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Fractions - Half, One-third, and One-fourth

Grade 3ICSE

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. To represent a fraction correctly, the whole object must be divided into equal parts. Visually, if a shape is divided into parts of different sizes, those parts do not represent standard fractions until they are made equal.

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One-half (12\frac{1}{2}): When a whole is divided into 2 equal parts, each part is called one-half. Visually, imagine a circular pizza cut into 2 identical pieces by a straight line through the center; each piece is 12\frac{1}{2} of the pizza.

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One-third (13\frac{1}{3}): When a whole is divided into 3 equal parts, each part is called one-third. Imagine a rectangular chocolate bar divided into three identical vertical strips; each strip represents 13\frac{1}{3} of the whole bar.

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One-fourth (14\frac{1}{4}): When a whole is divided into 4 equal parts, each part is called one-fourth or a quarter. Visually, if you fold a square piece of paper in half and then in half again, you create 4 smaller equal squares, each being 14\frac{1}{4} of the original paper.

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Numerator and Denominator: In the fraction 13\frac{1}{3}, the top number (11) is the Numerator, which tells us how many parts are being considered. The bottom number (33) is the Denominator, which tells us the total number of equal parts the whole is divided into.

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Fractions of a Collection: Fractions can also describe parts of a group. For example, if you have a collection of 4 stars and 1 is colored yellow, the yellow star represents 14\frac{1}{4} of the collection of stars.

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Concept of a Whole: When all the equal parts of a whole are taken together, it equals 11. For example, 22\frac{2}{2} (two halves), 33\frac{3}{3} (three thirds), and 44\frac{4}{4} (four fourths) all represent 11 whole.

📐Formulae

Fraction=Number of shaded or selected partsTotal number of equal parts\text{Fraction} = \frac{\text{Number of shaded or selected parts}}{\text{Total number of equal parts}}

One-half of a number=Total÷2\text{One-half of a number} = \text{Total} \div 2

One-third of a number=Total÷3\text{One-third of a number} = \text{Total} \div 3

One-fourth of a number=Total÷4\text{One-fourth of a number} = \text{Total} \div 4

💡Examples

Problem 1:

Rohan has a collection of 1212 buttons. He gives 13\frac{1}{3} of the buttons to his sister. How many buttons does his sister get?

Solution:

Total number of buttons = 1212. Portion given = 13\frac{1}{3}. To find 13\frac{1}{3} of 1212, we divide the total by 33: 12÷3=412 \div 3 = 4 So, Rohan's sister gets 44 buttons.

Explanation:

To find one-third of a collection, we divide the total quantity into three equal groups. The number of items in one such group is the answer.

Problem 2:

A rectangle is divided into 44 equal parts. If 11 part is painted blue, what fraction of the rectangle is blue and what fraction is not blue?

Solution:

Total equal parts = 44. Parts painted blue = 11. Parts not painted = 4−1=34 - 1 = 3. Fraction painted blue = 14\frac{1}{4}. Fraction not painted = 34\frac{3}{4}.

Explanation:

The denominator (44) represents the total number of equal parts. The numerator represents the specific parts we are counting (1 for blue, 3 for not blue).