My 7th grader needs help completing the above recipe by serving size, specifically the fields for the pancake mix. I seriously sucked at fractions while in school so turning to you fine folks for a little help.
First, you need to identify the appropriate operation. Presumably you know this; in the oil column you did something, perhaps dividing the number of servings by 2 because you saw that 2 is half of 4. So the operation there is Oil = Servings / 2.
Second, you'll need to carry out that operation, using fractions.
Now, what operation is needed for the mix? One way to see it is to look at what you multiply 4 by to get 1 2/4 (which could have been written as 1 1/2; I wonder why it wasn't?). Then you will want to multiply Servings by this number to get Oil. (By the way, you might find it helpful to fill in the bottom row first, which will help in this process.)
Another way is to see this as a proportion: Oil:Servings = 1.5:4, and solve for Oil.
I'd like to start with where the student is, so we will be using their knowledge, and a method that they have learned (well, at least one that they have been taught).
So please tell us what topic is being taught here. Is it part of a unit on proportions, or just on fractions, or introductory algebra, or something else? Are there any similar examples that have been given, that show a method?
Once we see what tools are available, we can try to help you (both) use them.
If the student can tell us directly what help is needed, and show some work, that will be even better.
I too am unsure why they wrote 1 2/4 instead of 1 1/2.
Now you know that 4 servings need 1 1/2 pancake mix.
If you multiple any of those two numbers by something then you must multiply the other number by the same number. For example, if we multiplied the 4 by 3, then we must multiply the 1 1/2 by 3 as well. This results in 12 servings needing 4 1/2 pancake mix.
Now when it comes to 5 servings you need to figure out what to multiply 4 by to get 5 (4 because that is the only number of servings which we know the amount of mix for). I like to do this in two steps. First, what do you multiply 4 by to get 1 and then what do you multiply 1 by to get 5. Both of these answers should be easy for your son. 4*(1/4)*(5) =5. So we multiply 4 by(1/4)*5=5/4 to get 5. Now multiply 1 1/2 by 5/4.
For 5.5 servings: Again we know 4 servings need 1 1/2 mix.
Now 4 (1/4)*5.5 = 5.5. That is 4*(5.5/4)= 5.5. So we multiply the 4 and the 1 1/2 by 5.5/4 or 11/8 to find the amount of mix we need.
Do the same for the rest of them.
Do you see why it might be easier to do the last one, first (as already pointed out)?
Hi socampo. That assignment looks like a review of several grade-school topics.
Rules for multiplying and dividing fractions and/or mixed numbers
Converting mixed numbers to/from rational and decimal form
Converting mixed numbers to improper-fraction form (or vice versa)
The concept of proportions (setting them up and solving for the unknown part)
If the mixed number 1+2/4 was given by the assignment, then it could be intended to review the notion of reducing fractions to lowest terms before doing the arithmetic.