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Mathematics Study Guide

Mathematics becomes easier when you understand why each step works. This guide explains equations, percentages, fractions, common mistakes, and practice problems. Work through each example yourself before checking the solution.

Study tip: Write each step clearly, show your calculations, and check whether your final answer satisfies the original question.

1. A reliable problem-solving method

Read the question: Identify the information provided and what you need to calculate.
Select a method: Decide whether to use arithmetic, an equation, a formula, or a diagram.
Show each step: Avoid skipping calculations that may be important.
Check the answer: Substitute your result into the original equation or estimate whether it makes sense.

2. Worked example: solving a linear equation

Question: Solve 3x + 5 = 20.

Subtract 5 from both sides: 3x = 15.
Divide both sides by 3: x = 5.
Check the answer: 3 × 5 + 5 = 20.

Answer: x = 5.

An equation remains balanced when the same operation is performed on both sides.

Another example: Solve 2x + 7 = 19.

Subtract 7 to get 2x = 12. Divide by 2 to get x = 6. Checking gives 2 × 6 + 7 = 19.

3. Understanding percentages

A percentage represents a value out of 100. To find a percentage of a number, convert the percentage into a fraction or decimal and multiply.

Example: Find 15% of 240.

15% = 15 ÷ 100 = 0.15

0.15 × 240 = 36

Answer: 36.

You can check this by finding 10% of 240, which is 24, and 5%, which is 12. Adding them gives 36.

Real-life example: If a product costs ₹500 and has a 10% discount, the discount is ₹50 and the price after discount is ₹450.

4. Working with fractions

When adding or subtracting fractions, first make the denominators equal.

Example: 1/3 + 1/6

Convert 1/3 to 2/6. Then add: 2/6 + 1/6 = 3/6 = 1/2.

For multiplication, multiply the numerators together and the denominators together. Simplify the result when possible.

Example: 2/3 × 3/4 = 6/12 = 1/2.

5. Common mathematics mistakes

Performing an operation on only one side of an equation.
Adding fraction denominators directly instead of making them equal.
Ignoring negative signs or brackets.
Using the wrong order of operations.
Forgetting units or rounding instructions.
Not checking whether the final answer fits the original question.

6. Practice questions with answers

Try each question before opening its answer.

Question 1: Solve 4x + 3 = 19

Subtract 3 from both sides: 4x = 16. Divide by 4: x = 4. Check: 4 × 4 + 3 = 19.

Question 2: Find 20% of 350

20 ÷ 100 × 350 = 70. Answer: 70.

Question 3: Simplify 6/12

Divide the numerator and denominator by 6. The simplified fraction is 1/2.

Question 4: Calculate 18 + 4 × 3

Multiply first: 4 × 3 = 12. Then add: 18 + 12 = 30.

Question 5: A book costs ₹200. What is 10% of its price?

200 × 10 ÷ 100 = 20. Answer: ₹20.

7. Using AI explanations responsibly

You can use the EduSolveX question solver to request a step-by-step explanation of a mathematics question. Include the complete question and any instructions provided by your teacher.

AI explanations can contain errors. Check calculations independently and compare important answers with your textbook, class notes, or teacher. Follow the method required by your school syllabus.

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