Problem Set 56 – Using Letters for NumbersClass 5 Maths · Chapter 16 Preparation for Algebra · Problem Set 56 – Maharashtra Board

Summary: Problem Set 56 – Using Letters for Numbers

Symbols make maths writing short and easy to grasp: 'dividing 60 by 12 gives 5' becomes 60 ÷ 12 = 5.

Letters can stand for 'any number'. Then one short line can state a rule for all numbers.

Changing the order of adding does not change the sum: (a + b) = (b + a). The same is true for multiplying: (a × b) = (b × a).

Other rules: a + 0 = a, a − 0 = a, a × 1 = a, a ÷ 1 = a and a × 0 = 0.

Some things do change with order: for two different numbers, (a ÷ b) ≠ (b ÷ a). Test any rule by putting in numbers.

Key points to remember

• A letter can stand for any number
• (a + b) = (b + a)
• (a × b) = (b × a)
• a + 0 = a and a − 0 = a
• a × 1 = a and a ÷ 1 = a
• a × 0 = 0
• If a ≠ b, then (a ÷ b) ≠ (b ÷ a)
• Check a rule by putting numbers in place of the letters

Problem Set 56 – Using Letters for Numbers – Notes

1. Why use symbols?

• Words take long to write: 'the number 60 divided by 12 gives 5'.
• With symbols it is just 60 ÷ 12 = 5 — shorter and quicker to read.
• Letters are another kind of symbol. They can stand for numbers.

2. Order does not matter for + and ×

• (7 + 5) = 12 and (5 + 7) = 12. This works for every pair of numbers.
• Let a and b be any two numbers. Then the rule is: (a + b) = (b + a).
• Multiplication too: (4 × 6) = (6 × 4) = 24, so (a × b) = (b × a).

3. Rules with 0 and 1

• Adding or subtracting zero leaves a number unchanged: a + 0 = a, a − 0 = a.
• Multiplying or dividing by one leaves it unchanged: a × 1 = a, a ÷ 1 = a.
• Multiplying by zero always gives zero: a × 0 = 0.

4. When order DOES matter

• Division: 10 ÷ 5 = 2, but 5 ÷ 10 is only half (½). They are not equal.
• So if a and b are two different numbers, (a ÷ b) ≠ (b ÷ a).
• Subtraction also changes with order: 9 − 4 = 5, but 4 − 9 is not even possible with the numbers you know so far.

5. Words ↔ letters

• To write a rule in short: choose a letter for 'any number' and use symbols for the words.
• To read a rule in words: say what happens to 'any number'.

Formulas at a glance

Key terms

Problem Set 56 – Using Letters for Numbers – Flashcards

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

Problem Set 56 – Using Letters for Numbers – MCQ Quiz

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

How to study Problem Set 56 – Using Letters for Numbers

⏱ About 20 minutes

1. Learn (5 min)
   Read each rule in words and then in letters.
2. Test (10 min)
   Put two numbers of your choice in place of a and b and check each rule.
3. Practise (5 min)
   Do the 4 'Try it yourself' questions, take the quiz and play 🎮 Play.