Determine whether the ratios given in the first column are equivalent or not.

Question

Ratios
Yes
No
11
7

�
�
�

77
63
7
11
​
and
63
77
​


3
5

�
�
�

45
75
5
3
​
and
75
45
​


1
8

�
�
�

10
80
8
1
​
and
80
10
​


2
9

�
�
�

18
81
9
2
​
and
81
18
​

Answer 1

To determine whether the ratios given in each row are equivalent, we need to simplify and compare them.

1. First pair:

   • \(\frac{11}{7}\) and \(\frac{77}{63}\)
   • Simplify \(\frac{77}{63}\): \[ \frac{77 \div 7}{63 \div 7} = \frac{11}{9} \]
   • These are not equivalent: \(\frac{11}{7} \neq \frac{11}{9}\)

2. Second pair:

   • \(\frac{3}{5}\) and \(\frac{45}{75}\)
   • Simplify \(\frac{45}{75}\): \[ \frac{45 \div 15}{75 \div 15} = \frac{3}{5} \]
   • These are equivalent: \(\frac{3}{5} = \frac{3}{5}\)

3. Third pair:

   • \(\frac{1}{8}\) and \(\frac{10}{80}\)
   • Simplify \(\frac{10}{80}\): \[ \frac{10 \div 10}{80 \div 10} = \frac{1}{8} \]
   • These are equivalent: \(\frac{1}{8} = \frac{1}{8}\)

4. Fourth pair:

   • \(\frac{2}{9}\) and \(\frac{18}{81}\)
   • Simplify \(\frac{18}{81}\): \[ \frac{18 \div 9}{81 \div 9} = \frac{2}{9} \]
   • These are equivalent: \(\frac{2}{9} = \frac{2}{9}\)

Here’s a summary:

• \( \frac{11}{7} \) and \( \frac{77}{63} \): No
• \( \frac{3}{5} \) and \( \frac{45}{75} \): Yes
• \( \frac{1}{8} \) and \( \frac{10}{80} \): Yes
• \( \frac{2}{9} \) and \( \frac{18}{81} \): Yes