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A Peek Beyond the Point - Addition and Subtraction of Decimals

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Decimal numbers consist of a whole number part and a fractional part separated by a decimal point. For example, in 45.6745.67, 4545 is the whole number part and 6767 is the decimal part.

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Place value positions to the right of the decimal point are: Tenths (110\frac{1}{10}), Hundredths (1100\frac{1}{100}), and Thousandths (11000\frac{1}{1000}).

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Like Decimals: These are decimals that have the same number of digits after the decimal point. For example, 1.251.25 and 13.7813.78 are like decimals.

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Unlike Decimals: These are decimals that have a different number of digits after the decimal point. For example, 4.54.5 and 4.524.52. They must be converted to like decimals by adding placeholder zeros at the end before adding or subtracting.

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Alignment Rule: When adding or subtracting, always align the decimal points vertically so that digits in the same place value are in the same column.

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The sum or difference is calculated just like whole numbers, and the decimal point is placed directly below the decimal points of the numbers being operated on.

📐Formulae

Expanded Form: a.bcd=a+b10+c100+d1000\text{Expanded Form: } a.bcd = a + \frac{b}{10} + \frac{c}{100} + \frac{d}{1000}

Conversion Rule: 1 mm=0.1 cm,1 Paise=₹0.01,1 g=0.001 kg\text{Conversion Rule: } 1 \text{ mm} = 0.1 \text{ cm}, 1 \text{ Paise} = ₹ 0.01, 1 \text{ g} = 0.001 \text{ kg}

💡Examples

Problem 1:

Add 25.6825.68, 7.37.3, and 145.004145.004.

Solution:

Step 1: Convert unlike decimals to like decimals by adding placeholder zeros: 25.68025.680, 7.3007.300, and 145.004145.004. Step 2: Align the decimal points vertically. 25.6807.300+145.004177.984\begin{array}{r} 25.680 \\ 7.300 \\ + 145.004 \\ \hline 177.984 \end{array} Final Answer: 177.984177.984

Explanation:

By adding zeros, we ensure all numbers have three decimal places (thousandths). Aligning the decimal points ensures tenths are added to tenths, hundredths to hundredths, etc.

Problem 2:

Subtract 18.72518.725 from 25.425.4.

Solution:

Step 1: Convert 25.425.4 to a like decimal: 25.40025.400. Step 2: Align and subtract, borrowing where necessary. 25.400−18.7256.675\begin{array}{r} 25.400 \\ - 18.725 \\ \hline 6.675 \end{array} Final Answer: 6.6756.675

Explanation:

We cannot subtract 55 from 00 in the thousandths place, so we borrow from the tenths and hundredths places. The decimal point in the result remains vertically aligned with the others.

Problem 3:

Rani bought a book for ₹35.65₹ 35.65 and a pen for ₹12.50₹ 12.50. She gave ₹100₹ 100 to the shopkeeper. How much money did she get back?

Solution:

Total Spent: ₹35.65+₹12.50=₹48.15₹ 35.65 + ₹ 12.50 = ₹ 48.15 Money Given: ₹100.00₹ 100.00 Money Back: 100.00−48.15100.00 - 48.15 100.00−48.1551.85\begin{array}{r} 100.00 \\ - 48.15 \\ \hline 51.85 \end{array} Final Answer: Rani got back ₹51.85₹ 51.85.

Explanation:

First, we find the total expenditure by adding the prices. Then, we subtract the total from the amount given (100100), ensuring we write 100100 as 100.00100.00 to align the decimal places.