Class 10 Mathematics: Real Numbers Worksheet

How this worksheet helps your child

• Builds confidence in core Mathematics concepts taught in Class 10 through repeated, varied practice.
• Aligned to CBSE and NCERT — questions mirror the pattern children see in school tests and unit assessments.
• Comes with an answer key so parents and students can self-check in minutes, without needing a teacher.
• Pitched at medium level — use it for daily homework, weekend revision or quick exam warm-ups.

About this worksheet

Help your child conquer fundamental mathematical concepts with our Class 10 Mathematics: Real Numbers Practice Worksheet, designed specifically for CBSE students. This worksheet provides a comprehensive review of essential topics from the "Real Numbers" chapter, a cornerstone of the Class 10 Maths curriculum. Understanding real numbers is crucial as it forms the basis for algebra, geometry, and higher-level mathematics. This practice set will help students strengthen their grasp on Euclid's Division Lemma, efficiently calculate HCF and LCM, and differentiate between rational and irrational numbers. It's an excellent resource for students aiming to solidify their understanding and prepare effectively for their CBSE Board examinations, offering a medium difficulty level to challenge and engage learners as they apply theoretical knowledge to practical problems. Parents looking for supplementary materials to support their child's learning will find this worksheet invaluable.

What your child will learn

• Apply Euclid's Division Lemma to solve problems.
• Calculate the HCF and LCM of numbers using prime factorization.
• Distinguish between rational and irrational numbers.
• Prove the irrationality of numbers like √2, √3, etc.
• Solve problems involving the decimal expansion of rational numbers.

Understanding the concept

The concept of Real Numbers forms a vast and essential part of mathematics, encompassing all numbers that can be represented on a number line. This includes both rational numbers (like 1/2, -3, 0.75, which can be written as a fraction p/q where q is not zero) and irrational numbers (like √2, π, which cannot be expressed as simple fractions and have non-terminating, non-repeating decimal expansions). A key tool for understanding properties of integers, a subset of real numbers, is Euclid's Division Lemma. This lemma states that for any two positive integers 'a' and 'b', we can always find unique integers 'q' (quotient) and 'r' (remainder) such that a = bq + r, where 0 ≤ r < b. We use this lemma primarily to find the highest common factor (HCF) of two positive integers. For example, to find the HCF of 12 and 18: 18 = 1 x 12 + 6, then 12 = 2 x 6 + 0. Since the remainder is 0, the HCF is 6. Understanding how to find HCF and LCM (Lowest Common Multiple) is vital for solving many real-world problems involving fractions, time, and work. This chapter also delves into proving why certain numbers are irrational and explores the nature of decimal expansions of rational numbers, helping students build a strong foundational understanding of number systems.

Tips for parents & teachers

• Encourage your child to review the definitions of rational and irrational numbers before attempting the worksheet.
• Guide your child through the steps of Euclid's Division Lemma with a small numerical example if they find it challenging.
• Ask your child to explain their reasoning for each answer to ensure they understand the concepts, not just the solution.
• Use a timer to simulate exam conditions and help your child practice efficient problem-solving.
• Review any incorrect answers together, focusing on the underlying concept rather than just providing the correct solution.

Topics covered

How to use this worksheet at home

Open the print view and use your browser's Print dialog to print on regular A4 paper or save as a PDF. Hand the printed sheet to your child (Class 10) and set a relaxed time limit — 15 to 25 minutes works for most Mathematics worksheets. When they're done, open the "With answer key" view and let them self-mark question by question. Re-print as many times as you need; the file never expires and there's no download limit.

Frequently asked questions

Is this Mathematics worksheet really free?

Yes — every workbook on WorkbookWala is 100% free to download and print. No login, no email, no paywall. We're free for students, parents and teachers.

Is it aligned to the CBSE / NCERT syllabus?

Yes. All Class 10 worksheets are built around the CBSE and NCERT pattern so they map cleanly to what your child is studying in school.

Can I print this worksheet at home?

Yes. Click "Open print view" and use your browser's Print dialog to print on standard A4 paper, or save it as a PDF for later. The layout is designed to fit cleanly without scaling.

Does it include an answer key?

Yes — click "With answer key" to print a version with answers included, so parents and students can self-mark in minutes.