To determine whether the ratio [tex]\( 3:5 \)[/tex] is less than the ratio [tex]\( 7:10 \)[/tex], we need to compare these two ratios numerically. Here's a detailed, step-by-step solution:
1. Convert each ratio to its decimal form:
- For the ratio [tex]\( 3:5 \)[/tex]:
[tex]\[
\frac{3}{5} = 0.6
\][/tex]
- For the ratio [tex]\( 7:10 \)[/tex]:
[tex]\[
\frac{7}{10} = 0.7
\][/tex]
2. Compare the two decimal values:
- We have:
[tex]\[
0.6 \quad \text{and} \quad 0.7
\][/tex]
- Clearly, [tex]\( 0.6 \)[/tex] is less than [tex]\( 0.7 \)[/tex].
3. Conclusion:
- The first ratio [tex]\( 3:5 \)[/tex], which is [tex]\( 0.6 \)[/tex] in decimal form, is indeed less than the second ratio [tex]\( 7:10 \)[/tex], which is [tex]\( 0.7 \)[/tex] in decimal form.
Thus, the statement "The ratio [tex]\( 3:5 \)[/tex] is less than the ratio [tex]\( 7:10 \)[/tex]" is true.
