Question

Find the product using suitable properties:
(a) \[738 \times 103\]
(b) \[854 \times 102\]
(c) \[258 \times 1008\]
(d) \[1005 \times 168\]

Answer 1

Hint: Here in this question, we have to find each product using suitable properties. First, we need to write any one of multiplier or multiplicand in the additional form of using a number by power of ten and further by applying a distributive property and simplifying or multiplying using a table of multiplication we get the required solution.

Complete step by step solution:
Multiplication is one of the four basic operations of arithmetic. The multiplication of whole numbers may be thought of as a repeated addition, that is, the multiplication of two numbers is equivalent to adding as many copies of one of them.
Usually, multiplication is represented by the cross sign ‘\[ \times \]’, sometimes we also use asterisk ‘\[*\]’ or dot ‘\[ \cdot \]’. In multiplication the multiplicand is the number to be multiplied, the multiplier is the number by which it is to be multiplied and the final answer of multiplication is called as product.
Now, consider the given question:
a.\[738 \times 103\]
Here,
Multiplicand-738
Multiplier-103
The multiplier 103 can be written as \[100 + 3\], then
\[ \Rightarrow 738 \times \left( {100 + 3} \right)\]
Now, apply a distributive property
\[ \Rightarrow 738 \times 100 + 738 \times 3\]
On multiplication, we get
\[ \Rightarrow 73,800 + 2,214\]
\[\therefore 76,014\]

b.\[854 \times 102\]
Here,
Multiplicand-854
Multiplier-102
The multiplier 103 can be written as \[100 + 2\], then
\[ \Rightarrow 854 \times \left( {100 + 2} \right)\]
Now, apply a distributive property
\[ \Rightarrow 854 \times 100 + 854 \times 2\]
On multiplication, we get
\[ \Rightarrow 85,400 + 1,708\]
\[\therefore 87,108\]



c.\[258 \times 1008\]
Here,
Multiplicand-258
Multiplier-1008
The multiplier 1008 can be written as \[1000 + 8\], then
\[ \Rightarrow 258 \times \left( {1000 + 8} \right)\]
Now, apply a distributive property
\[ \Rightarrow 258 \times 1000 + 258 \times 8\]
On multiplication, we get
\[ \Rightarrow 2,58,000 + 2,064\]
\[\therefore 2,60,064\]

d.\[1005 \times 168\]
Here,
Multiplicand-1005
Multiplier-168
The multiplicand 1005 can be written as \[1000 + 5\], then
\[ \Rightarrow \left( {1000 + 5} \right) \times 168\]
Now, apply a distributive property
\[ \Rightarrow 1000 \times 168 + 5 \times 168\]
On multiplication, we get
\[ \Rightarrow 1,68,000 + 840\]
\[\therefore 1,68,840\]

Note: When multiplying a whole number by a positive power of ten, just count how many zero(s) you have and attached that to the right of the whole number and remember properties of multiplication:
For numbers a, b and c
Commutative property: \[a \times b = b \times a\]
Associative property: \[\left( {a \times b} \right) \times c = a \times \left( {b \times c} \right)\]
Distributive property: \[a \times \left( {b + c} \right) = \left( {a \times b} \right) + \left( {a \times c} \right)\]
By using all these, it makes solving a multiplication problem easier.