CBSE Class 5 Mathematics Multiplication and Division of Large Numbers Notes Set 02

Multiplication and division of large numbers

Multiplication is repeated addition, and division is sharing equally or finding how many groups can be made. When the numbers are large, we use place value and short methods to keep the work neat. These notes cover the parts of a multiplication, its properties, multiplying by tens, hundreds and thousands, multi-digit multiplication and long division.

Key words

1. In 125 × 4 = 500, 125 is the multiplicand, 4 is the multiplier and 500 is the product.
2. In division, the number being divided is the dividend, the number we divide by is the divisor, the answer is the quotient and what is left over is the remainder.
3. Dividend = Divisor × Quotient + Remainder.

Properties of multiplication

1. Order property: changing the order does not change the product. 34 × 78 = 78 × 34.
2. Grouping property: changing the grouping of three numbers does not change the product. 23 × (14 × 25) = (23 × 14) × 25.
3. Distributive property over addition: 23 × (100 + 25) = (23 × 100) + (23 × 25).
4. Any number multiplied by 1 stays the same. 45 × 1 = 45.
5. Any number multiplied by 0 is 0. 234 × 0 = 0.

Multiplying by 10, 100 and 1,000

To multiply by 10, put one zero on the right of the number. For 100, put two zeros, and for 1,000, put three zeros. To multiply by 60, 700 or 4,000, first multiply by 6, 7 or 4, then add the zeros. For example, 675 × 4,000 = (675 × 4) × 1,000 = 2,700 × 1,000 = 27,00,000.

Multiplying by a bigger number

Break the multiplier into hundreds, tens and ones, multiply by each part and add the partial products.

Long division

1. Look at the leftmost digits of the dividend until they form a number that is at least as big as the divisor.
2. Find how many times the divisor fits into that number, write it in the quotient, and subtract.
3. Bring down the next digit and repeat until all digits are used.
4. What remains at the end is the remainder, and it must always be smaller than the divisor.

Worked examples

Example 1. Multiply 5,347 × 486.
486 = 400 + 80 + 6. 5,347 × 6 = 32,082, 5,347 × 80 = 4,27,760, 5,347 × 400 = 21,38,800.
Adding: 32,082 + 4,27,760 + 21,38,800 = 25,98,642.

Example 2. Use suitable grouping to find 4 × 237 × 25.
4 × 25 = 100, so the product is 100 × 237 = 23,700.

Example 3. Divide 29,506 by 35.
295 ÷ 35 gives 8 (35 × 8 = 280), remainder 15. Bring down 0 to get 150; 35 × 4 = 140, remainder 10. Bring down 6 to get 106; 35 × 3 = 105, remainder 1.
Quotient = 843, remainder = 1. Check: 35 × 843 + 1 = 29,506.

Remember

1. Estimate first by rounding, to catch big mistakes.
2. Check division using Dividend = Divisor × Quotient + Remainder.

Quick Check Questions