Skip to content

Class 7 Maths · Chapter 2 · NCERT (gegp102)

Arithmetic Expressions: common misconceptions

See the tempting mistake students make in Arithmetic Expressions, why it feels right at first glance, and a worked visual example that shows the right idea.

The tempting mistake & worked visual

Must every operation be done left to right?

Wrong

8 + 2 × 3 = 30

Why it feels right. I started with the first operation I saw.

Right

Multiplication takes precedence over addition here.

Worked example

8 + 2 × 3
8
33
(8 + 2) × 3
82
82
82
The brackets change what gets repeated three times.
  1. Two groups of 3 give 6.
  2. Add 8 to get 14.
  3. The expression (8 + 2) × 3 represents 30.

If your child says… (8 concept checks in this chapter)

As you work through Arithmetic Expressions, listen for these everyday misunderstandings and use the prompt alongside each one.

1. Simple Expressions See how to teach this step →

If your child says… “Equals means the answer comes next.”

Ask together
Could either spoon grouping go on the left of equals?
What’s true
Equals connects complete sides with matching values.
2. Comparing Expressions See how to teach this step →

If your child says… “The expression with the biggest number must win.”

Ask together
Which arrow lands farther right on the number line?
What’s true
The numbers and operations together determine each expression’s value.
3. Comparing Expressions See how to teach this step →

If your child says… “Both rows gain one, so the difference grows by two.”

Ask together
Does the added pair leave any extra chickpeas unmatched?
What’s true
Equal increases in both amounts leave their difference unchanged.
4. Brackets in Expressions See how to teach this step →

If your child says… “I can leave the brackets until last.”

Ask together
Are we doubling just three, or the sum of two and three?
What’s true
The bracketed group must be ready before its value is used outside.
5. Terms in Expressions See how to teach this step →

If your child says… “Two and three are separate terms.”

Ask together
Are we adding two and three separately, or using their product?
What’s true
A multiplication supplies one value, so its factors stay together.
6. Swapping and Grouping See how to teach this step →

If your child says… “I can move the number and leave its minus behind.”

Ask together
If negative two became positive two, would the pair still cancel?
What’s true
A term keeps its sign when you move it.
7. Removing Brackets—I See how to teach this step →

If your child says… “I change only the first sign after the minus.”

Ask together
If you removed two more, would you have taken away less than five?
What’s true
Subtracting a bracketed group reverses every internal sign when the brackets are removed.
8. Removing Brackets—II See how to teach this step →

If your child says… “I multiply only the first number inside.”

Ask together
Do both rows contain the group of two?
What’s true
Every part belongs to each copy of the group.

Use this chapter three ways