Calculate 2.94 divided by one and a fifth.
This calculation might look a little tricky. We’re dividing a decimal by a mixed number. It’ll be a lot easier if we could do something with that mixed number to turn it into a decimal. We know that one-fifth is the same as two-tenths. So we can write one and one-fifth as one and two-tenths. And two-tenths can be written with a two in the tenths place. So we can write one and two-tenths as the decimal 1.2. Now, we can write our calculation using two decimals, 2.94 divided by 1.2. And it still looks quite tricky. It’d be much easier if these numbers were whole numbers and not decimals. If we multiply 2.94 by 100, the digits are going to shift two places to the left. Instead of 2.94, we’ll have the number 294. We’ve turned it from a decimal into a whole number.
And if we want the answer to our division to stay the same, we’re going to have to do the same to the second number. We need to multiply 1.2 by 100, too. So the digits in 1.2 are going to shift two places to the left, too. This gives us the number 120. Now, working out 294 divided by 120 is going to be a little bit easier than working out 2.94 divided by one and one-fifth. But the answer will be the same. We’re going to need to use long division to find the answer. How many 120s are there in 294? We’re dividing by a three-digit number here. So we need to consider all three digits of 294 to begin with.
How many lots of 120 will fit into 294? We know what one lot of 120 is worth, and we can double this to find the answer to two lots of 120. Two times 120 equals 240. And we can see that this is the nearest we’re going to get to 294. There are two lots of 120 in 294. But we can see that there’s a remainder. Two lots of 120 is 240. And if we subtract this from 294, we can find out what we’ve got left. If we subtract each column, we can see we have a remainder of 54. Then we could say that the answer is two remainder 54. But there’s actually a clearer way to give the answer. And that’s as a decimal. So we can keep on dividing and move now into the decimal places.
Now, we can’t divide 54 by 120 because it’s too small. What we would normally do is bring down another digit. But if we look at the way that 294 has been written, we can see there are no more digits. The only way we can find more digits is if we move as we’ve said already into the decimal places. We know that 294 is exactly the same as 294.0. But if we choose to write the number like this, we now have another digit we can bring down, a zero. And so 54 becomes 540. Because we’ve moved into the decimal places, we must also remember to put a decimal point at the top, so that our answer is going to be a decimal, too.
Now, we can continue to divide. How many 120s are there in 540? We know that two lots of 120 was 240. What if we double this again? Four lots of 120 are 480. This looks quite close to 540. What about five lots of 120? Let’s add another lot of 120 to see what the answer is. If we have the two together, we can see that five lots of 120 are 600. This is too large. There are only four lots of 120 in 540. But again, there’s a remainder to calculate. Four lots of 120 are 480. And if we subtract this from 540, we can see that we have a remainder of 60. 60 is too small to be divided by 120. So again, we’re going to need an extra digit. And we can find an extra digit by writing in the hundreds digit.
Look again at the number we’re dividing. 294.00 is still the same as 294. We’re not changing this number in any way. We’ve just chosen to show the hundreds digit. By doing this, we can bring it down. Instead of 60, we have 600. How many lots of 120 are in 600? This is a calculation we’ve already looked at. Five lots of 120 are 600. We can write the digit five in the hundreds place at the top. And this time there is no remainder. Five lots of 120 are 600. If we take 600 from 600, there’s nothing left over. And we could see our answer at the top. It’s a decimal number to two decimal places.
We were asked to divide a decimal by a mixed number. The first thing that we did was to convert that mixed number into a decimal, too. This meant that our division then included two decimals. Then by multiplying both decimals by 100, we turned them both into whole numbers. The division became 294 divided by 120. But the answer was still the same. We could then use long division to find the answer. And so the answer to 2.94 divided by one and one-fifth is 2.45.