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Tamil Nadu (TNBSE)Class 5 Mathematics★ 4-5 marks in TN Class 5 Term 3 exam — expressions and equalities, inequality signs, and using letters

Algebra

Samacheer Kalvi (TN State Board) Class 5 Mathematics — Algebra. Expressions and equalities, the concept of inequality, and using letters to stand for unknown numbers.

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By the end of this chapter you'll be able to…

1Write and read an expression such as 7 + 5 without working it out
2Explain that an equality claims both sides have the same value, so 7 + 5 = 8 + 4 is true
3Test whether a given equality is true by evaluating BOTH sides
4Use the signs =, > and < correctly to compare two expressions
5Use a letter as a variable standing for an unknown number, and write expressions such as x + 3 and 2x
6Substitute a value for a letter to find the value of an expression
7Find the value of a letter in a simple equation using inverse operations, and check by substitution

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Why this chapter matters

Algebra is where the equals sign stops meaning 'the answer follows' and starts meaning 'both sides are worth the same'. That single shift is the foundation of every equation a student will ever solve, and getting it wrong here causes years of trouble later. Using letters for unknown numbers then turns arithmetic into a tool for answering questions rather than just computing.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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numbers

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Addition, subtraction, multiplication and division of whole numbers

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Comparing numbers with greater than and less than

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Finding a missing addend

Algebra — Class 5 Mathematics (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 5 Mathematics, Term 3 Unit. Understanding expressions and equalities, inequality, and using letters.

1. Expressions

An expression is a way of writing a calculation without working it out.

7 + 5 is an expression. So is 12 − 4, and so is 3 × 6.

Notice that an expression on its own is not a question and not an answer. It is simply a statement of what to do.

2. Equalities

Put an equals sign between two expressions and you are claiming they have the same value.

7 + 5 = 12

Both sides come to 12, so the statement is true. This is an equality.

Here is the point that matters most in this chapter, and it is one that trips up students for years afterwards.

The equals sign does not mean "here comes the answer". It means both sides are worth the same.

So 7 + 5 = 8 + 4 is a perfectly good equality. Both sides are 12. Nothing has been "worked out", yet the statement is true.

Test yourself on this one: is 9 + 6 = 15 + 3 true? Many students say yes, because 9 + 6 is 15 and they see the 15. But the right side is 18, not 15, so the statement is false. Always work out both sides before deciding.

3. Inequality

When the two sides are not equal, we say there is an inequality and use a different sign.

Sign	Meaning	Example
=	is equal to	7 + 5 = 12
>	is greater than	15 > 9
<	is less than	8 < 20

The wide end of the sign always faces the bigger number, and the point faces the smaller one. Some children picture a hungry crocodile that always opens its mouth towards the larger amount.

To compare two expressions, work out each side first, then choose the sign:

12 + 5 ___ 20 − 4. The left is 17 and the right is 16, so 12 + 5 > 20 − 4.
6 × 3 ___ 25 − 7. The left is 18 and the right is 18, so they are equal.

4. Using letters

Sometimes a number is missing and we do not yet know it. Instead of leaving a blank, we can write a letter in its place.

If a box holds an unknown number of pencils, call that number x. Then:

3 more pencils are put in: x + 3
2 pencils are taken out: x − 2
The number of pencils doubles: 2 × x, usually written 2x

A letter used this way is called a variable, because its value can vary. Once you know what the letter stands for, you can work the expression out.

If x = 7, then:

Expression	Value
x + 3	7 + 3 = 10
x − 2	7 − 2 = 5
2x	2 × 7 = 14

5. Finding the letter's value

If an equality contains a letter, you can often work out what the letter must be.

x + 4 = 9

Ask: what number added to 4 gives 9? Since addition and subtraction undo each other, x = 9 − 4 = 5.

Check it by putting 5 back in: 5 + 4 = 9. Correct.

x − 3 = 6 gives x = 6 + 3 = 9. Check: 9 − 3 = 6.

3x = 12 gives x = 12 ÷ 3 = 4. Check: 3 × 4 = 12.

Always check by substituting your answer back into the original statement. It costs a moment and catches almost every mistake.

6. Worked examples

Example 1. Is 8 + 7 = 10 + 5 true or false?

Solution: Left is 15, right is 15. True.

Example 2. Is 9 + 6 = 15 + 3 true or false?

Solution: Left is 15, right is 18. False.

Example 3. Fill in the correct sign: 14 + 6 ___ 25 − 4.

Solution: Left is 20, right is 21. So 14 + 6 < 25 − 4.

Example 4. If x = 6, find the value of x + 9.

Solution: 6 + 9 = 15.

Example 5. If y = 5, find the value of 4y.

Solution: 4 × 5 = 20.

Example 6. Solve x + 7 = 15.

Solution: x = 15 − 7 = 8. Check: 8 + 7 = 15.

Example 7. Solve 5x = 30.

Solution: x = 30 ÷ 5 = 6. Check: 5 × 6 = 30.

Example 8. A basket holds x mangoes. Five more are added. Write the expression, then find its value if x = 12.

Solution: The expression is x + 5. If x = 12, the value is 12 + 5 = 17.

7. Practice

What is an expression?
Is 6 + 8 = 9 + 5 true or false?
Is 10 + 4 = 14 + 2 true or false?
Fill in the sign: 20 − 5 ___ 3 × 5.
Fill in the sign: 7 × 2 ___ 9 + 6.
If x = 8, find x + 7 and 3x.
Solve x + 6 = 13.
Solve x − 4 = 11.
Solve 4x = 24.
A box has y sweets and 6 are eaten. Write the expression, then find its value if y = 20.

8. Answers

A way of writing a calculation without working it out, such as 7 + 5.
Left is 14 and right is 14, so it is true.
Left is 14 and right is 16, so it is false.
Left is 15 and right is 15, so they are equal.
Left is 14 and right is 15, so 7 × 2 < 9 + 6.
x + 7 = 15 and 3x = 24.
x = 13 − 6 = 7. Check: 7 + 6 = 13.
x = 11 + 4 = 15. Check: 15 − 4 = 11.
x = 24 ÷ 4 = 6. Check: 4 × 6 = 24.
The expression is y − 6, and its value is 20 − 6 = 14.

9. Summary

An expression writes a calculation without working it out, such as 7 + 5.
An equality claims both sides are worth the same, so 7 + 5 = 8 + 4 is true.
The equals sign does not mean "the answer follows"; always work out both sides.
Use > for greater than and < for less than, with the wide end facing the bigger number.
A letter standing for an unknown number is called a variable.
Substituting a value for the letter turns an expression into a number.
Addition and subtraction undo each other, and so do multiplication and division, which is how a letter's value is found.
Always check by putting your answer back into the original statement.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Expressions and equalities

An expression is a calculation written without being worked out, such as 7 + 5. An equality puts an equals sign between two expressions and claims they have the same value: 7 + 5 = 12, and also 7 + 5 = 8 + 4.

The equals sign does NOT mean 'here comes the answer'. It means both sides are worth the same, which is why 7 + 5 = 8 + 4 is a perfectly good true statement.

Testing an equality

Work out the left side, work out the right side, then compare. The statement is true only if the two values match.

Is 9 + 6 = 15 + 3 true? The left is 15 and the right is 18, so it is FALSE. Students who see the 15 and stop reading get this wrong.

Inequality signs

= is equal to; > is greater than; < is less than. The wide end of the sign faces the bigger number and the point faces the smaller.

To compare expressions, evaluate each side first. 12 + 5 > 20 - 4 because 17 is greater than 16, while 6 x 3 equals 25 - 7 since both are 18.

Using letters

A letter standing for an unknown number is called a variable. If a box holds x pencils, then adding 3 gives x + 3, removing 2 gives x - 2, and doubling gives 2x.

Once the letter's value is known, substitute it. If x = 7 then x + 3 = 10, x - 2 = 5 and 2x = 14.

Finding the value of a letter

Use the inverse operation. Addition and subtraction undo each other; multiplication and division undo each other. From x + 4 = 9, x = 9 - 4 = 5. From x - 3 = 6, x = 6 + 3 = 9. From 3x = 12, x = 12 / 3 = 4.

Always check by substituting the answer back into the original statement: 5 + 4 = 9 confirms it.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Reading the equals sign as 'write the answer here', so answering 9 + 6 = __ + 8 with 15

✓ The equals sign means both sides are worth the same. The left is 15, so the blank must make the right side 15 too, giving 7. Always evaluate both sides.

WATCH OUT

✗ Pointing the inequality sign the wrong way

✓ The wide open end always faces the bigger number and the point faces the smaller one. 15 > 9, and 8 < 20.

WATCH OUT

✗ Comparing two expressions without working them out first

✓ Evaluate each side, then choose the sign. 12 + 5 and 20 - 4 look similar until you get 17 and 16.

WATCH OUT

✗ Writing 2x when the meaning is 2 + x

✓ 2x means 2 multiplied by x. Two more than x is written x + 2. Read the words carefully before writing the expression.

WATCH OUT

✗ Solving for a letter and not checking

✓ Substitute your answer back into the original statement. If x + 7 = 15 gives x = 8, check that 8 + 7 = 15.

Practice problems

Work through this chapter's problems as a readiness check — reveal each solution, mark yourself honestly, and get your gap report at the end.

Readiness check

Are you exam-ready for Algebra?

11 problems from this chapter. Try each one, reveal the worked solution, mark yourself honestly — get your gap report at the end.

11 questions~8 min worth ~5 marks in Tamil Nadu (TNBSE) exams

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•An expression is a calculation written without being worked out.
•An equality claims both sides are worth the same, so 7 + 5 = 8 + 4 is true.
•The equals sign never means 'the answer follows'; evaluate both sides.
•The wide end of > and < faces the bigger number.
•A letter standing for an unknown is a variable; 2x means 2 multiplied by x.
•Substituting a value turns an expression into a number.
•Addition and subtraction undo each other; so do multiplication and division.
•Always check a solved letter by substituting it back.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 4-5 marks in TN Class 5 Term 3 Mathematics exam

Question type	Marks each	What it tests
Equalities	1-2	Deciding whether a statement is true by evaluating both sides
Inequality	1-2	Choosing =, > or < between two expressions
Using letters	1-2	Writing expressions with a variable and substituting a value
Solving	2	Finding the value of a letter using inverse operations and checking

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Working out how much more money is needed when you know t…

Working out how much more money is needed when you know the price and what you have.

Reading a balance scale

Reading a balance scale, where both pans must hold the same weight.

Filling in a missing number on a shop bill from the total

Filling in a missing number on a shop bill from the total.

Following a rule such as 'the fare is 20 rupees plus 8 ru…

Following a rule such as 'the fare is 20 rupees plus 8 rupees for each kilometre'.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Evaluate BOTH sides of any equality before deciding whether it is true; never stop at the first number you recognise.

Write the value of each side in the margin before choosing between =, > and <.

Read the words carefully when writing an expression: 'twice a number' is 2x, 'two more than a number' is x + 2.

When solving, name the inverse operation you are using before you apply it.

Always substitute your answer back into the original statement and show that check in your working.

In a fill-in-the-blank equality, work out the complete side first, then find what the blank must be.

Do not skip the checking step to save time; it catches nearly every slip in this unit.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 5 Term 3 examination

NMMS aptitude section

Sainik School entrance

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Yes. 7 + 5 = 8 + 4 is a true equality, because both sides are worth 12. The equals sign compares values, it does not announce an answer.

2x means 2 multiplied by x, so if x = 5 it is 10. x + 2 means 2 more than x, so if x = 5 it is 7.

Use the one that undoes what is being done to the letter. If something is added, subtract it; if the letter is multiplied, divide.

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