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Fractions - Introduction to Fractions

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 of objects. For example, if you cut a whole chocolate bar into equal pieces, each piece is a fraction of that bar.

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A fraction is written with two numbers separated by a horizontal line. The top number is the Numerator, which tells us how many equal parts are taken or shaded. The bottom number is the Denominator, which tells us the total number of equal parts the whole is divided into. In the fraction 34\frac{3}{4}, 33 is the numerator and 44 is the denominator.

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Equal Parts: Fractions only exist when a whole is divided into parts of exactly the same size. Imagine a circle divided by two perpendicular lines through the center into four identical wedge shapes; each shape is a true fraction (14)(\frac{1}{4}). If the parts are of different sizes, they cannot be represented as fractions.

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Half (12\frac{1}{2}): When a whole object, like a square or a circle, is divided into 2 equal parts, each part is called one-half. Visually, this is represented by a line splitting a shape into two identical mirror images.

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One-Third (13\frac{1}{3}) and One-Fourth (14\frac{1}{4}): When a whole is divided into 3 equal parts, each part is one-third. When divided into 4 equal parts, each part is one-fourth or a 'quarter'.

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Fractions of a Collection: Fractions can also describe a group of separate items. If you have a set of 5 stars and 2 of them are colored yellow, the yellow stars represent 25\frac{2}{5} of the entire collection.

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Reading Fractions: We use specific words to read fractions. 12\frac{1}{2} is read as 'one-half', 23\frac{2}{3} is read as 'two-thirds', and 58\frac{5}{8} is read as 'five-eighths'.

📐Formulae

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

Fraction=Number of equal parts shaded or selectedTotal number of equal parts in the whole\text{Fraction} = \frac{\text{Number of equal parts shaded or selected}}{\text{Total number of equal parts in the whole}}

Whole=nn=1\text{Whole} = \frac{n}{n} = 1 (where nn is any number of equal parts)

💡Examples

Problem 1:

A rectangular strip is divided into 6 equal parts. If 4 parts are colored red, what fraction of the strip is red?

Solution:

  1. Total number of equal parts (Denominator) = 66.
  2. Number of parts colored red (Numerator) = 44.
  3. The fraction of the strip that is red = NumeratorDenominator=46\frac{\text{Numerator}}{\text{Denominator}} = \frac{4}{6}.

Explanation:

To find the fraction, we identify how many equal parts make the whole and how many of those parts are selected (red).

Problem 2:

Riya has a collection of 9 balloons. 5 balloons are blue and the rest are pink. What fraction of the balloons are pink?

Solution:

  1. Total number of balloons = 99.
  2. Number of blue balloons = 55.
  3. Number of pink balloons = 9−5=49 - 5 = 4.
  4. The fraction of pink balloons = Number of pink balloonsTotal balloons=49\frac{\text{Number of pink balloons}}{\text{Total balloons}} = \frac{4}{9}.

Explanation:

First, calculate the number of pink balloons by subtracting the blue ones from the total. Then, place that number over the total count to form the fraction.