To determine which of the two mixed numbers is the smallest, we first need to convert these mixed numbers into improper fractions or their decimal equivalents. Let's start with each mixed number.
1. For the first mixed number [tex]\( 3 \frac{6}{10} \)[/tex]:
We can convert [tex]\( \frac{6}{10} \)[/tex] to its decimal form:
[tex]\[ \frac{6}{10} = 0.6 \][/tex]
So, adding the whole number part:
[tex]\[ 3 \frac{6}{10} = 3 + 0.6 = 3.6 \][/tex]
2. For the second mixed number [tex]\( 3 \frac{4}{5} \)[/tex]:
We can convert [tex]\( \frac{4}{5} \)[/tex] to its decimal form:
[tex]\[ \frac{4}{5} = 0.8 \][/tex]
So, adding the whole number part:
[tex]\[ 3 \frac{4}{5} = 3 + 0.8 = 3.8 \][/tex]
Now, we need to compare the two decimal values we obtained:
- The value for [tex]\( 3 \frac{6}{10} \)[/tex] is 3.6
- The value for [tex]\( 3 \frac{4}{5} \)[/tex] is 3.8
Comparing 3.6 and 3.8, we see that:
[tex]\[ 3.6 < 3.8 \][/tex]
Therefore, the smallest mixed number is [tex]\( 3 \frac{6}{10} \)[/tex] or 3.6.
[tex]\[
\text{Smallest mixed number:} \quad 3 \frac{6}{10}
\][/tex]
