To determine which of the given expressions represents a number less than 1, let's analyze each expression step by step.
### Expression (A):
[tex]\[
\frac{4}{3} \times 1
\][/tex]
When you multiply [tex]\(\frac{4}{3}\)[/tex] by 1, you get:
[tex]\[
\frac{4}{3}
\][/tex]
Since [tex]\(\frac{4}{3} \approx 1.333\)[/tex], it is greater than 1.
### Expression (B):
[tex]\[
1 \div \frac{9}{2}
\][/tex]
Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus,
[tex]\[
1 \div \frac{9}{2} = 1 \times \frac{2}{9} = \frac{2}{9}
\][/tex]
Since [tex]\(\frac{2}{9} \approx 0.222\)[/tex], it is less than 1.
### Expression (C):
[tex]\[
\frac{4}{3} \div \frac{1}{3}
\][/tex]
Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus,
[tex]\[
\frac{4}{3} \div \frac{1}{3} = \frac{4}{3} \times 3 = 4
\][/tex]
Since [tex]\(4\)[/tex] is greater than 1.
### Expression (D):
[tex]\[
\frac{9}{5} \div \frac{2}{10}
\][/tex]
Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus,
[tex]\[
\frac{9}{5} \div \frac{2}{10} = \frac{9}{5} \times \frac{10}{2} = \frac{9}{5} \times 5 = 9
\][/tex]
Since [tex]\(9\)[/tex] is greater than 1.
After analyzing all the expressions, we can conclude that:
[tex]\[ \boxed{B} \; 1 \div \frac{9}{2} \][/tex]
is the expression that represents a number less than 1.
