Beth needs 1 2/3 cups of sugar to make a cake and 2 1/4 cups to make a pie. how much sugar does she need to make both?

you are adding 1 2/3 + 2 1/4
 first these are mixed fractions lets change them to regular fractions for 1 2/3 take the whole number and multiply by the denominator 3 and add the numerator, then that number over denominator 3 so
 (1 x 3) +2 = 5/3 do that with 2 1/4
  what did you get?

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)