NCERT Solutions for Class 6 Maths: Fractions Exercise 7.2

Visualising Fractions: The Number Line

You already know how to mark whole numbers like 1, 2, and 3 on a number line. We can do the same for fractions! A fraction is a part of a whole. Think of the space between 0 and 1 as one whole object, like a chocolate bar. To show the fraction 3/4 on the number line, we look at the denominator, which is 4. This tells us to divide the segment between 0 and 1 into 4 equal parts. The numerator, 3, tells us to jump forward 3 of these parts starting from 0. The point where we land is 3/4! Similarly, for 1/2, we divide the space between 0 and 1 into 2 equal parts and mark the first one. What about improper fractions like 5/4? Since the numerator is bigger than the denominator, it's more than one whole. We still divide each whole unit (0 to 1, 1 to 2, etc.) into 4 parts. Then we count 5 parts from 0. This will take us past 1 to the first mark after it. So, 5/4 is the same as 1 and 1/4.

Meet the Fraction Family: Proper, Improper, and Mixed

Proper Fractions

A fraction where the numerator (the top number) is smaller than the denominator (the bottom number). It always represents a value less than 1 whole. Example: 2/5, 7/10, 1/3.

Improper Fractions

A fraction where the numerator is greater than or equal to the denominator. It represents a value that is 1 whole or more than 1 whole. Example: 5/2, 11/4, 8/8.

Mixed Fractions

A combination of a whole number and a proper fraction. It's another way to write an improper fraction. Example: 2 ½ (which is the same as 5/2), 3 ¼.

Switching Forms: Improper to Mixed and Back

1. How to Convert an Improper Fraction to a Mixed Fraction — Think of the fraction bar as a division sign. To convert 13/5 into a mixed fraction, we divide the numerator (13) by the denominator (5). 1. Divide: 13 ÷ 5 = 2 with a remainder of 3. 2. Identify Parts: The quotient (2) becomes the whole number. The remainder (3) becomes the new numerator. The denominator (5) stays the same. 3. Combine: So, 13/5 becomes 2 ⅗.
2. How to Convert a Mixed Fraction to an Improper Fraction — Let's convert 4 ½ into an improper fraction. We need to find out how many 'halves' are in 4 and a half. 1. Multiply: Multiply the whole number (4) by the denominator (2). So, 4 × 2 = 8. 2. Add: Add the result (8) to the numerator (1). So, 8 + 1 = 9. 3. Combine: This result (9) is the new numerator. The denominator (2) stays the same. So, 4 ½ becomes 9/2.

Important Points to Remember

• To represent a fraction on a number line, the denominator tells you how many equal parts to divide each unit into.
• Proper fractions (like 3/4) are always located between 0 and 1 on the number line.
• Improper fractions (like 5/3) are always located at or after 1 on the number line.
• When converting between mixed and improper fractions, the denominator never changes.
• A fraction like 4/4 or 5/5 is an improper fraction, and its value is exactly 1.

Practice Questions with Solutions

• Q: Represent the fraction 3/4 on a number line. A: Step 1: Draw a number line. Mark 0 and 1 on it. Step 2: Since the denominator is 4, divide the segment between 0 and 1 into 4 equal parts. Step 3: Each part represents 1/4. Mark the third division from 0 as 3/4. Final answer: The point representing 3/4 is the third mark after 0 on the number line, dividing the segment between 0 and 1 into 4 equal parts.
• Q: Convert the improper fraction 11/3 into a mixed fraction. A: Step 1: Divide the numerator (11) by the denominator (3). Step 2: 11 ÷ 3 = 3 with a remainder of 2. Step 3: The quotient (3) becomes the whole number part, the remainder (2) becomes the new numerator, and the denominator (3) remains the same. Final answer: 3 2/3
• Q: Convert the mixed fraction 2 3/5 into an improper fraction. A: Step 1: Multiply the whole number part (2) by the denominator (5). Step 2: Add the numerator (3) to the product: (2 × 5) + 3 = 10 + 3 = 13. Step 3: Keep the original denominator (5). Final answer: 13/5
• Q: Represent the fraction 7/2 on a number line. A: Step 1: Convert the improper fraction 7/2 to a mixed fraction: 3 1/2. Step 2: Draw a number line. Mark whole numbers 0, 1, 2, 3, 4. Step 3: The fraction 3 1/2 lies between 3 and 4. Divide the segment between 3 and 4 into 2 equal parts (as the denominator is 2). Step 4: Mark the first division after 3 as 3 1/2 or 7/2. Final answer: The point representing 7/2 is the midpoint between 3 and 4 on the number line.

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