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DIVISION ALGORITHM Suppose 75 is divided by 9, then the quotient is 8 and the 9) 75 ( 8 PROPERTIES OF DIVISION
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3 (i) If a and b are nonzero whole numbers, then a + b is not always a whole number.
remainder is 3. Clearly,
75 = (9 × 8) + 3. EXAMPLE: We know that 7 and 2 are whole numbers.
In general, let a and b be two given whole numbers such that a > b. On dividing a by b, But, 7 + 2 is not a whole number.
let q be the quotient a Then, we have: a= bq +r, where Os; r < b. (ii) DIVISION BY 0 if a is a whole number, then a + 0 is meaningless.
This result is known as division algorithm. (iii) If a is a nonzero whole number, then o + a = o.
Thus. dividend = (divisor x quotient) + remainder.
EXAMPLE: (i) 0 ÷ 3 = 0 (ii) 0 ÷ 57 = 0, etc.
EVEN AND ODD WHOLE NUMBERS A whole number divisible by 2 is called an even
number; e.g., 0, 2, 4, 6, 8, etc., are all even numbers. 1.Elephants 6.Bananas
A whole number which is not divisible by 2 is called an odd number; e.g., 1, 3, 5, 7, 9, etc., are all odd
numbers.

SOLVED EXAMPLES 2.Camels 7.Kites

EXAMPLE: Find the number which when divided by 53 gives 8 as quotient and 5 as remainder.

SOLUTION: Given: divisor = 53, quotient= 8 and remainder = 5.
By division algorithm, we have: 3.Bears 8.Pencils
dividend = (divisor × quotient) + remainder
= (53 × 8) + 5
= (424 + 5) = 429.
Hence, the required number is 429. 4.Apples 9.Umbrellas

EXAMPLE: Divide 535 by 31 and check the result by the division algorithm.

SOLUTION: By actual division, we have:
31) 535 ( 17 5.Oranges 10.Chocolates
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225 These are some of the things that can be counted with numbers.
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8 EXAMPLE 1: 100 + 50 = 150

dividend = 535, divisor = 31, quotient = 1 7 and remainder = 8. (natural number) (natural number) (natural number)
CHECK (31 × 17) + 8 = 527 + 8 = 535.
Hence, the above result is correct. EXAMPLE 2: 20 + 20 = 40

EXAMPLE 3. Divide 53068 by 25 7 and check the result by the division algorithm. (natural number) (natural number) (natural number)
SOLUTION: By actual division, we have:
257 ) 53068 ( 206 EXAMPLE 1: 100 - 50 = 50
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1668 (natural number) (natural number) (natural number)
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126 EXAMPLE 2: 20 - 20 = 0

dividend= 53068, divisor= 257, quotient = 206 and remainder = 126. (natural number) (natural number) (zero)
CHECK (257 × 206) + 126 = 52942 + 126 = 53068.
Hence, the above result is correct.