This MCQ module is based on: Decimal Operations and Patterns
TOPIC 10 OF 31
Decimal Operations and Patterns
🎓 Class 7
Mathematics
CBSE
Theory
Ch 3 — A Peek Beyond the Point
⏱ ~35 min
🌐 Language: [gtranslate]
🧠 AI-Powered MCQ Assessment
▲
📐 Maths Assessment
▲
This mathematics assessment will be based on: Decimal Operations and Patterns
Targeting Class 7 level in Decimals, with Basic difficulty.
Upload images, PDFs, or Word documents to include their content in assessment generation.
3.7 Addition and Subtraction with Decimals
Adding or subtracting decimals works exactly like whole-number arithmetic, provided the decimal points are aligned vertically. Tenths add with tenths, hundredths with hundredths, and so on.
Worked Example — 5.3 + 2.6
\(\quad 5.3\)
\(+\,2.6\)
\(\overline{\ 7.9}\)
Worked Example — 9.01 + 9.10
Pad missing digits with a zero: write 9.01 and 9.10, line them up, add each column. 1 hundredth + 0 = 1 hundredth. 0 + 1 = 1 tenth. 9 + 9 = 18. Result = 18.11.
Worked Example — 6.236 + 0.487
Add thousandths first: 6 + 7 = 13 → write 3, carry 1 to hundredths. 3 + 8 + 1 = 12 → write 2, carry 1. 2 + 4 + 1 = 7. 6 + 0 = 6. Answer = 6.723.
Column addition with decimal points aligned
Subtraction Examples
- 5.6 − 2.3 = 3.3
- 10.4 − 4.5 = 5.9
- 17 − 0.05: write 17.00 − 0.05 = 16.95
- 34.505 − 18.1 = 16.405
Key Rule
Before adding or subtracting decimals, rewrite them with the same number of digits after the decimal point by appending zeros. Then line up and operate as whole numbers.3.8 Decimal Sequences and Patterns
Look at the sequence \(4.4,\ 4.8,\ 5.2,\ 5.6,\ 6.0,\ \ldots\) Each term is 0.4 more than the one before. The common difference? is 0.4.
Next three terms: \(6.4,\ 6.8,\ 7.2\).
Another pattern: \(5.5,\ 6.4,\ 6.39,\ 7.29,\ 7.28,\ 8.18,\ 8.17,\ldots\) — alternating +0.9 then −0.01. Next terms: \(9.07,\ 9.06\).
Estimation and Closeness
Consider the decimals 0.9, 1.1, 1.01 and 1.11. Which is closest to 1.09?
Distances: \(|0.9-1.09|=0.19\); \(|1.1-1.09|=0.01\); \(|1.01-1.09|=0.08\); \(|1.11-1.09|=0.02\). The smallest is 0.01, so 1.1 is closest to 1.09.
Using digits 4, 1, 8, 2, 5 exactly once, make a decimal as close to 25 as possible. Answers: 25.148, 8.542, 124.58 (and more). The closest found is 25.148.
Activity: Build-a-Closest-Decimal
L3 ApplyMaterials: Ten number cards (0–9), a target card.
Predict: Can you build a decimal closer to the target using 5 digits than one using only 4?
- Choose a target like 10.5. Pick 5 or 6 digit cards at random.
- Place them to form a decimal (with or without a whole part) as close to the target as possible.
- Record your best. Swap a card; try again.
Strategy: place large digits in places worth less, keep the ones/tens close to target. Extra digits after the decimal point let you fine-tune.
Figure it Out
Q1. Find the sums: (a) 2.15 + 5.26 (b) 29.19 + 9.91 (c) 0.75 + 0.03 (d) 6.236 + 0.487.
(a) 7.41 (b) 39.10 (c) 0.78 (d) 6.723
Q2. Find the differences: (a) 17 − 0.05 (b) 34.505 − 18.1 (c) 6.236 − 0.487.
(a) 16.95 (b) 16.405 (c) 5.749
Q3. Continue the sequence 4.4, 4.8, 5.2, 6.0 for three more terms.
(Common difference 0.4 after correcting typo; using 4.4, 4.8, 5.2, 5.6, 6.0 the next three are 6.4, 6.8, 7.2.)
Competency-Based Questions
Scenario: A shopkeeper sells groceries. Rohan buys 1.25 kg rice, 0.75 kg dal, and 0.8 kg sugar, pays with a ₹500 note. The total billed is ₹267.45.
Q1. What is the total weight of grocery bought?
L3 Apply(a) 1.25 + 0.75 + 0.8 = 2.80 kg.
Q2. How much change should Rohan get? Analyse using column subtraction.
L4 Analyse500.00 − 267.45 = 232.55. So change is ₹232.55.
Q3. Rohan notices another customer's bill of ₹26.745 for the same items. Evaluate whether the bill is plausible.
L5 EvaluateNot plausible — it is exactly 1/10 of Rohan's bill, suggesting a misplaced decimal point. For the same items the amount should be the same (₹267.45).
Q4. Design a pattern of five successive bill amounts that increase by ₹12.35 each time, starting from ₹104.20.
L6 Create₹104.20, ₹116.55, ₹128.90, ₹141.25, ₹153.60.
Assertion–Reason Questions
A: 17 − 0.05 = 16.95.
R: To subtract a decimal from a whole number, pad the whole number with zeros after a decimal point.
R: To subtract a decimal from a whole number, pad the whole number with zeros after a decimal point.
(a)
A: A decimal with more digits is always larger.
R: Trailing zeros after the decimal never change the value.
R: Trailing zeros after the decimal never change the value.
(c) — A is false (2.05 < 2.1 even though 2.05 has more digits). R is true.
Frequently Asked Questions
How do you add decimals in Class 7?
Line up the decimal points vertically, add trailing zeros if needed so both numbers have the same number of decimal places, then add column by column just like whole numbers. Carry the decimal point straight down. NCERT Class 7 Chapter 3 follows this method.
How do you subtract decimals?
Stack numbers with decimal points aligned, pad shorter numbers with trailing zeros, then subtract column by column from right to left. Borrow across columns when needed. Place the decimal point in the answer. NCERT Class 7 Chapter 3 uses this approach.
What is 2.5 + 1.75?
Align: 2.50 + 1.75. Add hundredths: 0 + 5 = 5. Tenths: 5 + 7 = 12, write 2 carry 1. Ones: 2 + 1 + 1 = 4. Answer: 4.25. NCERT Class 7 Ganita Prakash Chapter 3 practises such sums.
What patterns occur in decimals?
Adding 0.1 repeatedly gives 0.1, 0.2, 0.3... Multiplying by 0.1 shrinks values to tenths. Adding 0.09 gives 0.09, 0.18, 0.27... Patterns help predict results. NCERT Class 7 Chapter 3 explores decimal patterns.
Why must decimal points be aligned in addition?
Each column must contain digits of the same place value. Misaligning the decimal point mixes tenths with hundredths and produces wrong answers. Aligning the points is the safeguard. NCERT Class 7 Chapter 3 emphasises this.
What happens if you forget a trailing zero?
For 3.4 + 2.75 written as 3.4 + 2.75, the tenths of 3.4 align with the tenths of 2.75, but the missing hundredth place can confuse beginners. Writing 3.40 + 2.75 makes all places visible and prevents errors. NCERT Class 7 Chapter 3 recommends this.
Frequently Asked Questions — A Peek Beyond the Point
What is Decimal Operations and Patterns in NCERT Class 7 Mathematics?
Decimal Operations and Patterns is a key concept covered in NCERT Class 7 Mathematics, Chapter 3: A Peek Beyond the Point. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Decimal Operations and Patterns step by step?
To solve problems on Decimal Operations and Patterns, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 7 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 3: A Peek Beyond the Point?
The essential formulas of Chapter 3 (A Peek Beyond the Point) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Decimal Operations and Patterns important for the Class 7 board exam?
Decimal Operations and Patterns is part of the NCERT Class 7 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Decimal Operations and Patterns?
Common mistakes in Decimal Operations and Patterns include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Decimal Operations and Patterns?
End-of-chapter NCERT exercises for Decimal Operations and Patterns cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 3, and solve at least one previous-year board paper to consolidate your understanding.
AI Tutor
Mathematics Class 7 — Ganita Prakash
Ready