- Maths
- Classes 6-8
- 4 min read
Algebra: first steps
Use letters for unknown numbers, write simple expressions and solve equations by keeping both sides balanced.
Let us begin
The big idea
Algebra uses letters to stand for numbers we do not know yet. It is like a puzzle: find the missing number so that both sides are equal.
A letter such as x or n that stands for a number is called a variable. If Ravi has x marbles and gets 5 more, he has x + 5 marbles. 3x means 3 times x. When we write 3x we leave out the × sign.
An expression such as 2m + 5 becomes a number when we put a value in place of the letter. If m = 6, then 2m + 5 = 2 × 6 + 5 = 17.
An equation says two things are equal, like x + 3 = 8. Think of a balance. To keep it balanced, whatever we do to one side we must do to the other side.
To solve x + 3 = 8, take away 3 from both sides. Then x = 8 − 3 = 5. To solve 3x = 21, divide both sides by 3. Then x = 7. Always check by putting your answer back into the equation.
Worked examples
See how it works
Writing an expression
Ravi has x marbles and wins 5 more: x + 5. If x = 12, he has 12 + 5 = 17 marbles.
Solve x + 7 = 15
Subtract 7 from both sides: x = 15 − 7 = 8. Check: 8 + 7 = 15. Correct.
Solve 3x = 21
Divide both sides by 3: x = 21 ÷ 3 = 7. Check: 3 × 7 = 21. Correct.
A number puzzle
I think of a number, double it and add 4. The answer is 18. Call the number x. Then 2x + 4 = 18. Subtract 4: 2x = 14. Divide by 2: x = 7. Check: 2 × 7 + 4 = 18.
Try it at home
Secret number cups
You will need
- Two paper cups or small bowls
- About 20 pebbles or beans
- Paper and a pencil
What to do
- Without telling your friend, put some pebbles under cup A, for example 5.
- Put 3 loose pebbles next to cup A. On the other side, put a pile with all the pebbles together, so 8.
- Ask your friend to find the secret number. They can take 3 pebbles away from each side to balance.
- Write the equation: x + 3 = 8, so x = 5. Lift the cup to check.
- Swap roles with a new secret number.
Ask a grown-up: Keep small pebbles away from younger children. An adult can play the secret-keeper.
Fun fact
The word algebra comes from al-jabr, a word in the title of a book written by the scholar al-Khwarizmi over 1,000 years ago.
Practice sheet
Check what you learned
Practice sheet: Algebra: first steps (Classes 6-8, Maths)
- Write "a number plus 9" using n for the number.
- Find the value of 3a when a = 4.
- Find the value of 2m + 5 when m = 6.
- Solve x + 6 = 14.
- Solve y − 4 = 9.
- Solve 5p = 35.
- Solve x ÷ 3 = 6.
- A square has side s. Write an expression for its perimeter and find it when s = 5.
- Solve 2x + 3 = 17.
- 3 boxes of mangoes and 2 extra mangoes make 26 mangoes. Each box has m mangoes. Write an equation and solve it.
Answer key
Answers: Algebra: first steps
- n + 9
- 12 (3 × 4).
- 17 (2 × 6 + 5).
- x = 8 (14 − 6).
- y = 13 (9 + 4).
- p = 7 (35 ÷ 5).
- x = 18 (6 × 3).
- 4s. When s = 5 the perimeter is 20.
- x = 7 (2x = 14, so x = 7).
- 3m + 2 = 26, so 3m = 24 and m = 8.