Using the rearrangement property find the sum of: 83+−14+−11 6+38
Answers
Answer:
-8/3-1/4-11/6+3/8
(-8/3-11/6)+(-1/4+3/8)
(-16/6-11/6)+(-2/8+3/8)
-27/6+1/8
-108/24+3/24
-105/24
Step-by-step explanation:
We arrange the numbers as such
3
−8
+
6
−11
+
4
−1
+
8
3
We take the LCM of 3,6 and 4,8
∴ LCM of 3 and 6 is 6
By multiplying both numerator and denominator with 2 we get,
3
−8
=
3×2
−8×2
=
6
−16
And by multiplying both numerator and denominator with 1 we get,
6
−11
=
6×1
−11×1
=
6
−11
6
−16
+
6
−11
Since it has the same denominators we can add directly
6
−16+(−11)
=
6
−16−11
⇒
6
−27
LCM of 4 and 8 is 8
By multiplying both numerator and denominator with 2 we get,
4
−1
=
4×2
−1×2
=
8
−2
And by multiplying both numerator and denominator with 1 we get,
8
3
=
8×1
3×1
=
8
3
8
−2
+
8
3
Since it has the same denominators we can add directly
8
−2+8
⇒
8
6
∴
6
−27
+
8
6
We take the LCM of 6 and 8 i.e. 24
By multiplying both numerator and denominator with 4 we get,
6
−27
=
6×4
−27×4
=
24
−108
And by multiplying both numerator and denominator with 3 we get,
8
1
=
8×3
1×3
=
24
3
8
−2
+
8
3
Since it has the same denominators we can add directly
24
−108+3
⇒
24
−105
24
−105
Can be further divided
24÷3
−105÷3
⇒
8
−35
.