Question

Explain the logic in fractions where 1/6+2/3+3/7 becomes 7/42+28/42+18/42

Answer 1

The logic in this fraction addition problem is to find a common denominator for all the fractions and then add the numerators. In this case, the common denominator is the least common multiple of the denominators, which is 42.

• To convert the first fraction, 1/6, to have a denominator of 42, we need to multiply both the numerator and denominator by 7. This gives us 7/42.

• To convert the second fraction, 2/3, to have a denominator of 42, we need to multiply both the numerator and denominator by 14. This gives us 28/42.

• To convert the third fraction, 3/7, to have a denominator of 42, we need to multiply both the numerator and denominator by 6. This gives us 18/42.

Now that all the fractions have a common denominator of 42, we can add the numerators to get the final answer:

`\begin{aligned} \sf (1)/(6) + (2)/(3) + (3)/(7) = (7)/(42) + (28)/(42) + (18)/(42) = \bold{(53)/(42)} \end{aligned}`

Therefore, the sum of the fractions is 53/42.

I hope this helps!

Answer 2

Explanation:

What are fractions?

Fractions are parts or pieces of a complete thing.

In this problem, the fractions start out with varying denominators, and then end with the same denominator. In order to go from different denominators to the same denominator, we must find a common denominator.

What is a common denominator?

A common denominator is a number that denominators of fractions can equal when multiplied by something else. Ex: 1/3 + 2/ 7 Multiples of 3: 3, 6, 9, 12, 15, 18, 21 Multiples of 7: 7, 14, 21. Both 3 and 7 have 21 in common, so this would be the common denominator.

A common denominator is needed so fractions with different denominators can be combined. To get from 6, 3, and 7 to 42, the multiples of 2, 3, and 7 must be listed.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 29, 42

Multiples of 7: 7, 14, 21, 28, 35, 42

All three numbers have 42 in common, so that is their common denominator. Whatever was done to the denominator, must be done to the numerator. Now, we must take the number that can be multiplied by the denominator to reach 42 and multiply it by the numerator.

`(1*7)/(6*7)}`

`=(7)/(42)`

`(2*14)/(3*14)`

`=(28)/(42)`

`(3*6)/(7*6)`

`=(18)/(42)`

So, to sum it up, when trying to add fractions with different denominators, find a common denominator by listing multiples of the denominators and multiply the numerator by the number the denominator was multiplied by to get the common denominator.