5th Class Mathematics Operations on Numbers Multiplication

    Multiplication

When a number is added to itself number of times, the process of addition becomes bigger and lengthy,therefore, a short cut method of addition was developed to perform such additions called multiplication. Thus multiplication is a short cut method of repeated addition.  

6035 + 6035 + 6035 + ...168 times. It is a tedious job to solve it. So a simple method is used to solve such questions. We can solve the above problem simply as 6035\[\times \]168 = 1013880

Multiplicand: The number which is multiplied is called multiplicand.

Multiplier: The number by which other number is multiplied is called multiplier.

Product: The result is called product.

Multiply 46898 and 64

Solution:

\[\frac{\frac{\begin{align}   & \begin{matrix}    4 & 6 & 8 & 9 & 8 & {}  \\ \end{matrix} \\  & \begin{matrix}    \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\times  & 6 & 4  \\ \end{matrix} \\ \end{align}}{\begin{align}   & \,\,\,\,\begin{matrix}    {} & 1 & 8 & 7 & 5 & 9\,\,\,\,2  \\ \end{matrix} \\  & \begin{matrix}    +2 & 8 & 1 & 3 & 8 & 8  \\ \end{matrix} \\ \end{align}}}{\begin{matrix}    3 & 0 & 0 & 1 & 4 & 7 & 2  \\ \end{matrix}}\begin{matrix}    \text{Multiplicand}  \\    \text{multiplier}  \\    \text{Produce}  \\ \end{matrix}\]  

How to Perform Multiplication

Multiply 890456 by 983

Step 1: Multiply 890456 by 3 (because 3 is at the unit place in the multiplier 983)  \[890456\times 3=2671368\]

Step 2: Now multiply 890456 by 80 (because 8 is at the tens place in the multiplier  \[983)890456\times 80=71236480\]

Step 3: Now multiply 890456 by 900 (because 9 is at the hundreds place in the multiplier  \[983)890456\times 900=801410400~-1\]

Step 4: Now add all the above results 2671368 + 71236480 + 801410400 = 875318248

Thus \[890456\times 983=875318248\]

It can be written as

\[\begin{align}   & \frac{\begin{align}   & 890456 \\  & \,\,\,\,\,\times 983 \\ \end{align}}{\,\,\,\,\,\,2671368} \\  & +71236480 \\  & \frac{801410400}{875318248} \\ \end{align}\]  

Find the product of 4568 and 305

Solution:

\[\frac{\frac{\begin{matrix}    \begin{matrix}    4 & 5  \\    \times  & 3  \\ \end{matrix}\,\,\,\,\,\,\,\,\,\begin{matrix}    6 & 8  \\    0 & 5  \\ \end{matrix}  \\ \end{matrix}}{\begin{align}   & \,\,\,\,\,\,\,\,\,\begin{matrix}    2 & 2 & 8 & 4 & 0  \\ \end{matrix} \\  & \begin{matrix}    + & 0 & 0 & 0 & 0\,\,\,0  \\ \end{matrix} \\  & \begin{matrix}    1 & 3 & 7 & 0 & 4  \\ \end{matrix} \\ \end{align}}}{\begin{matrix}    1 & 3 & 9 & 3 & 2 & 4 & 0  \\ \end{matrix}}\begin{matrix}    \text{Multiplicand}  \\    \text{multiplier}  \\    \text{Product}  \\ \end{matrix}\]

Word Problems Based on Multiplication  

There are 225 godowns. Each godowns has 5478 rice bags and each bag contains 20 kg of rice. Find the total amount of rice.

(a) 24651000kg                                 

(b) 6523600kg

(c) 546890 kg                     

(d) 1205630 kg

(e) None of these  

Answer: (a)

Explanation

There are 225 godowns and each godowns contains 5478 rice bags. Therefore, total number of rice bags = 225\[\times \]5478 = 1232550

One bag contains 20 kg of rice, so total amount of rice = 1232550 \[\times \]20 = 24651000kg  

There are 15 rows of trees in a garden. Each rows has 245 trees. Trees of 4 rows are cut down. Find the total number of remaining trees in the park.

(a) 3675                                               

(b) 980

(c) 4655                                               

(d) 2695

(e) None of these  

Answer: (d)

Explanation

There are 15 rows of trees in the garden and each rows has 245 trees

Therefore, total number of trees in the garden = 15\[\times \]245 = 3675

Total number of trees which was cut down = 245\[\times \]4 = 980

Remaining number of trees = 3675 - 980 = 2695.