Answer:
(i)
12
+
3
×
5
−
5
×
6
2
=
27
12+3×5−5×
2
6
=27
(ii)
10
+
(
−
3
)
2
+
3
×
(
−
5
−
5
)
×
6
2
=
−
11
10+(−3)
2
+3×(−5−5)×
2
6
=−11
(iii)
23
+
3
×
5
−
6
×
6
÷
(
−
4
)
−
5
−
7
=
35
23+3×5−6×6÷(−4)−5−7=35
(iv)
23
+
(
3
×
5
−
6
×
6
)
÷
(
−
7
)
−
15
÷
2
=
18.5
23+(3×5−6×6)÷(−7)−15÷2=18.5
Explanation:
Let's simplify each expression step by step:
(i)
12
+
3
×
5
−
5
×
6
2
12+3×5−5×
2
6
Step 1: Perform multiplication and division first.
12
+
15
−
5
×
3
12+15−5×3
Step 2: Continue with addition and subtraction.
12
+
15
−
15
=
27
12+15−15=27
(ii)
10
+
(
−
3
)
2
+
3
×
(
−
5
−
5
)
×
6
2
10+(−3)
2
+3×(−5−5)×
2
6
Step 1: Evaluate the exponent first.
10
+
9
+
3
×
(
−
5
−
5
)
×
6
2
10+9+3×(−5−5)×
2
6
Step 2: Perform addition and subtraction inside the parentheses.
10
+
9
+
3
×
(
−
10
)
×
6
2
10+9+3×(−10)×
2
6
Step 3: Perform multiplication and division.
10
+
9
−
30
=
−
11
10+9−30=−11
(iii)
23
+
3
×
5
−
6
×
6
÷
(
−
4
)
−
5
−
7
23+3×5−6×6÷(−4)−5−7
Step 1: Perform multiplication and division first.
23
+
15
−
6
×
6
(
−
4
)
−
5
−
7
23+15−6×
(−4)
6
−5−7
Step 2: Evaluate the division within the parentheses.
23
+
15
−
6
×
(
−
1.5
)
−
5
−
7
23+15−6×(−1.5)−5−7
Step 3: Perform the remaining multiplication and addition/subtraction.
23
+
15
+
9
−
5
−
7
=
35
23+15+9−5−7=35
(iv)
23
+
(
3
×
5
−
6
×
6
)
÷
(
−
7
)
−
15
÷
2
23+(3×5−6×6)÷(−7)−15÷2
Step 1: Perform the operations inside the parentheses first.
23
+
(
15
−
36
)
÷
(
−
7
)
−
15
÷
2
23+(15−36)÷(−7)−15÷2
Step 2: Perform the subtraction within the parentheses.
23
+
(
−
21
)
÷
(
−
7
)
−
15
÷
2
23+(−21)÷(−7)−15÷2
Step 3: Evaluate the division within the parentheses.
23
+
3
−
15
÷
2
23+3−15÷2
Step 4: Perform the final division and addition/subtraction.
23
+
3
−
7.5
=
18.5
23+3−7.5=18.5
So, the simplified expressions are:
(i)
12
+
3
×
5
−
5
×
6
2
=
27
12+3×5−5×
2
6
=27
(ii)
10
+
(
−
3
)
2
+
3
×
(
−
5
−
5
)
×
6
2
=
−
11
10+(−3)
2
+3×(−5−5)×
2
6
=−11
(iii)
23
+
3
×
5
−
6
×
6
÷
(
−
4
)
−
5
−
7
=
35
23+3×5−6×6÷(−4)−5−7=35
(iv)
23
+
(
3
×
5
−
6
×
6
)
÷
(
−
7
)
−
15
÷
2
=
18.5
23+(3×5−6×6)÷(−7)−15÷2=18.5