Two divided by 0.4 equals what?
In this question, we’re being asked to divide a whole number, or an integer, by a number that’s less than one whole, a decimal. What strategy can we use to find out the number of four-tenths, or 0.4s, that there are in two? To help us understand what the question’s asking, we can write out the division like a fraction.
Remember, we can use fractions to show division. Two divided by 0.4. We won’t try reading that as a fraction, we’re just going to say it as a division. Two divided by 0.4. Now we can use our knowledge of how fractions work to try and convert this decimal 0.4 into an integer.
What if we multiply it by 10? Then, the four digit will move one place to the left, and we will get the answer four ones, or four. To keep the answer to the division the same, we need to do the same to the top number. Two multiplied by ten gives us 20. Now we could read this as a fraction, 20 fourths. But let’s keep thinking of it as a division.
It shows 20 divided by four. And we know that 20 divided by four equals five. We were given a calculation that we weren’t sure how to answer because we had to divide an integer by a decimal. By writing the division out as a fraction and then multiplying the numerator and the denominator by ten is exactly the same as doing this, multiplying the first number in the division by ten and then multiplying the second number in the division by ten.
Because both numbers were multiplied by the same amount, we knew the answer would stay the same. And we wanted to multiply by ten to change 0.4 into a whole number. Two divided by 0.4 is the same as 20 divided by four. And the answer is five.