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We're asked to write if the following ratios are equal or not. To do this, we'll first simplify them if we can.
Problem 1
[tex]\sf 5:6 \ and \ 6:5[/tex]
Both of these ratios are in their simplest form, and we can see that they're not equal.
Problem 2
[tex]\sf 18:9 \ and \ 6:3[/tex]
Simplify each of these ratios.
Divide both sides of the first ratio by 9.
[tex]\sf 2:1[/tex]
Divide both sides of the second ratio by 3.
[tex]\sf 2:1[/tex]
As we can see, these ratios are equal.
Problem 3
[tex]\sf 36:100 \ and \ 108:300[/tex]
Divide the first one by 4
[tex]\sf 9:25[/tex]
Divide the second one by 2:
[tex]\sf 54:150[/tex]
Divide by 2 again:
[tex]\sf 27:75[/tex]
Finally, divide by 3:
[tex]\sf 9:25[/tex]