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?

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asked Apr 3, 2024 25.0k views

1 Answer

Irfan Akram · Answer 1 · 2024-04-08T12:31:19+0000

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.

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.

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

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.