McGraw Hill Math Grade 7 Lesson 4.1 Answer Key Order of Operations

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McGraw-Hill Math Grade 7 Answer Key Lesson 4.1 Order of Operations

Exercises Calculate

Question 1.
(4 + 2) × (4 – 2) – (2 × 3) + 2^4-2 =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
(4 + 2) × (4 – 2) – (2 × 3) + 2^4-2 = ?
First solve the parts that are inside parenthesis.
6 × 2 – 6 + 2^4-2 = ?
Second solve the parts that have exponents.
6 × 2 – 6 + 2² = ?
6 × 2 – 6 + 4 = ?
Third perform multiplication operation.
12 – 6 + 4 = ?
Fourth perform Addition and subtraction operation.
6 + 4 = 10
So, the expression (4 + 2) × (4 – 2) – (2 × 3) + 2^4-2  is equal to 10.

Question 2.
(5 – 4) × (10 – 6) – 2² + 4 =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
(5 – 4) × (10 – 6) – 2² + 4 = ?
First solve the parts that are inside parenthesis.
1 × 4 – 2² + 4 = ?
Second solve the parts that have exponents.
1 × 4 – 4 + 4 = ?
Third perform multiplication operation.
4 – 4 + 4 = ?
Fourth perform Addition and subtraction operation.
0 + 4 = 4
So, the expression (5 – 4) × (10 – 6) – 2² + 4  is equal to 4.

Question 3.
(4 – 2)³ + (4 – 2)² + 1 – 2 + 2² =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
(4 – 2)³ + (4 – 2)² + 1 – 2 + 2² = ?
First solve the parts that are inside parenthesis.
2³ + 2² + 1 – 2 + 2² = ?
Second solve the parts that have exponents.
8 + 4 + 1 – 2 + 4 = ?
Third perform Addition and subtraction operation.
12 + 1 – 2 + 4 = ?
13 – 2 + 4 = ?
11 + 4 = 15
So, the expression (4 – 2)³ + (4 – 2)² + 1 – 2 + 2² is equal to 15.

Question 4.
(4 + 2) × (9 – 7) + 3² – (8 – 5)² =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
(4 + 2) × (9 – 7) + 3² – (8 – 5)² = ?
First solve the parts that are inside parenthesis.
6 × 2 + 3² – 3² = ?
Second solve the parts that have exponents.
6 × 2 + 9 – 9 = ?
Third perform multiplication operation.
12 + 9 – 9 = ?
Fourth perform Addition and subtraction operation.
21 – 9 = 12
So, the expression(4 + 2) × (9 – 7) + 3² – (8 – 5)²  is equal to 12.

Question 5.
(6 – 4)³ – (6 – 4)³ + 2 – (2 – 1) =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
(6 – 4)³ – (6 – 4)³ + 2 – (2 – 1) = ?
First solve the parts that are inside parenthesis.
2³ –  2³ + 2 – 1 = ?
Second solve the parts that have exponents.
8 – 8 + 2 – 1 = ?
Third perform Addition and subtraction operation.
0 + 2 – 1 = ?
2 – 1 = 1
So, the expression (6 – 4)³ – (6 – 4)³ + 2 – (2 – 1)  is equal to 1.

Question 6.
2² – (2³ – 2) + (2² + 4) =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
2² – (2³ – 2) + (2² + 4) = ?
First solve the parts that are inside parenthesis.
2² – 6 + 8 = ?
Second solve the parts that have exponents.
4 – 6 + 8 = ?
Third perform Addition and subtraction operation.
– 2 + 8 = 6
So, the expression2² – (2³ – 2) + (2² + 4)  is equal to 6.

Question 7.
(5 – 2) + (6 – 4) – (3 – 1) =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
(5 – 2) + (6 – 4) – (3 – 1) = ?
First solve the parts that are inside parenthesis.
3 + 2 – 2 = ?
Second perform Addition and subtraction operation.
5 – 2 = 3
So, the expression (5 – 2) + (6 – 4) – (3 – 1) is equal to 3.

Question 8.
(4 + 3) × (5 – 2) × (2 – 1)² =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
(4 + 3) × (5 – 2) × (2 – 1)² = ?
First solve the parts that are inside parenthesis.
7 × 3 × 1² = ?
Second solve the parts that have exponents.
7 × 3 × 1 = ?
Third perform multiplication operation.
21 x 1 = 21
So, the expression (4 + 3) × (5 – 2) × (2 – 1)²  is equal to 21.

Question 9.
(4 – 2) + (5 × 2)² – 2 × 12 – 4² =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
(4 – 2) + (5 × 2)² – 2 × 12 – 4² = ?
First solve the parts that are inside parenthesis.
2 + 10² – 2 × 12 – 4² = ?
Second solve the parts that have exponents.
2 + 100 – 2 × 12 – 16 = ?
Third perform multiplication operation.
2 + 100 – 24 – 16 = ?
Fourth perform addition and subtraction operation.
102 – 24 – 16 = ?
76 – 16 = 60 
So, the expression (4 – 2) + (5 × 2)² – 2 × 12 – 4²  is equal to 60.

Question 10.
(1 + 1 + 2) × 7 – 4² =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
(1 + 1 + 2) × 7 – 4² = ?
First solve the parts that are inside parenthesis.
4 × 7 – 4² = ?
Second solve the parts that have exponents.
4 × 7 – 16 = ?
Third perform multiplication operation.
28 – 16 = ?
Fourth perform addition and subtraction operation.
28 – 16 = 12
So, the expression (1 + 1 + 2) × 7 – 4²  is equal to 12.

Question 11.
(13 – 2) – 3² + 10 – (2 × 4) =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
(13 – 2) – 3² + 10 – (2 × 4) = ?
First solve the parts that are inside parenthesis.
11 – 3² + 10 – 8 = ?
Second solve the parts that have exponents.
11 – 9 + 10 – 8 = ?
Third perform addition and subtraction operation.
2 + 10 – 8 = ?
12 – 8 = 4
So, the expression (13 – 2) – 3² + 10 – (2 × 4) is equal to 4.

Question 12.
7² + (4 – 1) × 5 – 2 × (3 – 1)³ =
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
7² + (4 – 1) × 5 – 2 × (3 – 1)³ = ?
First solve the parts that are inside parenthesis.
7² + 3 × 5 – 2 × 2³ = ?
Second solve the parts that have exponents.
49 + 3 × 5 – 2 × 8 = ?
Third perform multiplication operation.
49 + 15 – 16 = ?
Fourth perform addition and subtraction operation.
64 – 16 = 48
So, the expression 7² + (4 – 1) × 5 – 2 × (3 – 1)³   is equal to 48.