Examples with solutions for Parentheses in simple Order of Operations: Solving the problem

Exercise #1

Solve the following equation:

(12+8)÷4= (12 + 8) \div 4 =

Step-by-Step Solution

To solve the equation, follow these steps:

1. Start by solving the expression inside the parentheses: 12+8 12 + 8 .

2. Calculate 12+8 12 + 8 to get 20 20 .

3. Now divide the result by 4: 20÷4 20 \div 4 .

4. Calculate 20÷4 20 \div 4 to get 5 5 .

Therefore, the final answer is 5 5 .

Answer

5 5

Exercise #2

Solve the following equation:

(5010)×2= (50-10) \times 2 =

Step-by-Step Solution

To solve the equation, follow these steps:

1. Start with the expression inside the parentheses: 5010 50 - 10 .

2. Calculate 5010 50 - 10 to get 40 40 .

3. Now multiply the result by 2: 40×2 40 \times 2 .

4. Calculate 40×2 40 \times 2 to get 80 80 .

Therefore, the final answer is 80 80 .

Answer

80 80

Exercise #3

Solve the following expression:

(85+5):10= (85+5):10=

Video Solution

Step-by-Step Solution

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of them,

We will therefore start by simplifying the expression inside the parentheses and calculate the result of the addition within them, then - we will first perform the division operation:

(85+5):10=90:10=9 (85+5):10= \\ 90:10= \\ 9

Therefore, the correct answer is answer A.

Answer

9 9

Exercise #4

Solve the following problem:

187×(85)= 187\times(8-5)=

Video Solution

Step-by-Step Solution

Apply the distributive property and proceed to multiply each term inside of the parentheses by 187:

187×8187×5= 187\times8-187\times5=

Solve the first multiplication problem vertically, making sure to solve it in the correct order (ones multiplied by ones, ones multiplied by tens, ones multiplied by hundreds )

187×8 187\\\times8

We should obtain the following result: 1496

Proceed to solve the second multiplication problem vertically, once again making sure to solve it in the correct order (ones multiplied by ones, ones multiplied by tens, ones multiplied by hundreds )

187×5 187\\\times5

We should obtain the following result: 935

Now to tackle the next problem:

1496935= 1496-935=

We should once again solve this vertically. Make sure to align the digits properly, ones under ones, tens under tens, etc.:

1496935 1496\\-935

Subtract ones from ones, tens from tens, etc., to obtain the final result: 561 561

Answer

561 561

Exercise #5

Solve the following equation:

(294):5= (29-4):5=

Video Solution

Step-by-Step Solution

Let's simplify this expression while maintaining the order of operations.

Let's start by solving what's in the parentheses:

294=25 29-4=25

Now we get the expression:

25:5= 25:5=

In the next step, to make the division easier, we'll break down 25 into two smaller factors that are divisible by 5:

(20+5):5= (20+5):5=

Let's divide each factor in the parentheses by 5:

(20:5)+(5:5)= (20:5)+(5:5)=

We'll solve each expression in the parentheses and obtain:

4+1=5 4+1=5

Answer

5 5

Exercise #6

(159)×(73)= (15-9)\times(7-3)=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we must first solve the expressions inside of the parentheses:

159=6 15-9=6

73=4 7-3=4

We obtain the following expression:

6×4=24 6\times4=24

Answer

24 24

Exercise #7

Solve the following expression:

10(104):2= 10-(10-4):2=

Video Solution

Step-by-Step Solution

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of them,

Therefore we'll start by simplifying the expression inside the parentheses and perform the subtraction within them, then since division comes before subtraction, we'll first perform the division operation and then the subtraction operation

10(104):2=106:2=103=7 10-(10-4):2= \\ 10-6:2= \\ 10-3=\\ 7 Therefore the correct answer is answer D.

Answer

7 7

Exercise #8

Solve the following:

10(5+2×2)÷3= 10-(5+2\times2)\div3 =

Step-by-Step Solution

To solve the expression 10(5+2×2)÷3 10-(5+2\times2)\div3 , follow the order of operations:

1. Parentheses: Calculate inside the parentheses first, performing multiplication first: 2×2=4 2\times2 = 4 . Therefore, it is 5+4=9 5+4=9 .

2. Division: Now, we have 109÷3 10-9\div3 . Perform the division: 9÷3=3 9\div3 =3 .

3. Subtraction: 103=7 10-3=7 ,

Thus, the answer is 7 7 .

Answer

7

Exercise #9

(1.40.3)×10= (1.4-0.3)\times10=

Video Solution

Step-by-Step Solution

According to the order of operations, we will first solve the expression in parentheses.

We will solve the exercise vertically, making sure to align digits properly - ones under ones, tens under tens, and so on. Note that the decimal point is in place:

1.40.3 1.4\\-0.3\\

And we get the result:

1.1 1.1

Now we have the expression:

1.1×10= 1.1\times10=

The above expression doesn't need to be calculated, we simply need to move the decimal point one place to the right, since we are multiplying by ten, meaning we're adding a tens place.

Therefore, we get the result:

11 11

Answer

11 11

Exercise #10

153×(2+1)= 15-3\times(2+1)=

Step-by-Step Solution

To solve 153×(2+1) 15-3\times(2+1) , start by calculating the expression inside the parentheses, 2+1=3 2+1 = 3 .

Next, multiply by 3: 3×3=9 3\times3 = 9 .

Now, subtract from 15: 159=6 15-9 = 6 .

The final answer is 6.

Answer

6

Exercise #11

20÷(4+1)3= 20\div(4+1)-3=

Step-by-Step Solution

To solve 20÷(4+1)3 20\div(4+1)-3 , start by simplifying inside the parentheses: 4+1=5 4+1 = 5 .

Next, divide 20 by 5: 20÷5=4 20\div5 = 4 .

Then subtract 3: 43=1 4-3 = 1 .

The final answer is 1.

Answer

1

Exercise #12

25(5+0)= 25(5+0)=

Video Solution

Step-by-Step Solution

According to the order of operations, we will first solve the expression in parentheses:

5+0=5 5+0=5

Now we will get the expression:

25×5= 25\times5=

Let's solve the expression vertically:

25×5 25\\\times5

We will be careful to solve the expression in the correct order, ones with ones and then ones with tens

And we will get:

125 125

Answer

125 125

Exercise #13

Solve the following problem using the order of operations:

(166)×9+(73)= (16-6)\times9+(7-3)=

Video Solution

Step-by-Step Solution

According to the order of operations, we'll first solve the exercises in parentheses:

(166)=10 (16-6)=10

(73)=4 (7-3)=4

We should obtain the following exercise:

10×9+4 10\times9+4

We'll place the multiplication exercise in parentheses to avoid confusion in the rest of the solution:

(10×9)+4= (10\times9)+4=

According to the order of operations, we'll solve the multiplication exercise and then add:

90+4=94 90+4=94

Answer

94 94

Exercise #14

Solve the exercise:

2×3(4+5):2= 2\times3-(4+5):2=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, we first solve the exercise within parentheses:

4+5=9 4+5=9

Now we obtain the exercise:

2×39:2= 2\times3-9:2=

We place in parentheses the multiplication and division exercises:

(2×3)(9:2)= (2\times3)-(9:2)=

We solve the exercises within parentheses:

2×3=6 2\times3=6

9:2=4.5 9:2=4.5

Now we obtain the exercise:

64.5=1.5 6-4.5=1.5

Answer

1.5 1.5

Exercise #15

Solve the following:

4+(6+6:3)2= 4+(6+6:3)\cdot2=

Video Solution

Step-by-Step Solution

Let's simplify this expression while adhering to the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses take priority over all.

In our expression, there is a term in parentheses that needs to be multiplied. We'll start by simplifying this expression, remembering that division comes before addition, so we'll first perform the division operation within the parentheses and then the addition operation in this expression:

4+(6+6:3)2=4+(6+2)2=4+82= 4+(6+6:3)\cdot2= \\ 4+(6+2)\cdot2= \\ 4+8\cdot2=

Let's continue simplifying the expression we that we got in the last step. Since multiplication comes before addition, we'll first calculate the multiplication in the expression and then perform the addition operation:

4+82=4+16=20 4+8\cdot2= \\ 4+16= \\ 20

To summarise:

4+(6+6:3)2=4+82=20 4+(6+6:3)\cdot2= \\ 4+8\cdot2= \\ 20

Therefore the correct answer is answer C.

Answer

20

Exercise #16

10(104):2= 10-(10-4):2=

Video Solution

Step-by-Step Solution

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of them,

We will start by simplifying the expression inside the parentheses and calculate the result of the subtraction within them, then - since division comes before subtraction, we will first perform the division operation and then perform the subtraction operation:

10(104):2=106:2=103=7 10-(10-4):2= \\ 10-6:2= \\ 10-3= \\ 7

Therefore, the correct answer is answer B.

Answer

7

Exercise #17

(126+9)×(7+3)= (12-6+9)\times(7+3)= ?

Video Solution

Step-by-Step Solution

According to the order of operations, we will first solve the expressions in parentheses and then multiply:

(126+9)=(6+9)=15 (12-6+9)=(6+9)=15

(7+3)=10 (7+3)=10

Then solve the multiplication exercise:

15×10=150 15\times10=150

Answer

150 150

Exercise #18

(30+6):4×3= (30+6):4\times3=

Video Solution

Step-by-Step Solution

According to the order of operations, first we solve the exercise within parentheses:

30+6=36 30+6=36

Now we solve the exercise

36:4×3= 36:4\times3=

Since the exercise only involves multiplication and division operations, we solve from left to right:

36:4=9 36:4=9

9×3=27 9\times3=27

Answer

27

Exercise #19

(8:4:2)31= (8:4:2)-3-1=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, we first solve the exercise within parentheses from left to right:

8:4=2 8:4=2

2:2=1 2:2=1

Now we get the exercise:

131= 1-3-1=

We solve the exercise from left to right:

13=2 1-3=-2

21=3 -2-1=-3

Answer

3-

Exercise #20

8:2(2+2)= 8:2(2+2)=

Video Solution

Step-by-Step Solution

Let's start with the part inside the parentheses. 

2+2=4 2+2=4
Then we will solve the exercise from left to right 

8:2=4 8:2=4
4×(4)=16 4 × (4)=16

The answer: 16 16

Answer

16