Question

Find the product using suitable properties. Name the property used.
i) 674 X 110

Answer 1

$674 \times 110 \\ = (670 + 4) \times 110...distributive \: property \\ = (670 \times 110) + (4 \ \times 110) \\ = 73700 + 440 \\ = 74140(ans)$

Answer 2

Concept: Commutative Multiplication Property

According to the commutative property of multiplication, even if the order of the numbers is altered, the result will still be the same. The result is unchanged regardless of the multiplication's sequence.

Eg., 3 × 5 = 5 × 3 = 15

Associative Multiplication Property

The associative feature of multiplication states that regardless of the sequence in which we multiply the numbers, the result will always be the same if we want to multiply any three integers together.

Eg., (2 × 3) × 4 = 2 × (3 × 4) = 24

Multiplication's Distributive Property

Multiplication has the ability to be divided over both addition and subtraction, according to its distributive property. We can answer queries in brackets thanks to this characteristic. Additionally, it quickens our brain computations.

Eg., 6 × (4 + 1) = (6 × 4) + (6 × 1) = 24 + 6 = 30

Multiplication's identity property

According to the identity property of multiplication, any number multiplied by one will always result in the same number.

Eg., 9 × 1 = 9

Given: 674 × 110

To find: The product and the property used

Solution: Here, 110 can be written as 100 + 10

674 × 110

674 × (100 + 10)

(674 × 100) + (674 × 10)               [using distributive property]

67400 + 6740

74140

Hence, the product of 674×110 is 74140 and the property used is distributive property.

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