Question

Suppose you use 8 instead of 4 as a common denominator when finding 7 1/2−(−3 1/4). How will that change the process for finding the difference?

Answer 1

• If we use 8 instead of 4 as a common denominator,we can notice that the numerator gets doubled as compared to when we take 4 as the common denominator but there's no change in the final answer.

Task :

• To figure out the change in the process for finding the difference between the given two fractions if their common denominator is taken as 8 instead of 4.

Solution:

`\rightarrow \: 7(1)/(2) - ( - 3 (1)/(4) ) \\`

when the denominator is 4 :

`\rightarrow \: (15)/(2) + (13)/(4) \\`

`\rightarrow (30 + 13)/(4 \\ )`

`\rightarrow \: (43)/(4) \: or \: 10 (3)/(4) \\`

when the denominator is 8 :

`\rightarrow \: (15)/(2) + (13)/(4) \\`

`\rightarrow (60 + 26 \\ )/(8)`

`\rightarrow (86)/(8) \: \: or \: 10 (6)/(8) \: \: or \: \: 10 (3)/(4) \\`

• We can notice that as the denominator got doubled (4*2 = 8), the numerator got doubled (30*2 = 60, 13*2 = 26, 43*2 = 86) as well and in the final answer,we had to simplify 6/8 to 3/4 as it was when the denominator was 4 ,thus there was no change in the answer but during the process,the numerator got doubled just as the denominator did.