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Number - Calculations and mental strategies

Grade 7IGCSE

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

🔑Concepts

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Order of Operations (BIDMAS/BODMAS): Brackets, Indices (Powers), Division and Multiplication (left to right), Addition and Subtraction (left to right).

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Mental Strategies for Addition/Subtraction: Partitioning (breaking numbers into hundreds, tens, units) and Compensating (rounding to a near multiple of 10 and adjusting).

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Mental Strategies for Multiplication: Using the Distributive Law, doubling and halving, or partitioning factors.

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The Commutative Law: Addition and multiplication can be done in any order (a+b=b+aa+b=b+a).

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The Associative Law: The grouping of numbers does not change the result for addition and multiplication.

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Directed Numbers: Rules for calculating with positive and negative integers.

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Estimation: Rounding numbers to 1 significant figure to find an approximate answer and check for reasonableness.

📐Formulae

a(b+c)=ab+ac(Distributive Law)a(b + c) = ab + ac \quad \text{(Distributive Law)}

a+b=b+a(Commutative Law)a + b = b + a \quad \text{(Commutative Law)}

(a×b)×c=a×(b×c)(Associative Law)(a \times b) \times c = a \times (b \times c) \quad \text{(Associative Law)}

(−a)×(−b)=ab(-a) \times (-b) = ab

(−a)×b=−ab(-a) \times b = -ab

xn×xm=xn+mx^n \times x^m = x^{n+m}

💡Examples

Problem 1:

Evaluate 20−2×(3+1)220 - 2 \times (3 + 1)^2.

Solution:

-12

Explanation:

Following BIDMAS: First, Brackets (3+1)=4(3+1)=4. Next, Indices 42=164^2=16. Then, Multiplication 2×16=322 \times 16=32. Finally, Subtraction 20−32=−1220 - 32 = -12.

Problem 2:

Calculate 46×546 \times 5 using a mental strategy.

Solution:

230

Explanation:

Use the 'Multiply by 10 and halve' strategy: 46×10=46046 \times 10 = 460. Then 460÷2=230460 \div 2 = 230.

Problem 3:

Work out −15÷(−3)+(−4)×2-15 \div (-3) + (-4) \times 2.

Solution:

-3

Explanation:

First perform division and multiplication: −15÷−3=5-15 \div -3 = 5 and (−4)×2=−8(-4) \times 2 = -8. Then add the results: 5+(−8)=5−8=−35 + (-8) = 5 - 8 = -3.

Problem 4:

Estimate the value of 5.92×20.40.48\frac{5.92 \times 20.4}{0.48}.

Solution:

\approx 240

Explanation:

Round each value to 1 significant figure: 5.92≈65.92 \approx 6, 20.4≈2020.4 \approx 20, and 0.48≈0.50.48 \approx 0.5. The calculation becomes 6×200.5=1200.5=120×2=240\frac{6 \times 20}{0.5} = \frac{120}{0.5} = 120 \times 2 = 240.