# CLASS-5MULTIPLICATION OF DECIMAL FRACTION BY WHOLE NUMBER

Multiplication By A Whole Number -

We have to write the numbers in column form. Then we have to multiply the multiplicand with the multiplier as in common multiplication. But it is important to know where to put the decimal point in the product. The product should have the same number of decimal places as the multiplicand.

To multiply a decimal fraction by a whole number, you can follow these steps:

1. Treat the decimal fraction as a regular number and ignore the decimal point for now.
2. Multiply the whole number by the decimal fraction as if it were a whole number.
3. Count the total number of decimal places in the decimal fraction.
4. Place the decimal point in the product by starting from the right and counting the same number of decimal places as in step 3.

Here's an example:

Example. i) Multiply 2.5 by 3

Ignore the decimal point: 2.5 * 3 = 2.5 * 3

Multiply as whole numbers: 2.5 * 3 = 7.5

Count the decimal places in the decimal fraction (1 decimal place).

Place the decimal point in the product: 2.5 * 3 = 7.5

So, 2.5 multiplied by 3 is equal to 7.5.

Remember to consider the decimal places and place the decimal point correctly in the final product.

Other way of understanding -

To multiply a decimal fraction (a number less than 1) by a whole number, you can follow these steps:

1. Ignore the decimal point and perform the multiplication as if both numbers were whole numbers.
2. Count the total number of decimal places in the decimal fraction.
3. Place the decimal point in the product by counting from the right of the result, starting with the rightmost digit and moving the same number of places as counted in step 2.

Here's an example:

Example. 1) Multiply 0.75 by 3

Ignore the decimal point and perform the multiplication: 75 x 3 = 225

Count the number of decimal places in 0.75 (2 decimal places).

Place the decimal point in the product: 2 2 5 . 0 0

↑ 2 decimal places

The result is 2.25.

So, 0.75 multiplied by 3 equals 2.25.

Remember to count the decimal places and correctly place the decimal point in the product to obtain the correct result.

There are some examples are given below for your better understanding -

2) Find the product:

a) 1.88 × 16

1    .    8        8

×         1        6

----------------------------

1       1        2        8

+ 1       8        8        ×

--------------------------------

3        0  .    0        8

[As the multiplicand 1.88 has two decimal places so the product 30.08 also have two decimal places.]

b) 0.487 × 240

0   .    4        8        7

×        2        4        0

------------------------------

0        0        0         0

1      9        4        8         ×

+ 0    9      7        4        ×

--------------------------------------

1       1      6 .      8        8        0

[As the multiplicand 0.487 has three decimal places so the product 116.880 also have three decimal places. 116.880 = 116.88 as removing zeroes from the extreme right of the decimal point does not change the value of the number.]

.: Answer is 116.880 = 116.88     (Ans.)

3) If 614.6 × 9 = 5531.4 then find the product of each of the following without actually performing the multiplication.

a)  61.46 × 9                          d) 6.146 × 9

b)  0.6146 × 9                         e) 0.06146 × 9

c) 6146 × 9

Ans.) We know that, when we multiply a decimal fraction with a whole number the product should have the same number of decimal places as the multiplicand.

614.6 × 9 = 5531.4 (given)

a) 61.46 × 9 = 553.14

[As the multiplicand 61.46 has two decimal places so the product 553.14 also have two decimal places.]

b) 0.6146 × 9 = 5.5314

[As the multiplicand 0.6146 has four decimal places so the product 5.5314 also have four decimal places.]

c)  6146 × 9 = 55314

[As the multiplicand 6146 has no decimal places so the product 55314 also have no decimal places.]

d)  6.146 × 9 = 55.314

[As the multiplicand 6.146 has three decimal places so the product 55.314 also have three decimal places.]

e) 0.06146 × 9 = 0.55314

[As the multiplicand 0.06146 has five decimal places so the product 0.55314 also have five decimal places.]