Comparing Fractions: Reasoning with Pieces

What benchmarks were initially used for comparing fractions?

• 0 and 1

• 1 and 1/2

• 1/3 and 2/3

• 1/4 and 3/4

In the example, which fraction has more pieces, 10/13 or 9/14?

• Cannot be determined

• Both have the same

• 10/13

• 9/14

Which fraction has larger pieces, 10/13 or 9/14?

• Information not provided

• Both are the same

• 9/14

• 10/13

Which fraction is larger based on the number and size of pieces, 10/13 or 9/14?

• Cannot be determined

• Both are equal

• 9/14

• 10/13

In the comparison of 8/13 and 9/14, which fraction has more pieces?

• 8/13

• Cannot be determined

• Both have the same

• 9/14

Which fraction has bigger pieces, 8/13 or 9/14?

• Information not provided

• Both are the same

• 9/14

• 8/13

Why can't a conclusion be made about which fraction is bigger between 8/13 and 9/14 using the previous method?

• One has more but smaller pieces

• Both are exactly the same

• Insufficient data

• Both fractions are whole numbers

What common feature do the fractions 8/13 and 9/14 share?

• Both are less than 1

• Both are more than 1/2

• Both are 5 pieces away from being whole

• Both have the same denominator

Which fraction is closer to being a whole number, 8/13 or 9/14?

• 8/13

• Cannot be determined

• 9/14

• Both are equally close

When might it be necessary to use formal methods like common denominators to compare fractions?

• All the time

• When fractions are easy to compare

• When fractions are very different

• When fractions are very close