9.1: Understanding Fractions With The C-Strips

When dealing with fractions, the denominator tells you how many equal parts it takes to make 1 unit. The numerator tells you how many of those equal parts are taken.

Example 1

If H (hot pink) represents 1 unit, then which C-strip represents \(\frac{3}{4}\)?

Solution

The denominator is 4; so it takes 4 equal parts to make one unit, and each of those 4 equal parts = \(\frac{1}{4}\). Find the C-strip such that a train of 4 of them is as long as one unit (H). Since a train of 4 light green C-strips (L) is the length of H (1 unit), then each light green C-strip makes up one part of a whole, and is therefore worth \(\frac{1}{4}\). You need to find which C-strip represents \(\frac{3}{4}\), so make a train of 3 light green C-strips and find the C-strip having this length. This would be the Blue (B) C-strip. Therefore, the answer is B.

For exercises 1 - 13, explain how to find the solution. Do each step using your C-strips.

a. State how many C-strips (each an equal part of the whole) make up one unit.

b. State which C-strip makes up one part of the whole.

c. State the fraction that the C-strip in part b represents.

d. State how many of the C-strips in part b you need to make into a train.

e. State which C-strip is the length of the train you made in part c, this is the answer!!!

Exercise Example

If H represents 1 unit, then which C-strip represents \(\frac{3}{4}\)?

a. 4

b. L

c. \(\frac{1}{4}\)

d. 3

e. B

Exercise 1

If H represents 1 unit, then which C-strip represents \(\frac{1}{6}\)?

a. ___

b. ___

c. ___

d. ___

e. ___

Exercise 2

If H represents 1 unit, then which C-strip represents \(\frac{5}{12}\)?

a. ___

b. ___

c. ___

d. ___

e. ___

Exercise 3

If O represents 1 unit, then which C-strip represents \(\frac{2}{5}\)?

a. ___

b. ___

c. ___

d. ___

e. ___

Exercise 4

If B represents 1 unit, then which C-strip represents \(\frac{2}{3}\)?

a. ___

b. ___

c. ___

d. ___

e. ___

Exercise 5

If D represents 1 unit, then which C-strip represents \(\frac{5}{3}\)?

a. ___

b. ___

c. ___

d. ___

e. ___

Exercise 6

If N represents 1 unit, then which C-strip represents \(\frac{3}{4}\)?

a. ___

b. ___

c. ___

d. ___

e. ___

Example 2

If N (brown) represents \(\frac{4}{5}\), then which C-strip represents 1 unit?

Solution

The denominator is 5, so it takes 5 equal parts to make up 1 whole unit, where each equal part is \(\frac{1}{5}\). Since N is only \(\frac{4}{5}\), then a train of only 4 of the 5 equal parts will be the length of N. A train of 4 red C-strips is the same length as N. So a red C-strip is one of the 5 equal parts that make up a whole. Since it takes 5 equal parts (5 reds) to make one unit, form a train of 5 reds and see which C-strip has this length. It is the orange C-strip (O). Therefore, the answer is O.

For exercises 7 - 11, explain how to find the solution. Do each step using your C-strips.

a. State how many C-strips will make up the named C-strip stated in the problem. Look at the numerator.

b. Which C-strip makes up one equal part?

c. State the fraction that the C-strip in part b represents. Look at the denominator.

d. State how many of the C-strips in part b will make up one unit.

e. Form the unit by making a train from the equal parts (C-strip in part b) and state which C-strip has the same length as that train.

Exercise Example

If N represents \(\frac{4}{5}\), then which C-strip is 1 unit?

a. 4

b. R

c. 1/5

d. 5

e. O

Exercise 7

If D represents \(\frac{1}{2}\), then which C-strip is 1 unit?

a. ___

b. ___

c. ___

d. ___

e. ___

Exercise 8

If L represents \(\frac{1}{3}\), then which C-strip is 1 unit?

a. ___

b. ___

c. ___

d. ___

e. ___

Exercise 9

If P represents \(\frac{2}{3}\), then which C-strip is 1 unit?

a. ___

b. ___

c. ___

d. ___

e. ___

Exercise 10

If N represents \(\frac{4}{5}\), then which C-strip is 1 unit?

a. ___

b. ___

c. ___

d. ___

e. ___

Exercise 11

If R represents \(\frac{2}{5}\), then which C-strip is 1 unit?

a. ___

b. ___

c. ___

d. ___

e. ___

The type of problems on this page are a little more challenging. They take more steps. From the first piece of information, figure out which C-strip is the whole unit – just like you did in problems 7 - 11. Then, start over using that unit C-rod, and figure out the second part of the question – just like you did in problems 1 - 16.

Example 3

If N represents \(\frac{2}{3}\), then which C-strip represents \(\frac{3}{4}\)?

Solution

Begin these the same way the previous problems were done by first figuring out what the unit C-strip is. After doing the same steps you did for exercises 14-18, you will conclude that H is the unit C-strip. Now, on to part 2: Start over with H as the unit C-strip, and find \(\frac{3}{4}\) the same way you did it for the first 13 exercises. The key is to start over by looking only at the stated unit C- strip (H in this case), and not getting that confused with the first part of the problem. In other words, now that you have determined that the unit is H, determine what is 3/4 (in relation to the unit - H). You will find that the answer is B.

For exercises 12-14, discuss how to find the solution. Do each step using your C-strips.

a. State which C-strip is one unit.

b. State which C-strip is the answer.

Example 3

If N represents \(\frac{2}{3}\), then which C-strip represents \(\frac{3}{4}\)?

a. H

b. B

Exercise 12

If P represents \(\frac{2}{3}\), then which C-strip represents \(\frac{3}{2}\)?

a. _____

b. _____

Exercise 13

If O represents \(\frac{5}{6}\), then which C-strip represents \(\frac{3}{4}\)?

a. _____

b. _____

Exercise 14

If D represents \(\frac{2}{3}\), then which C-strip represents \(\frac{1}{3}\)?

a. _____

b. _____