Math 308B
The Meaning of Fractions

Some questions modified from Mathematics for Elementary Teachers, by Sybilla Beckmann

Let a and b represent whole numbers, with b 0. Then the fraction

The names make sense, because numerator comes from the Latin numeratus meaning “to number.” A numerator is literally “a numberer.” In arithmetic, the numerator tells us the number of equal parts being considered, where each part is an equal fraction of the whole. Denominator comes from the Latin words de (a demonstrative prefix) and nomen (name). The denominator names the kind of thing that we are dealing with, or what type of parts are being used. These parts can be halves, thirds, fourths, fifths, and so on. So, a fraction tells you how many of what type of equal parts.

Practice thinking about the meaning of fractions:

  1. If one serving of juice gives you of your daily value of vitamin C, how much of your daily value of vitamin C will you get in a of a serving of juice? Draw a picture to solve and explain this problem.
  1. Teresa was supposed to use of a cup of butter in her recipe but she only used of a cup of butter. What fraction of the butter that she should have used did Susan actually use? Draw a picture to solve and explain this problem.
  1. A container is filled with of a cup of cottage cheese. What fraction of the cottage cheese in the container should you eat if you want to eat 1 cup of cottage cheese? Draw a picture to solve and explain this problem.
  1. Jenny has a large piece of fabric which she has cut into two pieces: a larger piece and a smaller piece. By laying the pieces of fabric next to each other, Jenny can tell that the larger piece of fabric is the same size as of the smaller piece. What fraction of the original whole piece of fabric (before cutting) is the larger piece of fabric? Draw a picture to help you solve the problem and explain your answer.
  1. Brodrick inherited of his father’s land. Brodrick’s son, Rick, will bet of Brodrick’s land. What fraction of Brodrick’s father’s land will Rick get? Draw a picture to help solve this problem and explain your answer.
  1. Nan owns of the land her father had owned. Nan wants to give her son a piece of her land that is the same size as of the land owned by her father. What fraction of Nan’s land should Nan give her son? Draw a picture to help solve this problem and explain your answer.

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