What does it mean?
A variable names an amount that can be unknown or can change. Once you say that n is the number of apples, 2n + 5 describes doubling that number and then adding five. An expression describes a value; an equation states that two expressions are equal.
An expression describes a calculation using numbers, operations and possibly letters. Four times x is 4x; three more is 4x + 3. Brackets show a whole group is changed: add 6 then double gives 2(n + 6). Sharing 12 equally among n people gives 12 ÷ n.
Learning goal: Writing expressions. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Pre-algebra if an earlier idea needs revisiting.
See the idea
Read each diagram with its labels, then follow the worked examples. Practice questions include their own measurements and information.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Choose a method and explain why it works
Define the letter first, then translate the operations in order. “Add six, then double” groups the addition: 2(n + 6). “Double, then add six” gives 2n + 6. Test your expression with one small value to see whether it follows the original instructions. Keep any measurement unit attached to the meaning of the variable.
Notation: 4x means 4 × x
Key rule and when to use it
Multiplication is implicit in 3n. Brackets make a grouped quantity act as one input: 2(n + 6) doubles the whole sum.
Worked examples, step by step
Example 1: Write an expression for 3 more than four times x.
- Four times x is 4x.
- Three more means add 3.
Answer: 4x + 3
Example 2: Write an expression for 12 shared equally among n people.
- The total is 12.
- Sharing equally means divide by n.
Answer: 12 ÷ n
Check: For example, if n = 3, each person gets 12 ÷ 3 = 4. The expression for an unknown n remains 12 ÷ n.
Example 3: A club charges ₹40 plus ₹15 per visit. Write the cost for v visits and find it for 3 visits.
- Define v as the number of visits.
- The variable part is 15v; the fixed part is 40. Cost = 40 + 15v rupees.
- For v = 3, the cost is 40 + 45 = ₹85.
Common mistakes and important boundaries
Order matters for subtraction and division. “Four less than n” is n − 4, while “n less than four” is 4 − n. If n counts people sharing an amount, it must be a positive whole number; 12 ÷ n does not make a meaningful sharing model when n = 0.
A point to explain
Read the multiplication phrase first, then add the extra amount.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Writing Algebraic Expressions from Words — practice
Work on paper first. Open each answer afterwards and compare the reasoning. Print the questions with or without the separate answer key; no account is required.
Name: ____________________ Date: __________
Times 5, then add 2
Answer and a way to check
5x + 2
Underline the quantity, the multiplication, and the final change.
Add 6, then times 2
Answer and a way to check
2(x + 6)
Underline the quantity, the multiplication, and the final change.
A number minus 4
Answer and a way to check
x − 4
Underline the quantity, the multiplication, and the final change.
Times 8, then add 5
Answer and a way to check
8x + 5
Underline the quantity, the multiplication, and the final change.
A box has n apples. You double them, then add 5 more. Which expression is that?
Answer and a way to check
2n + 5
Underline the quantity, the multiplication, and the final change.
Let n be a number. Write an expression for seven less than three times n.
Answer and a way to check
3n − 7
Three times n is 3n. Seven less subtracts 7 from that complete quantity.
Write an expression for five times the sum of n and 2.
Answer and a way to check
5(n + 2)
The whole sum is multiplied, so keep n + 2 in brackets.
For n = 3, compare 2(n + 4) and 2n + 4.
Answer and a way to check
14 and 10; they are different.
First expression: 2 × 7 = 14. Second: 6 + 4 = 10. The operations occur in different orders.
Writing Algebraic Expressions from Words — answer key
5x + 2 Underline the quantity, the multiplication, and the final change.
2(x + 6) Underline the quantity, the multiplication, and the final change.
x − 4 Underline the quantity, the multiplication, and the final change.
8x + 5 Underline the quantity, the multiplication, and the final change.
2n + 5 Underline the quantity, the multiplication, and the final change.
3n − 7 Three times n is 3n. Seven less subtracts 7 from that complete quantity.
5(n + 2) The whole sum is multiplied, so keep n + 2 in brackets.
14 and 10; they are different. First expression: 2 × 7 = 14. Second: 6 + 4 = 10. The operations occur in different orders.
Questions students and parents ask
Can different-looking expressions have the same value for every n?
Yes. 2(n + 6) and 2n + 12 are equivalent because distribution multiplies both terms by 2. A single matching test value alone does not prove equivalence.
Do I need an equals sign in an expression?
No. 4x + 3 is an expression. Writing y = 4x + 3 creates an equation defining y in terms of x.
Is this a complete set of textbook exercise solutions?
No. This guide adapts BananaLearn’s own teaching examples and practice. It is not official NCERT material or a promise of the exact chapter sequence in a particular board, country or textbook edition.
What if the examples are still difficult?
Revisit Pre-algebra. Try the first example with its model, then attempt one fresh question independently. A correct copied answer is not evidence that the method can be used without support.
Help at home
Say two short sequences that differ only in order, such as “add, then double” and “double, then add”. Have your child test both with the same number.
Keep one example of the learner’s own working. A repeated difficulty across fresh questions can guide a discussion with their teacher; one short practice sheet does not establish a diagnosis or a full mastery profile.
Connect this idea to the next skill
About this guide
Based on BananaLearn’s Grade 5 course lesson “Writing expressions”. The explanations have been adapted for independent reading; course diagrams are reused where they fit the idea, and missing classroom givens are made explicit in questions.
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