2. Arithmetic Expressions

7 topics1 h

Chapter 2 of NCERT Mathematics for Class 7: Arithmetic Expressions. Three sections — An expression names a number, Terms and brackets and The properties that license rearranging. Seven videos, 1 h in all.

Worked answers to the 24 exercise questions in this chapter →

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Part 1

An expression names a number

9 minWriting a situation as an expression before computing itAn arithmetic expression is a name for a number, not an instruction to work one out. Almost everything fussy about notation follows from that.9 min · 10 partsहिंदी9 minComparing two expressions by reasoning, not by evaluatingDeciding which of two expressions is larger is a question about their values. It usually does not need either value.9 min · 10 partsहिंदी

Part 2

Terms and brackets

9 minBrackets decide which operation happens firstAn expression with two operations can be read two ways. While the story behind it is still attached, only one reading is right.9 min · 10 partsहिंदी10 minEvery expression can be rewritten as a sum of termsOne move turns any expression into a plain addition: replace every subtraction with the addition of an inverse.10 min · 10 partsहिंदी

Part 3

The properties that license rearranging

9 minCommutative and associative: why order and grouping are freeThe freedom to shuffle belongs to the terms of a sum, not to the symbols on the page. One second of carelessness is all it takes.9 min · 10 partsहिंदी10 minRemoving a bracket after a minus sign flips every term insideThe sign flip is not a rule to memorise. It is forced by what taking away means.10 min · 10 partsहिंदी9 minThe distributive property, and using it to compute fasterThe distributive property is not something you do to brackets. It is the record of one collection counted two ways.9 min · 10 partsहिंदी

What you will be able to do

  • Recognise a written arithmetic phrase as an arithmetic expression, and state that it has exactly one value
  • Place <, > or = between two expressions and explain that the sign is a statement about their values
  • Explain why an expression carrying more than one operation can be read in more than one way once its context is removed
  • Identify the terms of an expression by locating the plus signs
  • State that swapping two terms of a sum leaves the total alone, and that this is named the commutative property of addition
  • Rewrite an expression of the shape "a number minus a bracketed total" without its bracket, changing the sign of every term that comes out
  • State that multiplying a total is the same as multiplying each part and adding, and that the same holds for a difference

What this chapter assumes you already know

  • The four operations on whole numbers, and the signs +, –, ×, ÷
  • Reading a two-operand calculation aloud ("five times twenty-five")
  • Class 6 place value and comfort with three- and four-digit numbers
  • Ordering whole numbers, and the signs <, >, =
  • Addition and subtraction of three-digit numbers, at least well enough to check
  • Class 6 experience of "one more" and "one less" on a number line
  • Multiplication and subtraction of two- and three-digit numbers
  • Reading a word problem and identifying which quantities combine

It builds directly on What it actually takes to make one lakh.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "= means and the answer is."
  • "Writing 5 × 25 is leaving the job half done."
  • "Every number has one proper expression."
  • "13 + 2 and 15 are different numbers."
  • "An expression must contain an operation."
  • "To compare two expressions you must evaluate both."
  • "The side with the bigger first number is bigger."
  • "Adding 1 somewhere always adds 1 to the value."