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Fractions - Numerator and Denominator

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 group. Imagine a circular pizza cut into equal slices; each individual slice is a fraction of the whole pizza.

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The Numerator is the number written above the horizontal line. It tells us how many parts of the whole are being selected or shaded. For example, if you color 33 parts of a square, the numerator is 33.

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The Denominator is the number written below the horizontal line. It represents the total number of equal parts the whole is divided into. If a rectangle is divided into 55 equal strips, the denominator is 55.

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The Fraction Bar (also called the vinculum) is the straight horizontal line that separates the numerator and the denominator. It acts as a symbol for division.

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For a fraction to be valid, the whole must be divided into equal parts. If you see a circle divided into one large half and two small quarters, it cannot be represented by simple fractions like 13\frac{1}{3} because the pieces are not identical in size.

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Fractions can also describe a collection or a set. Visualize a bag of 1010 marbles where 44 are green; the fraction of green marbles is 410\frac{4}{10}.

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Reading Fractions: The numerator is read as a normal number, and the denominator is usually read as an ordinal number. For example, 14\frac{1}{4} is 'one-fourth' and 23\frac{2}{3} is 'two-thirds'.

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When the numerator and the denominator are the same, such as 66\frac{6}{6}, the fraction is equal to 11 whole. This means all available parts of the shape or group are selected.

📐Formulae

Fraction=NumeratorDenominator\text{Fraction} = \frac{\text{Numerator}}{\text{Denominator}}

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}}

nn=1\frac{n}{n} = 1 (where nn is the number of parts)

💡Examples

Problem 1:

In the fraction 47\frac{4}{7}, identify the numerator and the denominator. What does each number tell us?

Solution:

  1. The Numerator is 44.
  2. The Denominator is 77.

Explanation:

The denominator 77 indicates that a whole object (like a chocolate bar) has been divided into 77 equal pieces. The numerator 44 indicates that we are talking about 44 of those specific pieces.

Problem 2:

A collection has 1010 stars. If 33 stars are colored yellow and the rest are white, what fraction represents the yellow stars?

Solution:

  1. Total number of stars in the collection (Denominator) = 1010
  2. Number of yellow stars (Numerator) = 33
  3. Fraction of yellow stars = 310\frac{3}{10}

Explanation:

To find the fraction of a group, we count the specific items we are interested in for the numerator and the total number of items in the group for the denominator.