
Which ratio is greater?
or .
Answer
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Hint: In this problem we represent the given ratios in fractions. Using simplification or a calculator we can compare and we can tell which one is greater. Otherwise after representing the given ratios in fraction we can compare the fraction by making the denominator or numerator value the same in both the fractions.
Complete step-by-step answer:
Given,
and .
We know that the ratios can be represented as fractions. That is
.
Then above becomes
and .
Thus we have
and . ----(1)
Now to make the denominators of the both fractions the same, we take LCM of 21 and 28 and we multiply to the numerator and denominator of the both fractions.
Now prime factors of 21 are
The prime factors of 28 are
Now we can see that the LCM of 21 and 28 is
.
Now we multiply 84 in the numerator and the denominator of both fractions.
Then (1) becomes
and
and
and .
Now we know that if we have two fractions with same denominator, that is and then we have
If then
If then
If then
Now from and we can tell that .
Then we can say that
Hence is greater.
Thus is greater.
So, the correct answer is “ ”.
Note: We can solve this if we have a calculator. Now we have and . We can easily see that is greater. If we need to add two fractions we need to make sure that the denominator of both the fractions are equal. To make the denominator equal we use the LCM method as we did in above. Some numbers cannot be expressed as a fraction and they are called irrational. For example .
Complete step-by-step answer:
Given,
We know that the ratios can be represented as fractions. That is
Then above becomes
Thus we have
Now to make the denominators of the both fractions the same, we take LCM of 21 and 28 and we multiply to the numerator and denominator of the both fractions.
Now prime factors of 21 are
The prime factors of 28 are
Now we can see that the LCM of 21 and 28 is
Now we multiply 84 in the numerator and the denominator of both fractions.
Then (1) becomes
Now we know that if we have two fractions with same denominator, that is
If
If
If
Now from
Then we can say that
Hence
Thus
So, the correct answer is “
Note: We can solve this if we have a calculator. Now we have
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