# Decimal multiplication & division lesson

## Decimal numbers multiplication

Multiplication of decimals is similar to the whole number multiplication.

Ignore the decimal points and multiply the two given numbers.

Number of digits after decimal point (number of decimal places) in the product is same as the count of number of decimal places in the multiplier and multiplicand.

Place a decimal point in the product counting from the ones, so that the product has the same number of decimal places as the sum of the number of decimals in the multiplier and multiplicand.

### Example: Multiply the following numbers: 42.74 and 5.4

1. First arange numbers vertically.

2. Multiply the multiplicant by 4 and place the result.

3. Multiply the multiplicant by 5 and place the result.

4. Multiplicant has 2 decimal places and multiplier has 1. Total decimal places = 3.

5. In the result, put the decimal point after the 3rd digit from the right.

## Decimal numbers division

Division of decimals is similar to the whole number division.

Decimal point required to be placed in the quotient if tenths place of the dividend is considered in the division steps.

### Example: Divide 8.23 by 4

1. Divide 8 (number from the ones place) by 4 (divisor). There are 2 4s in 8. So, place 2 in the quotient.

2. Subtract 8 (2 * 4) from the 8 (one place of dividend). Result 0.

3. No more numbers in the whole number part. So, start dividing the decimal portion. Place a decimal point in the quotient.

4. Divide 2 (tenth place of dividend) by 4 (divisor). 2 can't be divided by 4. So, place zero in quotient .

5. Combine the number from hundredth place with the number from the tenth place. Number to be divided now is 23.

6. Divide 23 by 4. 23 has five fours. Place 5 in quotient. Subtract 20 (4 * 5) from the number 23.

7. Remainder = 3. Quotient = 2.05

## Easy way to divide decimals.

Easy way to divide decimal numbers are by removing decimal points.

Decimal points can be removed by adding trailing zeros (or multiplying by powers of ten) and ignoring decimal points.

The number of zeros (0) to be added is same as the maximum number of decimal place among the both numbers (or multiply by 10 power the maximum number of decimal place).

Once decimal points are removed the numbers can be divided similar to the whole number division.

## Dividing upto required numbers of decimals.

Number of digits in decimal places (after decimal point) can vary depending on the numbers (dividend & divisor )

Some times quotient will have infinite numbers of decimals.

Ex: dividing 8 by 7 results in infinite number of decimal places. Result = 1.14285714...

So, In decimal it is required stop dividing after reaching required number of decimal places.

### Example: Divide 8 by 7 up to 3 decimal places.

1. Divide 8 by 7 . There is one 7 in 8. So, place 1 in the quotient.

2. Subtract 7 from the 8. Remainder = 1.

3. Add 0 (zero) to the remainder from the previous step. New number to be divided = 10.

4. Divide 10 by 7. Place decimal point and 1 in the quotient. New remainder = 3, add zero to it.

5. Divide 30 by 7. Place 4 in the quotient. New remainder = 2, add zero to it.

6. Divide 20 by 7. Place 2 in the quotient. New remainder = 6