Madison has taken four-fifths of her cows or 16 cows to the next field. How many cows does she have in total?
In this problem, we’re being asked to find the total number of cows that Madison has. But the only information we’re given is about part of the number of cows that she has. We’re told that she takes four-fifths of her cows or 16 cows to the next field. And we can use this clue to calculate how many cows she has in total because this phrase tells us that four-fifths of Madison’s cows is the same as 16. To understand how this can help us, we could sketch a bar model. The whole bar represents the whole herd of cows. And this is the number we’re trying to find.
Now, to show four-fifths, we first need to divide our bar into five equal parts. Each one is worth one-fifth. If we shade four out of five of these parts, we’re representing four-fifths. And four-fifths of the whole herd of cows is 16 cows. How can we use this information to calculate the number of cows that Madison has in total? Well, we know that the total amount, which is the same as the whole bar, has a value of five-fifths. So if we could find out what one of our fifths was worth, we could then use this to find out the value of five-fifths. We know that four-fifths of the cows equals 16. So if we divide 16 by four, we can find out how many cows are one-fifth of the herd.
Let’s use repeat subtraction to find out how many fours there are in 16. 16 take away one lot of four gives us 12. If we take away another lot of four, we’re left with eight. Eight takeaway four equals four. And of course, that’s one more lot of four we can subtract to take us to zero. There are four lots of four in 16. And so we can say 16 divided by four equals four.
Now, if we apply this to our bar model, we can see that one-fifth is worth four because four of them or four-fifths equals 16. If one-fifth equals four, then to find five-fifths or one whole, we need to calculate five lots of four. We know four fours are 16. So five lots of four is four more than 16; it equals 20. Five lots of four equals 20. If four-fifths of Madison’s herd of cows equals 16 cows, we can use this to find out what one-fifth is worth. One-fifth of Madison’s cows is four cows. And so we know the total number of cows that Madison has is worth five lots of four equal to five-fifths. The number of cows that she has altogether is 20.