NCERT Solutions Class 7 Maths Chapter 8 — Fractions Operations

Solution:

Step 1: A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number).

Step 2: For example, 1/2, 3/4, and 5/7 are all proper fractions because their numerators are less than their denominators.

Step 3: Options A describes an improper fraction, B describes a fraction equal to 1, and D describes an undefined expression.

Solution:

Step 1: To add or subtract fractions with different denominators, you must first find a common denominator, which is usually the Least Common Multiple (LCM) of the denominators.

Step 2: Ravi incorrectly added the numerators and denominators directly without finding a common denominator.

Step 3: The correct way to add 1/3 and 1/2 is to find the LCM of 3 and 2, which is 6. Then, convert the fractions: 1/3 = 2/6 and 1/2 = 3/6. Finally, add: 2/6 + 3/6 = 5/6.

Solution:

Step 1: To find the remaining pizza, subtract the amount eaten from the initial amount: 5/6 - 1/3.

Step 2: Find a common denominator for 6 and 3. The LCM is 6. Convert 1/3 to an equivalent fraction with denominator 6: 1/3 = (1 × 2) / (3 × 2) = 2/6.

Step 3: Now, subtract the fractions: 5/6 - 2/6 = (5 - 2)/6 = 3/6.

Step 4: Simplify the result: 3/6 = 1/2.

Solution:

Step 1: The chocolate bar has 3 equal rows, so 2 shaded rows represent 2/3 of the total rows.

Step 2: The chocolate bar has 4 equal columns, so 3 shaded columns represent 3/4 of the total columns.

Step 3: When you find the region that is double-shaded, you are essentially finding a fraction 'of' a fraction, which corresponds to multiplication.

Step 4: Therefore, the double-shaded region represents the product 2/3 × 3/4.

Solution:

Step 1: Division is defined as the inverse operation of multiplication. When we divide a number 'a' by a number 'b', it is equivalent to asking how many times 'b' fits into 'a'.

Step 2: Multiplying by the reciprocal of a fraction is the method used to perform this inverse operation for fractions.

Step 3: For example, a/b ÷ c/d = a/b × d/c. This effectively 'undoes' the division by c/d.