**Category : **4th Class

When a quantity is added to itself number of times, use operation of multiplication to find the resulting quantity. Look at the following problems:

- If one bag contains 50 kg cement, what would be the amount of cement in such 45 bags?
- If 1500 books can be placed in one almirah, how many books can be placed in 5 almirah?
- If one row has 20 plants, how many plants are there in 132 rows?

To answer the first question we need to add 50 kg 45 times. 50 kg + 50 kg + 50 kg + 50 kg...........45 times It is a tedious job and chance of error is also very much. Therefore, a short cut method is used to solve such problems called multiplication. 50 kg + 50 kg + 50 kg + 50 kg ........... 45 times = 50 kg x 45

Here the quantity 50 kg is to be added 45 times. Therefore, 50 kg is multiplied by 45.

**If one box contains 20 pencils, how many pencils are there in 154 boxes? **

**Solution:**

To answer the question we will have to add the number of pencils contained by all 154 boxes.

Thus 20 + 20 + 20 + 20 ...... 154 times

Or 20 x 154 = 3080

There are 3080 pencils in 154 boxes.

**Find the correct option for \[\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}\]. **

(a)\[\text{7}\times \text{7}\]

(b) \[\text{7}\times \text{9}\]

(c)\[\text{7}\times \text{8}\]

(d) \[\text{9}\times \text{9}\]

(e) None of these

**Answer (b)**

**Explanation-**\[~\text{7}+\text{7}+\text{7}+\text{7}+\text{7}+\text{7}+\text{7}+\text{7}+\text{7}=\text{7}\times \text{9}\]

**Terms Related to Multiplication**

In the multiplication, the number which is multiplied is known as MULTIPLICAND, the number by which the multiplicand is multiplied is known as MULTIPLIER and the answer or the result of multiplication is known as PRODUCT.

\[\text{45}\times \text{5}=\text{225}\]. Here 45 is the multiplicand, 5 is the multiplier and 225 is the product.

**Multiplication of a Number by Power of 10**

Power of 10 = 10, 100, 1000, 10000 ......

** Step 1:** Write the required number and power of 10 in multiplication form Like\[\text{4568}\times \text{1}00\].

**Step 2:** Put as many zeroes extreme right to the number, as contained by the power of 10. For example like\[\text{4568}\times \text{1}00=\text{4568}00\]

**Multiply 89456 by 1000 **

**Solution:** The power of 10 contains three zeroes. Therefore, put three zeroes extreme right to the number 89456.

Thus\[\text{89456}\times \text{1}000\text{ }=\text{ 89456}000\]

** Operation on Multiplication**

**Step 1:** Write the multiplier below the multiplicand and put a sign of multiplication.

\[\,\,\,\,\,\,\,\,\,\,\,\begin{matrix} \text{Like} & \begin{align} & \text{4566}0\text{8} \\ & \underline{\times \,\,\,\,\,\,\,\text{546}} \\ \end{align} \\ \end{matrix}\]

**Step 2:** Now multiply the multiplicand with the first digit of multiplier from right and write the result below.

\[\begin{align} & \,\,\text{4}\,\text{5}\,\text{6}\,\text{6}\,0\,\text{8} \\ & \underline{\times \,\,\,\,\,\,\,\,\,\,\text{546}} \\ & \underline{2739648} \\ \end{align}\]

**Step 3:** Now multiply the multiplicand with the second digit of multiplier from right and write the result below leaving unit place

\[\begin{align} & \,\,\,\,\,\,\text{4}\,\text{5}\,\text{6}\,\text{6}\,0\,\text{8} \\ & \,\,\,\,\underline{\times \,\,\,\,\,\,\,\,\,\,\text{5}\,\text{4}\,\text{6}} \\ & \,\,\,\,\,\,2739648 \\ & \text{1826432} \\ \end{align}\]

**Step 4:** Now multiply the multiplicand with the third digit of multiplier from right and write the result below leaving unit and tens places

\[\begin{align} & \,\,\,\,\,\,\,\,\,\text{4}\,\text{5}\,\text{6}\,\text{6}\,0\,\text{8} \\ & \,\,\,\,\,\,\,\,\underline{\,\,\times \,\,\,\,\,\,\,\,\,\,\text{5}\,\text{4}\,\text{6}} \\ & \,\,\,\,\,\,\,\,\,\,2739648 \\ & \,\,\,\,\,\text{1826432} \\ & \underline{\text{2283}0\text{4}0\,\,\,\,\,\,\,\,\,} \\ \end{align}\]

Continue the process if more number of digits multiplier contains

**Step 5:** Now add the results obtained after multiplication

\[\begin{align} & \,\,\,\,\,\,\,\,\,\text{4}\,\text{5}\,\text{6}\,\text{6}\,0\,\text{8} \\ & \,\,\,\,\,\,\,\,\underline{\,\,\times \,\,\,\,\,\,\,\,\,\,\text{5}\,\text{4}\,\text{6}} \\ & \,\,\,\,\,\,\,\,\,\,2739648 \\ & \,\,\,\,\,\text{1826432} \\ & \underline{\text{2283}0\text{4}0\,\,\,\,\,\,\,\,\,} \\ & \underline{\text{2}\,\text{4}\,\text{9}\,\text{3}\,0\,\text{7}\,\text{9}\,\text{6}\,\text{8}} \\ \end{align}\]

**Find the product of 908731 and 392 **

**Solution:**

\[\begin{align} & \,\,\,\,\,\,\,\,\,\,\text{9}\,0\,\text{8}\,\text{7}\,\text{3}\,\text{1} \\ & \,\,\,\,\,\underline{\times \,\,\,\,\,\,\,\,\,\,\,\,\,\text{3}\,\text{9}\,\text{2}} \\ & \,\,\,\,\,\,\,\,\text{1817462} \\ & \,\,\,\,\,\text{8178579} \\ & \,\underline{\text{2}\,\text{7}\,\text{2}\,\text{6}\,\text{1}\,\,\text{9}\,\text{3}\,\,\,} \\ & \underline{\text{356222552}} \\ \end{align}\]

**Word Problem Based on Multiplication**

** In a park, there are 45672 trees in each row. Find the total number of trees in the park if there are 352 rows in the park. **

**Solution:**

Number of trees in one row = 45672

Thus, number of trees in 352 rows \[=\text{45672}\times \text{352}=\text{16}0\text{76544}\]

There are 16076544 trees in the park.

**B is 489875 times greater than A. If A = 458, find the value of B. **

**Solution:**

B is 489875 times greater than A and A = 458 Thus\[\text{B}=\text{458}\times \text{489875}=\text{22436275}0\]

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