This chapter explores multiplying decimals and whole numbers. No prior knowledge is required for this chapter.
Multiplying
Suppose we wanted to multiply 6 x 0.8, that is;
The problem here is it may be difficult to multiply a decimal with a whole number since 0.8 is too small. It may be a good idea to make it large first by turning it into a whole number, to do that we multiply it by 10.
…0.8 x 10 is 8. Now it will be easier to multiply with the other whole number.
…6×8 is equal to 48 as shown below but that won’t be it, because we increased the decimal number. Since we multiplied by 10 we must undo the operation in the final answer.
The opposite of x10 is ÷10.
Remember we multiplied by 10 to get rid of the decimal and then divide by 10 at the end to reverse the multiplication operation to return to decimal.
Another example
Here is another example;
Above we’re trying to multiply by 0.03. Again the multiplication of a while number with a decimal may be difficult. So we simplify the problem by turning 0.03 into a whole number. We do that by multiplying it by 100 as shown below.
…100 multiplied by 0.03 is 3. Now we can multiply 7 by 3.
Since we multiplied by 100 along the way we must undo this operation. The opposite of x100 is ÷100.
You must remember that we multiplied by 100 to get rid of the decimal and then divided by 100 at the end to undo the multiplication operation.
Another example
Here is another example. Suppose we wanted to multiply 9×8.4 that is;
Just like in the previous examples it may be difficult to multiply the decimal number with a while number, so we turn 8.4 into whole number we do that by multiplying it with 10 as shown below.
We multiplied 8.4 with 10 to get 84. Now we can multiply 9 by 84…
Remember we must undo the multiplication operation. The opposite of x10 is ÷10. So we divide the answer by 10.
Remember we multiplied by 10 to get rid of the decimal and then divided by 10 at the end to undo the operation to return to decimal.