Question

Determine whether the following ratios are equivalent ratios 2:3 and 10:15.​

Answer 1

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As we know,

product of extremes = product of means

2×15 = 3×10

30 = 30

Hence, they are equivalent.

Answer 2

In context of question asked,

We have to determine that whether the given ratio 2:3 and 10:15 are equivalent or not.

As we know that,

If the both ratio are when expressed into into simplest form, and then after converting it into simplest form, if the value of both ratio are same, then it will be considered as equivalent ratio.

Here,10:15 is not in its simplest form.

So, factorizing the given number,

$10 = 2\times 5\\15 = 3\times 5$

As 5 is common in both number.

So, we will divide both 10 and 15 by 5.

Thus we will get it as,

$\frac{10}{5} :\frac{15}{3} = 2:3$

Hence, both the ratio 2:3 and 10:15 are equivalent.