Welcome to decimal division! Decimal division is a fundamental mathematical operation that extends whole number division to include decimal numbers. Let's start with a simple example: twelve point six divided by three equals four point two. In this division, twelve point six is the dividend, three is the divisor, and four point two is the quotient.
Now let's use the traditional long division method to solve twelve point six divided by three. First, we set up the division house with three as the divisor and twelve point six as the dividend. We start by dividing twelve by three, which gives us four. We write four above the one and two. Next, we multiply four by three to get twelve, and subtract this from twelve to get zero. Then we bring down the six and divide six by three to get two. We write the decimal point in our quotient and then the two. The final answer is four point two.
Another method for decimal division is converting decimals to fractions. Let's solve twelve point six divided by three using this approach. Step one: Convert twelve point six to a fraction. Twelve point six equals one hundred twenty-six over ten. Step two: Set up the division as multiplication by the reciprocal. One hundred twenty-six over ten divided by three equals one hundred twenty-six over ten times one over three. Step three: Multiply the fractions to get one hundred twenty-six over thirty. Step four: Simplify the fraction. One hundred twenty-six over thirty equals forty-two over ten, which equals four point two.
When dividing by a decimal number, we need to move the decimal point to make the divisor a whole number. Let's solve eight point four divided by two point one. Step one: Move the decimal point one place to the right in both numbers. Two point one becomes twenty-one, and eight point four becomes eighty-four. Step two: Now we can perform the division. Eighty-four divided by twenty-one equals four. The answer is four.