krit.club logo

Halves and Quarters - Numerator and Denominator

Grade 4CBSE

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

🔑Concepts

•

A fraction represents a part of a whole or a part of a collection. Imagine a whole chocolate bar as one unit; if you break it into equal pieces, each piece is a fraction of that bar.

•

The Denominator is the bottom number of a fraction, such as the 44 in 14\frac{1}{4}. It tells us the total number of equal parts the whole is divided into. Visually, if a circle is divided into four equal slices like a pizza, the denominator is 44.

•

The Numerator is the top number of a fraction, such as the 11 in 14\frac{1}{4}. It tells us how many equal parts are being considered or shaded. If one slice of the four-slice pizza is colored, the numerator is 11.

•

A 'Half' is created when a whole is divided into 22 equal parts. It is written as 12\frac{1}{2}. Visually, this looks like a straight line drawn through the center of a shape, splitting it into two identical mirror images.

•

A 'Quarter' or 'One-fourth' is created when a whole is divided into 44 equal parts. It is written as 14\frac{1}{4}. Visually, you can see this by drawing both a horizontal and a vertical line through the center of a square to create four smaller equal squares.

•

Three-quarters represents 33 out of 44 equal parts and is written as 34\frac{3}{4}. Visually, if you have a circle divided into four parts and you shade three of them, you have represented three-quarters.

•

Two quarters combined are equal to one half. Mathematically, 14+14=24=12\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}. Visually, if you take two slices of a four-slice pizza, you have exactly half of the pizza.

•

A whole can be represented as a fraction where the numerator and denominator are the same, such as 22=1\frac{2}{2} = 1 or 44=1\frac{4}{4} = 1. This means all the equal parts are being considered.

📐Formulae

Fraction=Numerator (Parts selected)Denominator (Total equal parts)\text{Fraction} = \frac{\text{Numerator (Parts selected)}}{\text{Denominator (Total equal parts)}}

Half of a number=Number÷2=12×Number\text{Half of a number} = \text{Number} \div 2 = \frac{1}{2} \times \text{Number}

Quarter of a number=Number÷4=14×Number\text{Quarter of a number} = \text{Number} \div 4 = \frac{1}{4} \times \text{Number}

Three-quarters of a number=(Number÷4)×3=34×Number\text{Three-quarters of a number} = (\text{Number} \div 4) \times 3 = \frac{3}{4} \times \text{Number}

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

💡Examples

Problem 1:

Rohan has 1212 apples. He gives half of the apples to his sister. How many apples does he give away?

Solution:

  1. Total apples = 1212. \n2. To find half, we divide the total by 22. \n3. Calculation: 12÷2=612 \div 2 = 6. \n4. Rohan gives away 66 apples.

Explanation:

To find 12\frac{1}{2} of a collection, we divide the total quantity by the denominator 22.

Problem 2:

In a fraction 34\frac{3}{4}, identify the numerator and denominator. Also, if a cake is cut into 44 equal pieces and 33 pieces are eaten, what fraction remains?

Solution:

  1. In 34\frac{3}{4}, the Numerator is 33 and the Denominator is 44. \n2. Total pieces of cake = 44. \n3. Pieces eaten = 33. \n4. Pieces remaining = 4−3=14 - 3 = 1. \n5. Fraction remaining = Remaining piecesTotal pieces=14\frac{\text{Remaining pieces}}{\text{Total pieces}} = \frac{1}{4}.

Explanation:

The denominator represents the total parts the cake was cut into, while the numerator for the remainder represents the parts that were not eaten.