Processing math: 100%
Fraction comparison practice
Click on the links to show or hide the hints
Which of these pairs can be compared directly (without using by considering residual amounts) by arguing from the
number and size of pieces? (Same numerator, Same denominator and similar arguments)
38 and 37
Yes. These can be compared because eighths are smaller than sevenths, so
38 has 3 small parts and 37 has the same number of larger parts, so 37 is larger.
512 and 23
No. Twelfths are smaller than thirds, but 512 has more small parts, and 23 has fewer larger parts.
That's not enough information to know which is bigger.
415 and 615
Yes. Both fractions are made of fifteenth pieces. 415 has only 4 pieces, and 615
has more of the same sized pieces, so 615 is larger.
38 and 215
Yes. Eighths are larger than fifteenths. There are more larger pieces (3) in 38, and fewer (only 2) smaller
pieces in 215. More larger pieces is bigger, so 38 is larger.
34 and 56
No, Fourths are bigger than sixths, but there are more sixths in 56 and fewer fourths in
34. We're comparing more small pieces to fewer large pieces, and that's not enough information to compare.
Which of these pairs of fractions can be compared using the residual strategy?
34 and 56
Yes, 34 is 14 less than 1. 56 is 16 less than 1.
We can compare and say 14 is greater than 16.
That means that 34 is farther from 1 than 56, so it's smaller than 56.
78 and 1921
No. 78 is 18 less than 1 and 1921 is 221 less than 1
We know 18 is bigger than 121, but there is only one eighth (fewer) and there are two
twenty-firsts, which is more small pieces, so we don't know which is bigger: 18 or 121.
That means we can't use this reasoning to figure out which fraction is bigger.
78 and 1012
No, for the same reason as the previous example.
78 is 18 less than 1 and 1012 is 212 less than 1
We know 18 is bigger than 112, but there is only one eighth (fewer) and there are two
twenty-firsts, which is more small pieces, so we don't know which is bigger: 18 or 112.
That means we can't use this reasoning to figure out which fraction is bigger.
79 and 1012
Yes, 79 is 29 less than 1. 1012 is 212 less than 1.
We know ninths are bigger than twelfths, so since there are the same number of parts, we
can and say 29 is greater than 212.
That means that 79 is farther from 1 than 1012, so it's smaller than 1012.
Find the error or omission in each of these explanations
A.
23 is bigger than 34 because thirds are larger than fourths.
Thirds are larger than fourths, but there are more fourths and fewer thirds, so we don't have enough information to
compare the fractions this way.
B.
35 is bigger than 38 because fifths are bigger than eighths.
Fifths are bigger than eighths, but you also need to check (and explain) that there are the same number
(or more) of the large pieces as compared to the small pieces to know that the total fraction is bigger.
C.
78 is bigger than 1012 because 78 is fewer parts away from the whole.
78 is only one part away from the whole, and 1012 is two parts away from the whole,
but those parts aren't the same size, If we can't be sure which is bigger 78 or 212, then
we can't use the distance from the whole to explain which fraction is bigger
D.
78 is bigger than 34 because it has more parts.
OR
68 is bigger than 34 because it has more parts.
OR
58 is bigger than 34 because it has more parts.
This explanation's biggest problem is that it's vague.
It might be saying that 7>3 (or 6>3 or 5>3)so we have more parts taken in the first fraction than the second. If that's what it's saying, then there's a problem
because it's not explaining what happens with the size of the parts. In fact, this start isn't going to help
much with these fractions because the fraction with more parts also has smaller parts, so that doesn't give
us enough information to compare the two.
Alternately, it might be saying that the first fraction is bigger because 8>4. That's probably a bigger
misconception because eighths are smaller than fourths, so knowing that 8>4 isn't a reason to thing the first fraction
is larger.
E.
78 is smaller than 34 because it has more parts in the whole.
OR
68 is smaller than 34 because it has more parts in the whole.
OR
58 is smaller than 34 because it has more parts in the whole.
This is another vague explanation
It seems to be saying that it takes more eighths to make a whole than fourths, so eighths are smaller. It doesn't
include an explanation of the total amount because it doesn't use the information about how many parts are taken.
F.
78 is bigger than 34 because it's closer to a whole.
This explanation is incomplete because it doesn't tell how we know that 78 is closer to a whole than 34.
G.
78 is bigger than 34 because 7 is a bigger part of 8 than 3 is of 4.
This seems to be an explanation, but if you look closer, all this says is that 78 is bigger because it's bigger.
H.
25 is smaller than 58 because 25 is smaller than 12
and 58 is larger than 12 .
This explanation is missing an explanation of how you know that 25 is smaller than 12
and 58 is larger than 12
I.
28 is smaller than 38 because 2 is less than 3
This explanation is missing the detail that both of the fractions are eighths, so the pieces are the same size for both fractions.