Let's evaluate each expression step-by-step to determine which represents a number greater than 1.
### Expression (A):
[tex]\[
\frac{7}{5} \times 1
\][/tex]
To solve this, we multiply [tex]\( \frac{7}{5} \)[/tex] by 1:
[tex]\[
\frac{7}{5} \times 1 = \frac{7}{5} = 1.4
\][/tex]
Since [tex]\( 1.4 > 1 \)[/tex], Expression (A) represents a number greater than 1.
### Expression (B):
[tex]\[
1 \div \frac{10}{7}
\][/tex]
To solve this division, we multiply 1 by the reciprocal of [tex]\( \frac{10}{7} \)[/tex]:
[tex]\[
1 \div \frac{10}{7} = 1 \times \frac{7}{10} = \frac{7}{10} = 0.7
\][/tex]
Since [tex]\( 0.7 < 1 \)[/tex], Expression (B) does not represent a number greater than 1.
### Expression (C):
[tex]\[
\frac{5}{3} \div \frac{15}{4}
\][/tex]
To solve this division, we multiply [tex]\( \frac{5}{3} \)[/tex] by the reciprocal of [tex]\( \frac{15}{4} \)[/tex]:
[tex]\[
\frac{5}{3} \div \frac{15}{4} = \frac{5}{3} \times \frac{4}{15} = \frac{5 \times 4}{3 \times 15} = \frac{20}{45} = \frac{4}{9} \approx 0.4444444444444445
\][/tex]
Since [tex]\( 0.4444444444444445 < 1 \)[/tex], Expression (C) does not represent a number greater than 1.
### Expression (D):
[tex]\[
\frac{1}{4} \div \frac{1}{3}
\][/tex]
To solve this division, we multiply [tex]\( \frac{1}{4} \)[/tex] by the reciprocal of [tex]\( \frac{1}{3} \)[/tex]:
[tex]\[
\frac{1}{4} \div \frac{1}{3} = \frac{1}{4} \times \frac{3}{1} = \frac{1 \times 3}{4 \times 1} = \frac{3}{4} = 0.75
\][/tex]
Since [tex]\( 0.75 < 1 \)[/tex], Expression (D) does not represent a number greater than 1.
### Conclusion
After evaluating all the expressions:
- Expression (A): [tex]\(1.4 > 1\)[/tex]
- Expression (B): [tex]\(0.7 < 1\)[/tex]
- Expression (C): [tex]\(0.4444444444444445 < 1\)[/tex]
- Expression (D): [tex]\(0.75 < 1\)[/tex]
Only Expression (A) represents a number greater than 1.
