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Arithmetic Expressions - Reading and Evaluating Complex Expressions

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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An arithmetic expression is a combination of numbers and operations like addition, subtraction, multiplication, and division. Complex expressions often contain multiple operations and various types of brackets.

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The order of operations is governed by the BODMAS rule: Brackets, Of (multiplication), Division, Multiplication, Addition, and Subtraction.

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Brackets must be solved in a specific order: 1. Bar bracket or Vinculum (x‾\overline{x}), 2. Round brackets or Parentheses ()(), 3. Curly brackets or Braces {}\{\}, 4. Square brackets or Box brackets [][ ].

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The term 'Of' in an expression like '55 of 1010' represents multiplication (5×105 \times 10) but takes precedence over division and multiplication in the sequence.

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If an expression contains only addition and subtraction, or only multiplication and division, we generally evaluate from left to right.

📐Formulae

BODMAS: Brackets→Of→Division→Multiplication→Addition→Subtraction\text{BODMAS: Brackets} \rightarrow \text{Of} \rightarrow \text{Division} \rightarrow \text{Multiplication} \rightarrow \text{Addition} \rightarrow \text{Subtraction}

a−[b+{c−(d−e)}]a - [b + \{c - (d - e)\}]

x×(y+z)=(x×y)+(x×z) (Distributive Law)x \times (y + z) = (x \times y) + (x \times z) \text{ (Distributive Law)}

💡Examples

Problem 1:

Simplify the expression: 25−[20−{10−(7−5−3‾)}]25 - [20 - \{10 - (7 - \overline{5 - 3})\}]

Solution:

Step 1: Solve the bar bracket: 5−3‾=2\overline{5 - 3} = 2. Expression becomes 25−[20−{10−(7−2)}]25 - [20 - \{10 - (7 - 2)\}]. Step 2: Solve the round bracket: (7−2)=5(7 - 2) = 5. Expression becomes 25−[20−{10−5}]25 - [20 - \{10 - 5\}]. Step 3: Solve the curly bracket: {10−5}=5\{10 - 5\} = 5. Expression becomes 25−[20−5]25 - [20 - 5]. Step 4: Solve the square bracket: [20−5]=15[20 - 5] = 15. Expression becomes 25−1525 - 15. Step 5: Final subtraction: 25−15=1025 - 15 = 10.

Explanation:

We follow the hierarchy of brackets starting from the innermost (Vinculum) to the outermost (Square brackets).

Problem 2:

Evaluate: 15+24÷3×2−515 + 24 \div 3 \times 2 - 5

Solution:

15+(24÷3)×2−515 + (24 \div 3) \times 2 - 5 =15+8×2−5= 15 + 8 \times 2 - 5 =15+16−5= 15 + 16 - 5 =31−5= 31 - 5 =26= 26

Explanation:

Applying BODMAS: First perform Division (24÷3=824 \div 3 = 8), then Multiplication (8×2=168 \times 2 = 16), then Addition (15+16=3115 + 16 = 31), and finally Subtraction (31−5=2631 - 5 = 26).

Problem 3:

Perform the following vertical subtraction: 8500−32758500 - 3275

Solution:

8500−32755225\begin{array}{r} 8500 \\ - 3275 \\ \hline 5225 \end{array}

Explanation:

Align the numbers by place value and subtract column by column starting from the units place, borrowing where necessary.