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Fractions - Marking Fraction Lengths on the Number Line

Grade 6CBSE

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

🔑Concepts

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A number line is a visual representation of numbers where each point corresponds to a specific value. Fractions can be represented as points on this line.

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The distance between 00 and 11 is called a unit length. To represent a fraction ab\frac{a}{b} on the number line, the unit length is divided into bb (the denominator) equal parts.

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The numerator aa indicates how many of these equal parts are taken, starting from 00.

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Proper fractions (where the numerator is less than the denominator) always lie between 00 and 11.

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Improper fractions (where the numerator is greater than or equal to the denominator) are equal to or greater than 11. They can be converted to mixed numbers to find their position between two whole numbers.

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For any fraction ab\frac{a}{b}, if a=ba = b, the fraction represents the whole number 11.

📐Formulae

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

Value of 1 unit division=1Denominator\text{Value of } 1 \text{ unit division} = \frac{1}{\text{Denominator}}

Mixed Fraction=Whole Number+NumeratorDenominator\text{Mixed Fraction} = \text{Whole Number} + \frac{\text{Numerator}}{\text{Denominator}}

💡Examples

Problem 1:

Show the fraction 35\frac{3}{5} on a number line.

Solution:

  1. Draw a line and mark 00 and 11.
  2. Since the denominator is 55, divide the space between 00 and 11 into 55 equal parts.
  3. Each part represents 15\frac{1}{5}.
  4. Starting from 00, move 33 parts to the right.
  5. The third mark represents 35\frac{3}{5}.

Explanation:

The denominator 55 tells us to divide the unit into 55 equal segments. The numerator 33 tells us to count 33 such segments from zero.

Problem 2:

Represent the improper fraction 74\frac{7}{4} on the number line.

Solution:

  1. Convert 74\frac{7}{4} into a mixed number: 14)7‾−43\begin{array}{r} 1 \\ 4 \overline{) 7} \\ - 4 \\ \hline 3 \end{array} So, 74=134\frac{7}{4} = 1 \frac{3}{4}.
  2. This point lies between 11 and 22.
  3. Divide the segment between 11 and 22 into 44 equal parts.
  4. Take the 33rd mark after 11.

Explanation:

Since 74\frac{7}{4} is greater than 11, we first find how many wholes it contains. 1341 \frac{3}{4} means we move past 11 and then take 33 out of 44 subdivisions of the next unit.

Problem 3:

Identify the fraction represented by point PP if the unit length between 00 and 11 is divided into 88 equal parts and PP is the 55th mark.

Solution:

P=58P = \frac{5}{8}

Explanation:

On a number line divided into 88 equal sections, each section is 18\frac{1}{8}. Counting 55 sections from 00 brings us to 58\frac{5}{8}.

Marking Fraction Lengths on the Number Line Class 6 Notes & Examples