i need help with this question can u please show me how to figure this out and show me how you figured out the problem. the question is 1/3 pnut butter sandwiches 1/6 cheese and 9 ham how many total?
i assume you mean how many sandwhiches total? in that case just add the fractions, if you don't have a calculator then start by finding the GCD or greatest common denominator, then add! :)
let x = total sandwitches
1/3 x + 1/6 x + 9 = x
Or 2/6x +1/6x + 9 = x
combine like terms
3/6x + 9 = x
or
1/2x +9 =x
multiply both sides by 2
so
x +18 = 2x
Now adda -x to both sides
18 = x
To solve the problem, we need to add the fractions representing the number of sandwiches for each ingredient. In this case, the fractions are 1/3 for peanut butter sandwiches and 1/6 for cheese.
To add fractions, we need to find a common denominator. In this case, the common denominator is 6, which we get by multiplying the denominators of the fractions.
So, we have:
1/3 x (2/2) + 1/6 x (1/1) + 9 = x
Now, let's simplify:
2/6 + 1/6 + 9 = x
Combining the numerators:
(2 + 1)/6 + 9 = x
3/6 + 9 = x
To add the fractions, we need to convert them to have the same denominator, which is 6. We do this by multiplying the numerator and denominator of the first fraction (2/6) by 3/3 to get 6/6.
So, we have:
6/6 + 1/6 + 9 = x
(6 + 1)/6 + 9 = x
7/6 + 9 = x
Now, we can simplify further:
7/6 + 9 = x
Multiplying both sides by 6 to eliminate the fraction:
7 + 54 = 6x
61 = 6x
Dividing both sides by 6:
61/6 = x
x = 10.17
Since the number of sandwiches should be a whole number, we can round down or up. In this case, rounding up to the nearest whole number gives us:
x = 11
So, the total number of sandwiches is 11.