5th grade foundations (Eureka Math/EngageNY)
- Multiplying fractions and whole numbers visually
- Multiply fractions and whole numbers
- Compare with multiplication
- Compare with multiplication word problems
- Multiplication word problem: carrots
- Division word problem: row boat
- Multiplication and division word problems
- Multi-step unit conversion examples (U.S. Customary)
- US customary conversion word problems
Multiplication word problem: carrots
Created by Sal Khan.
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- At2:10Isn't it Same as finding Area ?
What if we had 1 carrot in 1st row 2 carrots in 2nd ................ n carrots in nth row Then what is Total number of carrots ? is there a General Formula ?(30 votes)
- The problem you described is this.. how much is 1 + 2 + 3 + 4 + 5 + ... + n and there is a formula that gives you the answer n*(n+1) / 2. The reason this is true is because you can always couple the smallest and largest numbers and get some constant (the constant is always n+1).. an example:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8
1 + 8 = 9
2 + 7 = 9
3 + 6 = 9
4 + 5 = 9
So because you couple numbers you get n/2 pairs so to add all of them up we just have to multiply n/2 * constant = n/2 * (n+1) = n*(n+1)/2. I used an example where n is even, but it also works with odd n.(48 votes)
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Toby is a farmer. He plants 12 rows of carrots in a field. Each row has 6 carrots. How many carrots did Toby plant? So let's try to visualize this thing. So they tell us each row has 6 carrots. So let's try to visualize a row. So that's 1 carrot, that's 2 carrots, that's 3 carrots, that's 4 carrots, that's 5 carrots, and that's 6 carrots. And I can even do, just so it looks nice, the little leafy part of the carrots. So we can visualize these as carrots. So that's 1 row of carrots. They tell us each row has 6 carrots. Now, there're 12 of these. He plants 12 rows of carrots. Let me see if I can copy and paste this. So copy and paste. So that's 2 rows. I want to make sure I have enough space. 2 rows. That's 3 rows. That's 4 rows. This is 5 rows. This is 6 rows. And actually, I can just copy and paste the whole thing. This is 6 rows. I just need to double that to get to 12 rows. So let me do that. So copy and paste. There you go. So there's 12 rows right over here. And let's number this. So they tell us each row has 6 carrots-- 1, 2, 3, 4, 5, 6. They tell us he plants a total of 12 rows-- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. How many carrots did Toby plant? Well, you could do this exercise and then try to count all of these carrots. But that seems a little bit crazy. These are already a lot of carrots. And especially if these were even larger numbers, it would take you forever to count it. Luckily for us, we have multiplication as a tool that we can use. So if you have 12 rows and each of those rows have 6, this is really 12 times 6. You're going to have 12 rows. In each of those, you have 6 carrots. So you could say you have 6 carrots 12 times. So it's going to be 12 times 6. If you remember your multiplication tables up to 12, you'll remember that 12 times 6 is 72. So he has 72 carrots. Even if you only remember-- well, I'll just leave it there. If you remember your multiplication-- which you should, because that is one of the things in life that will have long-lasting benefits-- it's 72 carrots.