To solve these problems, we need to compare the two mixed numbers in each question and decide which symbol goes in the box:
-
> (greater than) if the first number is bigger.
-
< (less than) if the first number is smaller.
-
= (equal to) if they are the same.
Here is the step-by-step comparison for each problem:
1. Compare $2\frac{2}{3}$ and $1\frac{1}{3}$
* Look at the whole numbers first: 2 and 1.
* Since 2 is greater than 1, the first number is larger.
*
Answer: $>$
2. Compare $1\frac{5}{6}$ and $1\frac{3}{8}$
* The whole numbers are both 1, so we look at the fractions: $\frac{5}{6}$ and $\frac{3}{8}$.
* To compare them, find a common denominator. The least common multiple for 6 and 8 is 24.
* $\frac{5}{6} = \frac{20}{24}$
* $\frac{3}{8} = \frac{9}{24}$
* Since 20 is greater than 9, $\frac{5}{6}$ is larger.
*
Answer: $>$
3. Compare $2\frac{3}{5}$ and $2\frac{3}{4}$
* The whole numbers are both 2. Compare the fractions: $\frac{3}{5}$ and $\frac{3}{4}$.
* When numerators are the same, the fraction with the smaller denominator is larger (because the pieces are bigger).
* Since 4 is smaller than 5, fourths are bigger than fifths. So, $\frac{3}{4} > \frac{3}{5}$.
* This means the second number is larger.
*
Answer: $<$
6. Compare $1\frac{1}{4}$ and $2\frac{1}{2}$
* Look at the whole numbers: 1 and 2.
* Since 1 is less than 2, the first number is smaller.
*
Answer: $<$
7. Compare $1\frac{7}{8}$ and $1\frac{1}{2}$
* The whole numbers are both 1. Compare the fractions: $\frac{7}{8}$ and $\frac{1}{2}$.
* Convert $\frac{1}{2}$ to eighths: $\frac{1}{2} = \frac{4}{8}$.
* Compare $\frac{7}{8}$ and $\frac{4}{8}$. Since 7 is greater than 4, the first fraction is larger.
*
Answer: $>$
8. Compare $2\frac{1}{5}$ and $1\frac{5}{8}$
* Look at the whole numbers: 2 and 1.
* Since 2 is greater than 1, the first number is larger.
*
Answer: $>$
11. Compare $1\frac{5}{6}$ and $1\frac{5}{9}$
* The whole numbers are both 1. Compare the fractions: $\frac{5}{6}$ and $\frac{5}{9}$.
* The numerators are the same (5). The fraction with the smaller denominator is larger.
* Since 6 is smaller than 9, sixths are bigger than ninths. So, $\frac{5}{6} > \frac{5}{9}$.
*
Answer: $>$
12. Compare $1\frac{1}{8}$ and $1\frac{1}{3}$
* The whole numbers are both 1. Compare the fractions: $\frac{1}{8}$ and $\frac{1}{3}$.
* The numerators are the same (1). The fraction with the smaller denominator is larger.
* Since 3 is smaller than 8, thirds are bigger than eighths. So, $\frac{1}{3} > \frac{1}{8}$.
* This means the second number is larger.
*
Answer: $<$
13. Compare $2\frac{3}{5}$ and $1\frac{1}{2}$
* Look at the whole numbers: 2 and 1.
* Since 2 is greater than 1, the first number is larger.
*
Answer: $>$
Final Answer:
1. $>$
2. $>$
3. $<$
6. $<$
7. $>$
8. $>$
11. $>$
12. $<$
13. $>$
Parent Tip: Review the logic above to help your child master the concept of comparing mixed numbers worksheet.
