Fractions Decimals and Exponents (Class 7)

What this worksheet covers

This is an eighteen-question practice worksheet on fractions, decimals and exponents for Class 7, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on fractions, decimals and exponents at Class 7 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Rough work may be done in the space at the side of each page.

Sample questions from this worksheet

A preview of what's inside Fractions Decimals and Exponents (Class 7) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. 2⁵ × 2³ = _______

   • A2²
   • B2¹⁵
   • C4⁸
   • D2⁸correct
   Solution: When multiplying powers with the same base, add the exponents.
   2⁵ × 2³ = 2⁵⁺³ = 2⁸ = 256.

2. 2. The distance from the earth to the sun is about 15,00,00,000 km. Written in standard form this is _______.

   • A1.5 × 10⁹ km
   • B15 × 10⁷ km
   • C1.5 × 10⁷ km
   • D1.5 × 10⁸ kmcorrect
   Solution: 15,00,00,000 = 150000000, which has 9 digits. The decimal point moves 8 places to give 1.5, so the number is 1.5 × 10⁸ km.

3. 3. Consider the following statements.(i) aⁿ × bⁿ = (ab)ⁿ for all non-zero a and b.(ii) (−1) raised to any even power equals 1.(iii) 2³ + 2³ = 2⁶.Which of the statements is/are correct?

   • A(i) and (ii) onlycorrect
   • B(ii) and (iii) only
   • C(i) and (iii) only
   • DAll three
   Solution: Statement (i) is true, for example 2² × 3² = 4 × 9 = 36 = 6². Statement (ii) is true. Statement (iii) is false; 2³ + 2³ = 8 + 8 = 16 = 2⁴, not 2⁶ = 64 — exponents are added when powers are multiplied, not added. Hence (i) and (ii).