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Calculations - Addition and subtraction of numbers up to 5 digits

Grade 4IGCSE

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

🔑Concepts

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Place Value Alignment: Always align numbers vertically according to their place value (Units, Tens, Hundreds, Thousands, Ten Thousands).

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Regrouping (Carrying) in Addition: When the sum of a column is 10 or more, carry the digit to the next column on the left.

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Regrouping (Borrowing) in Subtraction: When a digit in the top number is smaller than the digit below it, 'borrow' 1 from the next column on the left.

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Estimation: Round numbers to the nearest 100 or 1000 before calculating to predict a reasonable answer.

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Inverse Operations: Use addition to check the result of a subtraction problem and vice versa.

📐Formulae

Sum=Addend1+Addend2\text{Sum} = \text{Addend}_1 + \text{Addend}_2

Difference=Minuend−Subtrahend\text{Difference} = \text{Minuend} - \text{Subtrahend}

a+b=b+a (Commutative Property)a + b = b + a \text{ (Commutative Property)}

\text{If } a - b = c, \text{ then } c + b = a \text{ (Inverse Check)}$

💡Examples

Problem 1:

Calculate 24,568+17,23524,568 + 17,235.

Solution:

41,80341,803

Explanation:

Align the digits. Units: 8+5=138+5=13 (write 3, carry 1). Tens: 6+3+1=106+3+1=10 (write 0, carry 1). Hundreds: 5+2+1=85+2+1=8. Thousands: 4+7=114+7=11 (write 1, carry 1). Ten Thousands: 2+1+1=42+1+1=4.

Problem 2:

Subtract 12,45612,456 from 50,00050,000.

Solution:

37,54437,544

Explanation:

Since there are zeros in the minuend, regroup across columns. 50,00050,000 becomes 44 ten-thousands, 99 thousands, 99 hundreds, 99 tens, and 1010 units. Then subtract: 10−6=410-6=4, 9−5=49-5=4, 9−4=59-4=5, 9−2=79-2=7, 4−1=34-1=3.

Problem 3:

A school library has 15,20015,200 books. After a donation, it has 21,45021,450 books. How many books were donated?

Solution:

6,2506,250 books

Explanation:

Use subtraction to find the difference between the final amount and the starting amount: 21,450−15,200=6,25021,450 - 15,200 = 6,250.