NCERT Solutions Class 6 Maths Fractions Exercise 7.1

What is a Fraction? The Part-Whole Relationship

A fraction is a number representing a part of a whole. The whole can be a single object (like a circular pie or a rectangular strip) or a collection of objects (like a box of crayons or a group of students). Mathematically, we write a fraction in the form of $a/b$, where '$a

How to Identify and Write Fractions from Shaded Figures

1. Step 1: Check for Equal Division — Inspect the given figure carefully. Ensure that the shape is divided into parts of equal size. If the parts are unequal, you must partition them further into equal segments before writing a fraction.
2. Step 2: Count the Total Equal Parts — Count the total number of equal divisions in the entire shape. Write this count down as your Denominator (the bottom number of the fraction).
3. Step 3: Count the Shaded or Targeted Parts — Count only the parts that are colored, shaded, or specified by the question. Write this count down as your Numerator (the top number of the fraction).
4. Step 4: Formulate the Fraction — Place the numerator over the denominator to write your final fraction. For Exercise 7.1, you usually leave the fraction in its basic counting form without needing complex simplification.

The Common 'Equal Parts' Trap

A common mistake in Class 6 exams is writing a fraction for a shape divided into unequal parts. For instance, if a rectangle is split down the middle but one half is further divided, writing a simple fraction without ensuring equal sizes will lose you marks. Always check if the slices are identical in area. If they are not, explain why the representation is incorrect. This is a very popular question type in CBSE Ex 7.1!

Practice Questions with Solutions

• Q: Identify the fraction represented by the shaded portion: A square is divided into 4 equal smaller squares. 3 of these smaller squares are shaded green. A: Step 1: Count the total number of equal parts in the shape. Here, the large square is divided into 4 equal smaller squares. So, Denominator = 4. Step 2: Count the number of shaded parts. There are 3 shaded green squares. So, Numerator = 3. Step 3: Write the fraction in the form of Numerator/Denominator. Final answer: The fraction of the shaded portion is 3/4.
• Q: What fraction of an hour is 40 minutes? A: Step 1: Identify the relationship between minutes and hours. We know that 1 hour = 60 minutes. Therefore, the 'whole' (denominator) is 60. Step 2: Identify the 'part' being considered. The question asks about 40 minutes. Therefore, the numerator is 40. Step 3: Write the fraction as Part / Whole = 40/60. Step 4: Simplify the fraction by dividing both numerator and denominator by 20. 40 ÷ 20 = 2, and 60 ÷ 20 = 3. Final answer: 40 minutes is 2/3 of an hour.
• Q: Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished? A: Step 1: Find the total number of dresses Kanchan needs to dye. Total dresses = 30. This is our denominator. Step 2: Find the number of dresses she has completed. Completed dresses = 20. This is our numerator. Step 3: Write the fraction representing the completed work: 20/30. Step 4: Simplify the fraction by dividing both numerator and denominator by 10. 20 ÷ 10 = 2, and 30 ÷ 10 = 3. Final answer: Kanchan has finished 2/3 of the dresses.
• Q: Write the natural numbers from 2 to 12. What fraction of them are prime numbers? A: Step 1: List the natural numbers from 2 to 12. They are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Step 2: Count the total number of items in this list. There are 11 natural numbers. So, Denominator = 11. Step 3: Identify and list the prime numbers from this list. Prime numbers are numbers with exactly two factors (1 and themselves). The prime numbers here are: 2, 3, 5, 7, 11. Step 4: Count the prime numbers. There are 5 prime numbers. So, Numerator = 5. Step 5: Form the fraction as Prime Numbers / Total Numbers = 5/11. Final answer: The fraction of prime numbers is 5/11.

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