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CBSE Class 7 · Mathematics

Arithmetic Expressions

Official NCERT chapter from Ganita Prakash Part I (book code gegp1). ExamMaster notes are original teaching at CBSE Class 7 depth.

This lesson follows the official chapter “Arithmetic Expressions” in Ganita Prakash Part I. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 7
  • Easy level
  • 8 concepts

1Simple Expressions

A simple expression is numbers and operations you can evaluate in one or two steps: 12 + 5, or 9 × 4. The value is the result after the allowed order.

A hanging plus with no second number is not an expression you can evaluate.

Figure. A simple expression names numbers and one operation. 3 + 4 is 7. The boxes are the terms; the sign is the job. A later expression with brackets is a different, longer reading.

How it works

  1. Write the expression12 + 5.
  2. Do the operation17.
  3. Call 17 the valueNot a new expression.

2Reading and Evaluating Complex Expressions

A complex expression needs an order: brackets first, then × and ÷ as they come, then + and −. Reading left to right without that order is a miss when × sits next to +.

3 + 2 × 5 is 13, not 25.

Figure. Read 3 × (2 + 5) from the brackets: 2 + 5 = 7, then 3 × 7 = 21. Dropping the brackets and doing 3 × 2 + 5 left-to-right as if it were 6 + 5 gives 11 — a different expression. The brackets are the reading order.

How it works

  1. Spot bracketsDo those first.
  2. Then multiply and divide, left to rightThe middle jobs.
  3. Then add and subtract, left to rightThe value.

× before +

Evaluate 3 + 2 × 5.

  • × first2 × 5 = 10
  • Then +3 + 10
  • Value13

Pro tip. Do not add 3 and 2 first unless brackets say so.

3A definition is a test you can run

An expression is a test: write it, run the order, get one value. Two different writings can share a value; that is allowed. A writing you cannot evaluate is not yet an expression here.

A pretty arrangement of signs is not a value.

Figure. A definition is a test you can run. Simple here means one operator: 8 − 3 passes. 2 + 4 × 5 fails that test, so you must use order of operations or brackets, not treat it as a single simple move.

How it works

  1. Write it so each sign has numbersA testable writing.
  2. Run the orderOne value.
  3. If a sign hangs, it is not readyFix the writing.

4Name the given before the unknown

The given is the written expression. The unknown is the value (or a missing number if that is asked). Read the writing before you invent a value.

Guessing 20 because it is a favourite even number is not evaluating.

Figure. Name the given before the unknown. 18, 3, and 6 are given; the question mark is not. (18 - 6) / 3 = 12 / 3 = 4. Check: 3 × 4 + 6 = 18.

How it works

  1. Copy the expressionThe given.
  2. Name what is askedValue, or a missing piece.
  3. Then run the orderGiven first.

5One worked case is enough at this class

One evaluated case is enough to show the order. You do not need a page of twins. A second case is a check, not a new theory.

Ten clones of 3+2×5 do not teach a new order.

Figure. One worked case is enough at this class: 4 × (3 + 2). Inside first, 3 + 2 = 5, then 4 × 5 = 20. The same reading works for the next expression; you do not need a harder contest example.

How it works

  1. Evaluate one mixed expressionThe case.
  2. If you want a check, change one numberA second case.
  3. Stop — the order does not grow with more clonesThis class.

6A miss: swapping the school name for the picture

The picture (a story of apples) is not the expression. The expression is the writing. Swapping them — doing the story and skipping the order — is the miss.

Eight apples in a drawing do not evaluate 3+2×5.

Figure. A miss is swapping the written order for the idea. 14 − 6 is 8. 6 − 14 is a different expression, not the same subtraction with a new name. Keep the numbers in the order they are written.

How it works

  1. Keep the story as a settingApples, or a shop.
  2. Write the expressionThe maths.
  3. Evaluate the writing, not the drawing’s countThe miss is swapping them.

7Check by the opposite action or the opposite test

Check an evaluation by a second route when you can: redo the order slowly, or use an opposite (if you added 7, take 7 off the value). A check that repeats the same rush is not a check.

Staring at 13 and saying “looks right” is not the opposite test.

Figure. Check by the opposite action. 5 × 4 = 20 is checked by 20 ÷ 4 = 5, which returns the first factor. Addition checks by subtraction the same way.

How it works

  1. Get a valueThe candidate.
  2. Redo the order or undo a last stepThe check.
  3. If they disagree, the first run failedMend it.

8Keep the claim at this chapter, not the next

This chapter evaluates writings with numbers. It does not yet solve letter-unknowns — that is a later official chapter. Keep the claim at order-and-value.

Inventing x here is the next chapter stealing this one.

Figure. Stay with this chapter’s order: multiplication before addition, so 2 + 3 × 4 = 2 + 12 = 14. Putting brackets that the expression does not have, (2 + 3) × 4 = 20, is a later-chapter move and a different claim.

How it works

  1. Stay with number expressionsThis chapter.
  2. Get a valueThe job.
  3. Leave letter-numbers for their chapterNot the next.
3 + 2 × 5 equals
  1. 13
  2. 25
  3. 10

Multiply first unless brackets say otherwise.

Notes

  • The official chapter title is “Arithmetic Expressions”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • Evaluate: ( ) then ×÷ left-to-right, then +− left-to-right

Recap

Hold these pegs from the official chapter “Arithmetic Expressions”. The wording is ExamMaster’s teaching, not a textbook recap.

Simple Expressions
A simple expression is numbers and operations you can evaluate in one or two steps: 12 + 5, or 9 × 4.
Reading and Evaluating Complex Expressions
A complex expression needs an order: brackets first, then × and ÷ as they come, then + and −.
A definition is a test you can run
An expression is a test: write it, run the order, get one value.
Name the given before the unknown
The given is the written expression. The unknown is the value (or a missing number if that is asked). Read the writing before you invent a value.
One worked case is enough at this class
One evaluated case is enough to show the order.
A miss: swapping the school name for the picture
The picture (a story of apples) is not the expression.

Practise Arithmetic Expressions

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