Hi Holly, how did you work through the problem? Are you drawing circles and making divisions? Using numbers only (what was your equation)? How did you check your answer of 2 and 1/2 servings?
Everyone learns differently. Sometimes it makes sense to picture what's left-over. Let's try it more visually (as best we can with only typed words).
I drew 3 circles and divided into 6 sections, like a pie. If each serving is 5/6 of a cake, that means there is a little sliver of 1/6 of a cake left over from each cake. So if you have three cakes, you know you have 3 servings of 5/6 of a cake. You also have 3 slivers of 1/6 of a cake leftover, or a total of 3/6 (or 1/2) of a cake. What's left (1/2) of the cakes, is not a full serving, since a full serving is 5/6 of a cake.
[So now you have to figure out what portion of a 5/6 serving is 1/2 of a cake.]
You can keep with our picturing method: If you have 3 slivers of cake left, and you know that it takes 5 slivers of cake to make a serving, then you only have 3 out of 5 (3/5) needed to make a serving.
Or, we can take our words (above, in [brackets]) and make them into math symbols to help us set up an equation, where "what portion" is our variable (we can use "z"), "of" is multiplication (x), and "is" is equals (=).
So 5/6 x z = 1/2.
Or 5z/6 = 1/2.
Cross multiply: 10z = 6.
Divide to isolate our variable: z = 6/10.
Simplify: z = 3/5.
Final answer: If Marc makes a serving of cake to be 5/6 of the cake, then Marc can have 3 and 3/5 servings of cake if he makes 3 cakes.
(I hope Marc is making very small cakes... ha!)
