Dividing With Decimals (1970)

[Music] Once there was a yellow-bellied for flusher who spent his summers in Ireland. It's a final land island. But he migrated each autumn and wintered in the south of France. Oh. Yeah. One September before Flusher made his usual preparations for migration. He packed his bag, blasted weight allowances, checked his umbrella, and consulted his map. The forefr like to migrate in a leisurely way. He divided each day's journey into three equal distances. That way he could have a bit of a fly before lunch, a bit before afternoon tea, and a bit before dinner. The for flusher knew how to divide whole numbers. He also knew how to divide with fractions. What number divided by three will equal 27? What number multiplied by 1 gives four? So his journey completely planned. The four flushers set out. But over the English Channel, he ran into a bad storm, botheration. And though he reached shelter, he lost his luggage, his umbrella, and worst of all, his map. No matter, he went to the nearest gas station and got another map. Oh, mercy, Missure. But the bird saw with horror that on this map all the distances were given in decimals, and the four flusher didn't know how to divide with decimals. Oh, horrors. Is my journey to be disrupted? The four flusher's first thought was that perhaps he could find the right distances by estimating. For example, the next stop was 15.6 km away. If it were only 15 km away, dividing the trip into three parts would make each part 5 km long. If it were 18 km away, each part of the trip would be 6 km long. Since on the map 15.6 is somewhere between 15 and 18. 15.6 / 3 must be somewhere between five and six. But where? Now, the forefer did know how to add numbers expressed as decimals and how to subtract them and how to multiply them. To multiply decimals, we think of them as whole numbers, compute their product, and then place the decimal point. Let's try the same method in division. 156 / 3 is 52. Since by estimating we know the answer to the four flushes problem must be between 5 and 6, where should we put the decimal point? 5.2 or 5 and 2/10. Let's check our answer by multiplying. It checks. Let's try some others. It looks as though when a number expressed as a decimal is divided by a whole number, we can divide as if we were working with whole numbers and then place the decimal point in the quotient right over the decimal point in the dividend. What would the quotient be here? Let's check our answer by multiplying. So the forefrusser was able to compute how far he should fly before lunch. But when he tried to take off, he discovered he had hurt himself in the storm. I am afraid, Missure, that you have pulled a muzzle in the wing. But I must get on. I would recommend no more than 9.8 kilometers a day until you are fully recovered. The forer still had 147 km to go. If he could only go 9.8 8 km a day. How many days would it take him? Unfortunately, the forefr still hadn't figured out a way of dividing with a decimal. Is there any way of changing this problem into one which requires us to divide by a whole number? Let us see a simple division problem. 12 / 3 is 4. Now let us see what happens when we multiply both 12 and 3 by the same number 2. Well 12 * 2 is 24 and 3 * 2 is 6. What is 24 / 6? 24 / 6 is 4. Same answer as 12 / 3. Oo, we see that if we multiply both of our original numbers 12 and three by the same number two, we get the very same quotient four. By what number could we multiply both divisor and dividend in this number sentence so as to change 9.8 to a whole number? 10. Correct. Now we can divide the whole numbers. So the for flusher resumed his trip knowing it would take him 15 days to reach his destination. But suppose that instead of 147 km, his destination was 159.74 km away. Then the fore flusher would have to divide a number expressed as a decimal by another number expressed as a decimal. Could you discover how to do that? [Music]