Question

HELP!!! My question is "determine whether each ratio is equivalent to 1/2 3/9 or 5/7. Thee ratios are : 2/6,3/6,5/10,10/14,50/100,20/28,1/3,8/24. please show how to do the work with the answer!!​

Answer 1

Answers:

Ratios equivalent to 1/2 are...

• 3/6
• 5/10
• 50/100

Ratios equivalent to 3/9 are...

• 2/6
• 1/3
• 8/24

Ratios equivalent to 5/7 are...

• 10/14
• 20/28

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Step-by-step explanation:

Let's see if 2/6 is equivalent to 1/2. For now, let's assume they are equal fractions. If so, then,

2/6 = 1/2

2*2 = 6*1 ... cross multiplying

4 = 6

The last equation is of course false, which then causes a domino effect to make the first equation false as well. This means 2/6 is not equivalent to 1/2.

You can use a calculator to find that

• 2/6 = 0.3333 approximately
• 1/2 = 0.5 exactly

Which is another way to see how the fractions aren't the same.

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Let's check to see if 2/6 is equivalent to 3/9.

2/6 = 3/9

2*9 = 6*3 ... cross multiplying

18 = 18

We get the same thing on both sides, which means the third equation is true. By extension, the first equation is true as well. We have shown that 2/6 and 3/9 are equivalent.

Take note how both of those fractions reduce to 1/3, which is another way to see how they are equivalent.

Yet another way is to use a calculator to find that

• 2/6 = 0.3333...
• 3/9 = 0.3333...

Both approximate decimal values involve '3's going on forever.

Apply any of the methods discussed to check the other values, so you can properly sort each ratio mentioned. Let me know if you have any questions.