Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Learning Math Home
Number and Operation Session 8: Rational Numbers and Proportional Reasoning
Session 8 Part A Part B Part C Homework
number Site Map
Session 8 Materials:

A B C 


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

<< back to Problem A1


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.

<< back to Problem A2


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.

<< back to Problem A3


Problem A4


The unit would be three small rectangles, or 3/4 of one large rectangle.


Four small rectangles would represent 1 1/3 units in this situation.


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.

<< back to Problem A4


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.

<< back to Problem A5


Learning Math Home | Number Home | Glossary | Map | ©

Session 8 | Notes | Solutions | Video

Home | Catalog | About Us | Search | Contact Us | Site Map

  • Follow The Annenberg Learner on Facebook

© Annenberg Foundation 2013. All rights reserved. Privacy Policy