Solutions for Session 8, Part A

See solutions for Problems: A1 | A2 | A3 | A4 | A5

 Problem A1 This works because the fractions 3/4 and 1/2 represent part-part relationships, and we are finding the ratio of the combined group (or "mixture"). In part-whole problems, adding fractions represents adding new parts to the same whole (more pieces of pie, for example); therefore, the denominator (the whole) stays the same. In part-part problems, adding these ratios (expressed as fractions) changes the whole --- Elizabeth has more of each type of balloon now, both the numerator and the denominator, so you would add each part. Here's a similar example from baseball: In one game, a batter gets two hits in three at-bats. In a second game, he gets one hit in four at-bats. In total, he gets three hits in seven at-bats. 2/3 + 1/4 = 3/7

 Problem A2 If the shaded part represents 5, the unit is one circle. If the shaded part represents 2 1/2, the unit is two circles. If the shaded part represents 5/8, the unit is all eight circles. If the shaded part represents 1 1/4, the unit is four circles. Other units are also possible.

 Problem A3 Probably the easiest way to solve this problem is to find a common denominator so you can find the difference between the two named fractions. The lowest common denominator is 12: 3/4 - 1/3 = 9/12 - 4/12 = 5/12. There are five spaces between 1/3 and 3/4, so each space must represent 1/12. Then A is 4/12 (or 1/3), B is 5/12, C is 6/12 (or 1/2), D is 7/12, E is 8/12 (or 2/3), and F is 9/12 (or 3/4). Therefore, E is 2/3.

Problem A4

 a. The unit would be three small rectangles, or 3/4 of one large rectangle. b. Four small rectangles would represent 1 1/3 units in this situation. c. The shaded part could represent 2 3/4 if one large rectangle is the unit. It could represent 11 if one small rectangle is the unit. It could represent 11/12 if all three large rectangles is the unit. Other units are also possible.

 Problem A5 Jake can eat only 1/4 of a pound. Since three slices weigh 1/3 of a pound, the "unit" (one pound) is equivalent to nine turkey slices. Jake can eat 1/4 of that "unit," so he can eat 9/4, or 2 1/4, turkey slices. Notice there are many other ways to do this problem. The given solution, however, uses the concept of a "unit" and is probably the most concise.