IGCSE Class 5 > Class 5 Notes > Year 5 Mathematics (Cambridge) > Chapter Notes: Calculation, Addition and Subtraction
Chapter Notes: Calculation, Addition and Subtraction
Addition and Subtraction
Addition and subtraction involve combining or removing quantities, often requiring estimation to predict results.Estimation involves rounding numbers to make approximate calculations:
- Example: For 3,250 - 1,115, estimate by rounding to 3,200 - 1,100 = 2,100.
- Example: For 1,972 + 2,853 + 287, estimate by rounding to 2,000 + 2,900 + 300 = 5,200.
The commutative law applies to addition, allowing addends to be reordered:
- Example: 1,972 + 287 = 287 + 1,972.
Regrouping simplifies calculations:
- Example: For 4,350 + 654, regroup 654 as 600 + 50 + 4 to add to 4,350.
- Example: For 654 - 554, regroup 654 as 600 + 50 + 4 to subtract 554.
- Addends are the numbers being added in an addition calculation (e.g., in 1,972 + 287, the addends are 1,972 and 287).
- Mental methods are used for simpler calculations, while column methods are used for more complex ones.
Adding and Subtracting Decimal Numbers
Decimal numbers include a whole part and a fractional part (e.g., tenths, hundredths).Addition and subtraction of decimals use place value and known facts:
Example: 3.4 + 2.3:
- Decompose: 3.4 = 3 + 0.4, 2.3 = 2 + 0.3.
- Add: 3 + 2 = 5, 0.4 + 0.3 = 0.7.
- Total: 5 + 0.7 = 5.7.
Example: 6.8 - 2.5:
- Decompose: 6.8 = 6 + 0.8, 2.5 = 2 + 0.5.
- Subtract: 6 - 2 = 4, 0.8 - 0.5 = 0.3.
- Total: 4 + 0.3 = 4.3.
Number line representation:
- For 3.4 + 2.3, start at 3.4, add 2 to reach 5.4, then add 0.3 to reach 5.7.
Estimation for decimals:
- Example: For 4.8 + 3.1, round to 5 + 3 = 8.
- Example: For 9.3 - 3.7, round to 9 - 4 = 5.
Multiplying by a 2-Digit Number
Multiplying a 3-digit number by a 2-digit number requires breaking down the calculation into manageable parts.Example: 247 × 26:
Break into 247 × 20 + 247 × 6:
- 247 × 20 = 4,940.
- 247 × 6 = 1,482.
- Total: 4,940 + 1,482 = 6,422.
Place value method:
- 200 × 20 = 4,000, 200 × 6 = 1,200.
- 40 × 20 = 800, 40 × 6 = 240.
- 7 × 20 = 140, 7 × 6 = 42.
- Total: 4,000 + 800 + 1,200 + 140 + 240 + 42 = 6,422.
Column method for 247 × 26:
- Multiply 247 × 6 = 1,482.
- Multiply 247 × 20 = 4,940.
- Add: 1,482 + 4,940 = 6,422.
Estimation helps predict the product:
- Example: For 192 × 33, estimate 200 × 30 = 6,000.
Division
Division involves splitting a quantity into equal groups, often resulting in a quotient and a remainder.Example: 694 ÷ 3 = 231 remainder 1:
- 231 × 3 = 693, plus remainder 1 gives 693 + 1 = 694.
Example: 85 ÷ 4 = 21 remainder 1:
- 21 × 4 = 84, plus remainder 1 gives 84 + 1 = 85.
- Remainder as a fraction: 1 ÷ 4 = 1/4, so 85 ÷ 4 = 21 1/4.
- Remainders represent the amount left after forming complete groups of the divisor.
Checking division with multiplication:
- Example: For 85 ÷ 4 = 21 r 1, check 21 × 4 + 1 = 84 + 1 = 85.
Order of Operations
The order of operations determines the sequence for performing calculations involving multiple operations.Rule: Multiplication and division have priority over addition and subtraction, unless brackets are used.
Example: 5 + 6 × 2:
- Multiply first: 6 × 2 = 12.
- Add: 5 + 12 = 17.
Example: 10 - 6 ÷ 2:
- Divide first: 6 ÷ 2 = 3.
- Subtract: 10 - 3 = 7 (not 10 - 6 = 4, then 4 ÷ 2 = 2).
Addition and subtraction are inverse operations and can sometimes be reordered without changing the result:
Example: 10 + 5 - 3 = 10 - 3 + 5 = 12.
Multiplication and division order matters:
Example: 10 × 6 ÷ 2 ≠ 10 ÷ 2 × 6 (60 ÷ 2 = 30, but 10 ÷ 2 × 6 = 5 × 6 = 30 only coincidentally).
The document Chapter Notes: Calculation, Addition and Subtraction is a part of the Class 5 Course Year 5 Mathematics IGCSE (Cambridge).
All you need of Class 5 at this link: Class 5
FAQs on Chapter Notes: Calculation, Addition and Subtraction
| 1. What is the process for adding decimal numbers? |  |
Ans. To add decimal numbers, align the numbers by their decimal points. Start from the rightmost digit and add each column, carrying over any value greater than 10 to the next column on the left. Ensure to place the decimal point in the sum directly below the other decimal points.
| 2. How do I subtract decimal numbers accurately? | |
Ans. To subtract decimal numbers, first align the numbers by their decimal points. Start from the rightmost digit and subtract each column, borrowing from the next column if necessary. Place the decimal point in the result directly below the other decimal points.
| 3. What is the method for multiplying a number by a 2-digit number? | |
Ans. To multiply a number by a 2-digit number, first break down the 2-digit number into its tens and units. Multiply the original number by each part separately, and then add the two products together. For example, to multiply 23 by 15, calculate (23 x 10) + (23 x 5).
| 4. How can I perform division with decimal numbers? | |
Ans. To divide decimal numbers, you can eliminate the decimal point in the divisor by multiplying both the divisor and the dividend by 10 until the divisor is a whole number. Then, perform the division as you would with whole numbers. Finally, place the decimal point in the quotient directly above where it appears in the dividend.
| 5. What are the rules for the order of operations in calculations? | |
Ans. The order of operations can be remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Always perform calculations in this order to ensure accurate results.
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