To compare fractions, we can use a few simple tricks. Let's go through each problem step-by-step.
A. $\frac{1}{2}$ vs $\frac{2}{4}$
If you simplify $\frac{2}{4}$ by dividing the top and bottom by 2, you get $\frac{1}{2}$. Since they are exactly the same value:
$\frac{1}{2} = \frac{2}{4}$
B. $\frac{1}{2}$ vs $\frac{2}{3}$
Let's find a common denominator, which is 6.
$\frac{1}{2} = \frac{3}{6}$
$\frac{2}{3} = \frac{4}{6}$
Since 4 is bigger than 3, $\frac{2}{3}$ is larger.
$\frac{1}{2} < \frac{2}{3}$
C. $\frac{1}{5}$ vs $\frac{1}{3}$
When the top numbers (numerators) are the same, look at the bottom numbers. The fraction with the *smaller* bottom number is actually *larger* because the pieces are bigger. 3 is smaller than 5, so thirds are bigger than fifths.
$\frac{1}{5} < \frac{1}{3}$
D. $\frac{1}{2}$ vs $\frac{1}{2}$
These are identical.
$\frac{1}{2} = \frac{1}{2}$
E. $\frac{4}{5}$ vs $\frac{1}{2}$
Think about halves. Half of 5 is 2.5. Since 4 is much bigger than 2.5, $\frac{4}{5}$ is more than half.
$\frac{4}{5} > \frac{1}{2}$
F. $\frac{2}{3}$ vs $\frac{1}{2}$
Half of 3 is 1.5. Since 2 is bigger than 1.5, $\frac{2}{3}$ is more than half.
$\frac{2}{3} > \frac{1}{2}$
G. $\frac{2}{5}$ vs $\frac{1}{5}$
The bottom numbers are the same, so we just compare the top numbers. 2 is bigger than 1.
$\frac{2}{5} > \frac{1}{5}$
H. $\frac{1}{3}$ vs $\frac{1}{2}$
Again, the top numbers are the same. The fraction with the smaller bottom number (2) represents larger pieces. So, one-half is bigger than one-third.
$\frac{1}{3} < \frac{1}{2}$
I. $\frac{1}{2}$ vs $\frac{1}{2}$
These are identical.
$\frac{1}{2} = \frac{1}{2}$
J. $\frac{2}{6}$ vs $\frac{1}{2}$
Let's simplify $\frac{2}{6}$. If you divide the top and bottom by 2, it becomes $\frac{1}{3}$.
Now compare $\frac{1}{3}$ and $\frac{1}{2}$. As we saw in problem H, $\frac{1}{3}$ is smaller than $\frac{1}{2}$.
$\frac{2}{6} < \frac{1}{2}$
Final Answer:
A. $=$
B. $<$
C. $<$
D. $=$
E. $>$
F. $>$
G. $>$
H. $<$
I. $=$
J. $<$
Parent Tip: Review the logic above to help your child master the concept of comparing fractions with unlike denominators worksheet.
