Issue with mixed fractions

[Yuseph]

Hey guys,

Why does the plus sign between 5 and 3/7 turn into a minus sign ? Is it a mistake in my book or is it a rule i never heard of ? Thanks

 

[Otis]

Hi Yuseph. The grouping symbols around (5+3/7) tell us that each number inside is being subtracted.

A - (B + C)

To remove the grouping symbols, B is subtracted and C is subtracted.

A - B - C

?

 

[Yuseph]

Hi Yuseph. The grouping symbols around (5+3/7) tell us that each number inside is being subtracted.

A - (B + C)

To remove the grouping symbols, B is subtracted and C is subtracted.

A - B - C

?

It s crystal clear bro

 

[HallsofIvy]

That is a special case of the "distributive law" \(\displaystyle \ \to \ \ \)a(b+ c)= ab+ ac. If a= -1, -(a+ b)= -1(a+ b)= -1a+ (-1)b= -a- b.

 

[Otis]

… a(b + c) = ab + ac …
If a = -1,
-(a + b) = -1(a + b) = -1a + (-1)b = -a - b

When a = -1, you meant to say

(-1)(b + c) = (-1)(b) + (-1)(c) = -b - c

\(\;\)

 

[Otis]

@Yuseph

As HallsofIvy mentioned, we can change subtraction to addition, by "adding the opposite".

(7 + 1/8) + (-1) (5 + 3/7)

From this viewpoint, we "distribute" the -1 across the sum 5+3/7. (I'm not sure why HallsofIvy calls it a special case.)

7 + 1/8 + (-5) + (-3/7)

Adding -5 is the same as subtracting 5.
Adding -3/7 is the same as subtracting 3/7.

7 + 1/8 - 5 - 3/7

---

Have you seen this?

(7 + 1/8) - (5 + 3/7)

57/8 - 38/7

[ 7(57) - 8(38) ] ÷ [ (8)(7) ]

95/56

95 - 56 = 39

1 + 39/56

?

 

[Steven G]

Suppose you had 15-(2+3). Now remember that 2+3 is the sams as 3+2. So 15-(2+3) is the same as 15-(3+2).

Now if you think that 15-(2+3) = 15-2+3 then you are in trouble as 15-(3+2) would then be 15-3+2. Now 15-2+3 is not the same as 15-3+2!!! so it can't be that you only subtract the 1st number.