The title says 8 divided by 1 and 1/3, but the body underneath asks for 8 divided by 1 and 1//4. I'll just do both :)
First, instead of 1 and 1/3, let's make that all one fraction, so it's easier to look at. There are 3/3 in 1, so 1 and 1/3 is essentially 3/3 and 1/3, or 3/3 +1/3. In addition, we only add the numerators, not the denominators, because we're counting the parts. The answer is 4/3, so we can write 1 and 1/3 as 4/3.
Also, let's make 8 a fraction, too, so we're working with two fractions instead of one fraction and a whole number. Any number over 1 is that same number, so 8 is just 8/1.
So, 8/1 ÷ 4/3
The rule for dividing fractions is you take the second fraction (4/3 in this case) and flip it upside down and multiply it.
8/1 X 3/4
So we multiply our numerators, 8 and 3, to get 24. Multiplying our denomiators, 1 and 4, we get 4. We can write this as:
24/4
Now, we can reduce this fraction. What is the largest number that goes into both 24 and 4? Well, the only numbers that go into 4 are 1, 2, and 4. The biggest number is 4, so we try that one first. If it goes into 24 evenly, then we're all done- and it does! 24÷4=6
So your answer is: 6
We're going to turn both numbers into fractions again. Anything over 1 is itself, so 8 can be rewritten as 8/1.
For 1 and 1/4, we're basically saying 1+1/4. Any number over itself is 1, so 1=4/4. Substitute that in so that it reads 4/4+1/4, and we get 5/4. With these new fractions, rewrite your equation:
8/1 ÷ 5/4
Now remember the rule! Dividing by a fraction means multiplying by its inverse, or its upside down version.
8/1 X 4/5
Multiplying our numerators, 8 and 4, we get 32. Multiplying our denominators, 1 and 5, we get 5. So let's rewrite that fraction before we try to reduce it.
32/5
We're looking for the greatest number that can go into both 32 and 5. The only numbers that go into 5 are 1 and 5. Now, dividing by 1 does nothing to our fraction, so that won't reduce it. And 5 doesn't go into 32 evenly! This means we can do one of two things: 1. Make it a mixed number OR 2. Make it a decimal.
METHOD 1: Mixed number
If you go through your 5s times table, you get 5x6=30 and 5x7=35. 32 falls right in between those two numbers. To make sure we have stuff left over, we use the smaller number, which is 5x6. Therefore, 32/5=6. But, 5x6 is only 30. 32 is 2 bigger than 30. So we have a remainder of 2. That makes our answer 6 R2. If we put 2 over our denominator, we have our remainder written as a fraction. So our answer becomes:
ANSWER #1: 6 and 2/5
METHOD 2: Decimal
Start with the fraction we just finished: 6 and 2/5. We can leave the 6 alone for a bit and just work with our fraction to make it a decimal. A decimal is simply a number over 100. So, set the fraction 2/5 equal to something over 100.
2/5 = n/100
Now, focus on the denominators, because we know what those are. In order to get from 5 to 100, you have to multiply by 20, because 100/5 =20. So if you had to multiply by 20 to get the bottom numbers, why not do the exact same thing on the top?
n=2x20=40
So our fraction is 40/100, or, in decimal form, .40. Because there is a 0 as the last number in our decimal and nothing behind it, we can drop it, because .40 and .4 are the same thing. Now, tack .4 onto 6 (which we got from our original fraction of 6 and 2/5).
ANSWER #2: 6.4
The title says 8 divided by 1 and 1/3, but the body underneath asks for 8 divided by 1 and 1//4. I'll just do both :)
First, instead of 1 and 1/3, let's make that all one fraction, so it's easier to look at. There are 3/3 in 1, so 1 and 1/3 is essentially 3/3 and 1/3, or 3/3 +1/3. In addition, we only add the numerators, not the denominators, because we're counting the parts. The answer is 4/3, so we can write 1 and 1/3 as 4/3.
Also, let's make 8 a fraction, too, so we're working with two fractions instead of one fraction and a whole number. Any number over 1 is that same number, so 8 is just 8/1.
So, 8/1 ÷ 4/3
The rule for dividing fractions is you take the second fraction (4/3 in this case) and flip it upside down and multiply it.
8/1 X 3/4
So we multiply our numerators, 8 and 3, to get 24. Multiplying our denomiators, 1 and 4, we get 4. We can write this as:
24/4
Now, we can reduce this fraction. What is the largest number that goes into both 24 and 4? Well, the only numbers that go into 4 are 1, 2, and 4. The biggest number is 4, so we try that one first. If it goes into 24 evenly, then we're all done- and it does! 24÷4=6
So your answer is: 6
We're going to turn both numbers into fractions again. Anything over 1 is itself, so 8 can be rewritten as 8/1.
For 1 and 1/4, we're basically saying 1+1/4. Any number over itself is 1, so 1=4/4. Substitute that in so that it reads 4/4+1/4, and we get 5/4. With these new fractions, rewrite your equation:
8/1 ÷ 5/4
Now remember the rule! Dividing by a fraction means multiplying by its inverse, or its upside down version.
8/1 X 4/5
Multiplying our numerators, 8 and 4, we get 32. Multiplying our denominators, 1 and 5, we get 5. So let's rewrite that fraction before we try to reduce it.
32/5
We're looking for the greatest number that can go into both 32 and 5. The only numbers that go into 5 are 1 and 5. Now, dividing by 1 does nothing to our fraction, so that won't reduce it. And 5 doesn't go into 32 evenly! This means we can do one of two things: 1. Make it a mixed number OR 2. Make it a decimal.
METHOD 1: Mixed number
If you go through your 5s times table, you get 5x6=30 and 5x7=35. 32 falls right in between those two numbers. To make sure we have stuff left over, we use the smaller number, which is 5x6. Therefore, 32/5=6. But, 5x6 is only 30. 32 is 2 bigger than 30. So we have a remainder of 2. That makes our answer 6 R2. If we put 2 over our denominator, we have our remainder written as a fraction. So our answer becomes:
ANSWER #1: 6 and 2/5
METHOD 2: Decimal
Start with the fraction we just finished: 6 and 2/5. We can leave the 6 alone for a bit and just work with our fraction to make it a decimal. A decimal is simply a number over 100. So, set the fraction 2/5 equal to something over 100.
2/5 = n/100
Now, focus on the denominators, because we know what those are. In order to get from 5 to 100, you have to multiply by 20, because 100/5 =20. So if you had to multiply by 20 to get the bottom numbers, why not do the exact same thing on the top?
n=2x20=40
So our fraction is 40/100, or, in decimal form, .40. Because there is a 0 as the last number in our decimal and nothing behind it, we can drop it, because .40 and .4 are the same thing. Now, tack .4 onto 6 (which we got from our original fraction of 6 and 2/5).
ANSWER #2: 6.4
