12÷4=312 \div 4 = 3. Then multiply by the numerator: 3×1=33 \times 1 = 3. So, the sister gets 33 pencils.

Explanation:

To find a quarter of a quantity, we divide the total amount into 4 equal groups and count how many are in one group.

Problem 2:

A water tank is 34\frac{3}{4} full. If the total capacity of the tank is 4040 litres, how many litres of water are in the tank?

Solution:

Total capacity = 4040 litres. Fraction full = 34\frac{3}{4}. First, find the value of one quarter: 40÷4=1040 \div 4 = 10 litres. Since the tank has 33 quarters, multiply by 33: 10×3=3010 \times 3 = 30 litres. The tank contains 3030 litres of water.

Explanation:

This problem requires finding three-fourths of a number. We first find what 14\frac{1}{4} (one part) is worth and then multiply it by 33 to find the value of 34\frac{3}{4}.