Problem Set 54 – Expressions and EqualitiesClass 5 Maths · Chapter 16 Preparation for Algebra · Problem Set 54 – Maharashtra Board

Summary: Problem Set 54 – Expressions and Equalities

Algebra uses numbers and letters to state and solve problems. We start with numbers.

Adding, subtracting, multiplying or dividing two numbers always gives a number: 9 + 4 = 13.

Writing an operation in brackets, like (9 + 4), names 'the number we get by adding 4 to 9'. Such an arrangement is called an expression.

Different expressions can have the same value: (8 + 7), (20 − 5), (3 × 5) and (45 ÷ 3) are all 15.

When two expressions have the same value we join them with '=' — for example (8 + 7) = (3 × 5). This is called an equality. If the values differ we use '≠'.

Key points to remember

• Algebra = numbers and letters used to state and solve problems
• Expression: an operation written in brackets, e.g. (6 × 4)
• Value of an expression = the answer of the operation
• Many expressions can have the same value
• Equality: two equal expressions joined by '='
• (8 + 7) = (20 − 5) is an equality
• 9 + 4 = 13 is also an equality
• '≠' means 'is not equal to'

Problem Set 54 – Expressions and Equalities – Notes

1. What is algebra?

• In algebra we use numbers and also letters to write and solve problems.
• Before using letters, we practise writing short statements with numbers and brackets.

2. Expressions

• (9 + 6) means 'the number got by adding 9 and 6'.
• (20 − 5) means 'the number got by taking 5 from 20'; (3 × 5) means '3 multiplied by 5'; (45 ÷ 3) means '45 divided by 3'.
• These bracket forms are expressions. Work out the operation to find the value of an expression.

3. Many expressions, one value

• Think of a number, say 15. Many expressions give it: (8 + 7), (10 + 5), (20 − 5), (3 × 5), (45 ÷ 3).
• Since they all have the value 15, they are equal to each other.

4. Writing equalities

• Join two expressions with the same value by '='.
• (8 + 7) = (20 − 5), (3 × 5) = (45 ÷ 3) and (10 + 5) = (3 × 5) are equalities.
• Simple sums like 9 + 4 = 13 or 6 × 1 = 6 are equalities too.

5. When values are different

• (6 + 4) is 10 but (6 × 4) is 24. They are not equal.
• We write (6 + 4) ≠ (6 × 4). The sign '≠' is read 'is not equal to'.
• Such a statement is an inequality — you will learn more about it in the next set.

Formulas at a glance

Key terms

Problem Set 54 – Expressions and Equalities – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 54 – Expressions and Equalities – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 54 – Expressions and Equalities

⏱ About 20 minutes

1. Learn (5 min)
   Understand that an expression in brackets stands for one number — its value.
2. Write (10 min)
   Pick a number and write four expressions for it, one with each operation.
3. Practise (5 min)
   Do the 4 'Try it yourself' questions, take the quiz and play 🎮 Play.