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Calculations - Mental arithmetic strategies

Grade 4IGCSE

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

🔑Concepts

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Partitioning: Breaking numbers into hundreds, tens, and ones to add or subtract separately (e.g., 34+25=(30+20)+(4+5)34 + 25 = (30+20) + (4+5)).

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Compensation: Adjusting one number to the nearest 10 or 100 to make the calculation easier, then correcting the difference (e.g., to add 19, add 20 and subtract 1).

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Bridging: Moving to the next multiple of 10 or 100 first (e.g., for 85+785 + 7, do 85+5=9085 + 5 = 90, then 90+2=9290 + 2 = 92).

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Doubling and Halving: Using known doubles to solve multiplication or halving to solve division (e.g., to multiply by 4, double and double again).

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Inverse Operations: Using the relationship between addition/subtraction and multiplication/division to check or solve problems.

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Near Doubles: Using known doubles to solve close additions (e.g., 15+1615 + 16 is double 15 plus 1).

📐Formulae

a+b=b+aa + b = b + a (Commutative Property)

a+(b−c)=(a+b)−ca + (b - c) = (a + b) - c (Compensation Rule)

x×4=(x×2)×2x \times 4 = (x \times 2) \times 2 (Double-Double Rule)

x×5=(x×10)÷2x \times 5 = (x \times 10) \div 2 (Multiply by 10 and Halve)

💡Examples

Problem 1:

Calculate 57+3957 + 39 mentally.

Solution:

96

Explanation:

Use the compensation strategy. Round 39 up to 40. 57+40=9757 + 40 = 97. Since we added 1 too many, subtract 1 from the total: 97−1=9697 - 1 = 96.

Problem 2:

Find the result of 125−38125 - 38 using bridging.

Solution:

87

Explanation:

Bridge to the nearest hundred. 125−25=100125 - 25 = 100. We still need to subtract 13 more (because 38−25=1338 - 25 = 13). 100−10=90100 - 10 = 90, and 90−3=8790 - 3 = 87.

Problem 3:

Calculate 16×516 \times 5 mentally.

Solution:

80

Explanation:

Use the 'Multiply by 10 and Halve' strategy. 16×10=16016 \times 10 = 160. Half of 160 is 80. Alternatively, halve the 16 to get 8 and double the 5 to get 10: 8×10=808 \times 10 = 80.

Problem 4:

Solve 46+4746 + 47 using near doubles.

Solution:

93

Explanation:

Recognize that 47 is 46+146 + 1. Double 46 is 92 (40+40=80,6+6=12,80+12=9240+40=80, 6+6=12, 80+12=92). Then add the extra 1: 92+1=9392 + 1 = 93.