NCERT Class 7 Maths Fractions and Decimals Exercise 2.4

Understanding Reciprocals and Division of Fractions

To divide fractions, we must first master a key concept: the reciprocal (or multiplicative inverse). Two non-zero numbers are reciprocals of each other if their product is exactly 1. For instance, the reciprocal of 3/4 is 4/3 because (3/4) (4/3) = 1. What about a whole number? The whole number 5 can be written as 5/1, so its reciprocal is 1/5. Note that the number 0 has no reciprocal because division by zero is undefined! When we divide a number by a fraction, we are essentially finding out how many times the divisor fits into the dividend. The golden rule of dividing fractions is: Multiply the dividend (first number) by the reciprocal of the divisor (second number). This is often remembered by the simple rule: Keep, Change, Flip*. Keep the first fraction, Change the division sign to multiplication, and Flip the second fraction.

Step-by-Step Method to Divide Fractions

1. Step 1: Simplify Mixed Fractions — If any number in the division problem is a mixed fraction, convert it into an improper fraction first.
2. Step 2: Find the Reciprocal of the Divisor — Look at the second fraction (the divisor) and flip it upside down to find its reciprocal. Swap its numerator and denominator.
3. Step 3: Change to Multiplication — Change the division sign (÷) to a multiplication sign (×) and write down the reciprocal of the divisor.
4. Step 4: Multiply and Simplify — Multiply the numerators together and the denominators together. Simplify the resulting fraction to its lowest terms.

Common Pitfalls & Exam Tips

When solving questions from fractions and decimals ex 2 4 class 7 ncert, students often make these mistakes:

1. Flipping the wrong fraction: Always flip the divisor (the second number). Never flip the dividend (the first number).
2. Ignoring Mixed Fractions: You cannot directly divide mixed fractions. Always convert them to improper fractions (e.g., 2 1/3 to 7/3) before performing division.
3. Forgetting to simplify: Always check if your final fraction can be reduced to its simplest form. CBSE examiners deduct marks for leaving fractions unsimplified.

Practice Questions with Solutions

• Q: Solve: $12 \div \frac{3}{4}$ A: Step 1: Write the whole number 12 as a fraction: $\frac{12}{1}$. Step 2: Find the reciprocal of the divisor $\frac{3}{4}$, which is $\frac{4}{3}$. Step 3: Convert the division problem into multiplication: $\frac{12}{1} \times \frac{4}{3}$. Step 4: Multiply the numerators and denominators: $\frac{12 \times 4}{1 \times 3} = \frac{48}{3}$. Step 5: Simplify the fraction: $\frac{48}{3} = 16$. Final answer: 16
• Q: Solve: $\frac{4}{9} \div 5$ A: Step 1: Write the whole number 5 as a fraction: $\frac{5}{1}$. Step 2: Find the reciprocal of the divisor $\frac{5}{1}$, which is $\frac{1}{5}$. Step 3: Convert to multiplication: $\frac{4}{9} \times \frac{1}{5}$. Step 4: Multiply numerators and denominators: $\frac{4 \times 1}{9 \times 5} = \frac{4}{45}$. Final answer: $\frac{4}{45}$
• Q: Solve: $\frac{2}{5} \div \frac{1}{2}$ A: Step 1: Find the reciprocal of the divisor $\frac{1}{2}$, which is $\frac{2}{1}$ or 2. Step 2: Convert to multiplication: $\frac{2}{5} \times \frac{2}{1}$. Step 3: Multiply: $\frac{2 \times 2}{5 \times 1} = \frac{4}{5}$. Final answer: $\frac{4}{5}$
• Q: Solve: $2\frac{1}{5} \div 1\frac{1}{5}$ A: Step 1: Convert the mixed fractions to improper fractions. $2\frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}$. $1\frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{6}{5}$. So, the problem becomes: $\frac{11}{5} \div \frac{6}{5}$. Step 2: Find the reciprocal of the divisor $\frac{6}{5}$, which is $\frac{5}{6}$. Step 3: Convert to multiplication: $\frac{11}{5} \times \frac{5}{6}$. Step 4: Multiply and simplify (cancel out 5 from numerator and denominator): $\frac{11 \times 5}{5 \times 6} = \frac{11}{6}$. Step 5: Convert back to a mixed fraction: $\frac{11}{6} = 1\frac{5}{6}$. Final answer: $1\frac{5}{6}$

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