NCERT Solutions Class 7 Maths Fractions and Decimals Ex 2.7

Understanding Decimal Division: The Core Logic

Dividing decimals might seem intimidating at first, but it is incredibly straightforward once you understand the underlying patterns. The simplest way to handle decimal division is by converting the decimals into fractions. For instance, dividing 0.4 by 2 can be visualised as dividing 4 tenths into 2 equal parts. Mathematically, we convert 0.4 into 4/10. So, 0.4 ÷ 2 becomes (4/10) × (1/2) = 2/10 = 0.2. This fractional approach ensures you never get confused by the position of the decimal point. When dividing by 10, 100, or 1000, we use a simple mental shortcut: shift the decimal point to the left by counting the number of zeros in the divisor. With YoLearn's step-by-step visualization, you will master these simple rules in no time!

How to Divide a Decimal by Another Decimal

1. Step 1: Convert Decimals to Fractions — Rewrite both the dividend and the divisor as fractions by looking at their decimal places. For example, write 2.5 as 25/10 and 0.5 as 5/10.
2. Step 2: Multiply by the Reciprocal — Change the division sign (÷) to a multiplication sign (×) and write the reciprocal (invert) of the second fraction (the divisor).
3. Step 3: Simplify and Cancel Common Factors — Simplify the resulting expression by multiplying the numerators together and the denominators together, cancelling out common factors (like 10s or 100s) to keep calculations simple.
4. Step 4: Write the Final Quotient — Convert the simplified fraction back into decimal form if needed, or state the final whole number answer clearly.

Exam Tip: The 'D-L' Rule for Dividing by Powers of 10

A common mistake students make is shifting the decimal point in the wrong direction. To avoid this, remember the D-L Rule: Division moves the decimal point to the Left.

• When dividing by 10: Shift the decimal point 1 place to the left (e.g., 4.8 ÷ 10 = 0.48).
• When dividing by 100: Shift the decimal point 2 places to the left (e.g., 4.8 ÷ 100 = 0.048).
• If you run out of digits on the left while shifting, simply place placeholder zeros to keep your place value correct!

Practice Questions with Solutions

• Q: Find: 0.35 ÷ 5 A: Step 1: Convert the decimal number 0.35 into a fraction. Since there are two decimal places, 0.35 = 35/100. Step 2: Set up the division as a multiplication with the reciprocal of 5: (35/100) ÷ 5 = (35/100) × (1/5). Step 3: Simplify the expression: (35 × 1) / (100 × 5) = 7/100. Step 4: Convert the fraction 7/100 back to a decimal. Final answer: 0.07
• Q: Find: 32.5 ÷ 0.5 A: Step 1: Convert both decimal numbers into fractions. 32.5 = 325/10 and 0.5 = 5/10. Step 2: Change division to multiplication by the reciprocal of the divisor: (325/10) ÷ (5/10) = (325/10) × (10/5). Step 3: Cancel out the 10 in the numerator and denominator: 325/5. Step 4: Divide 325 by 5 to find the final value: 325 ÷ 5 = 65. Final answer: 65
• Q: Find: 2.7 ÷ 100 A: Step 1: Identify that you are dividing by 100, which has two zeros. Step 2: Use the 'D-L' rule to shift the decimal point two places to the left. Step 3: Move the decimal point in 2.7 one place left to get .27, and another place left to get .027. Final answer: 0.027
• Q: A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it cover in one litre of petrol? A: Step 1: Write down the given values: Total distance covered = 43.2 km, Total petrol consumed = 2.4 litres. Step 2: Formulate the division expression to find distance per litre: Distance covered in 1 litre = 43.2 ÷ 2.4. Step 3: Convert the decimals to fractions: (432/10) ÷ (24/10). Step 4: Multiply by the reciprocal of the divisor: (432/10) × (10/24) = 432/24. Step 5: Perform the division 432 ÷ 24 = 18. Final answer: 18 km

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