# Multiplication and division of decimal numbers

## Multiplication of decimal numbers

To multiply decimal numbers just multiply the numbers as if they were whole numbers, placing the comma so that the result has as many decimal digits as the sum of decimals of both numbers.

Note that the quantity of decimal digits is $$5+2=7$$

This would be the way to multiply on paper, however, to create and solve items we suggested the following table format:

 3 3, 4 2 6 1 2 x 2, 6 9 3 0 0 8 3 5 0 8 2 0 0 5 5 6 7 2 6 8 5 2 2 4 = 8 9, 9 1 6 2 6 2 8

## Division of decimal numbers

There are three possible cases when dividing with decimal numbers:

1) The denominator is decimal:

Calculate the following division: $$\dfrac{189}{2,34}=\dfrac{189}{\Big(\dfrac{234}{100}\Big)}=\dfrac{189}{234}\cdot(100)$$

We compute the integer division first $$\Big(\dfrac{189}{234}\Big)$$ and then we multiply by $$100$$ (moving the comma two positions to the right) $$\dfrac{189}{2,34}=0,80769\cdot100=80,769$$$Generally, if we divide by a number with one fractional digit, it will be necessary to multiply the integer division by 10, if we divide by a number with three fractional digits it will be necessary to multiply by $$1000,\ldots$$ 2) The numerator is decimal: Calculate the division: $$\dfrac{1,89}{234}=\Big(\dfrac{189}{234}\Big)\cdot\dfrac{1}{100}$$ Now, the integer division is calculated within the brackets and then it is divided by $$100$$, because the numerator has $$2$$ fractional digits. That is, the comma is moved two positions to the left $$\dfrac{1,89}{234}=0,80769 \cdot \dfrac{1}{100}=0,0080769$$$

3) The numerator and the denominator are decimals.

Calculate the division $$\dfrac{12,33}{1,5469}$$

The commas are omitted in the calculation, and we add to the number with less fractional digits as many zeros as there are in the difference between the number of fractional digits in the numerator and in the denominator. That is, if the numerator has $$2$$ fractional digits and the denominator has $$4$$, two zeros are added to the numerator: $$\dfrac{12,33}{1,5469}=\dfrac{1233\fbox{00}}{15469}=7,97$$\$