Are you excited to know more about using parentheses in mathematics? If yes, then use this Parentheses Worksheet pdf. Parentheses is a word where we separate several things into one group or insert in a sentence to add information or explain something. Usually, in maths, we use parentheses to separate the group of numbers and to perform arithmetic operations on that particular number.

We use the BODMAS or PEMDAS rule to solve a set of mathematical operations and both BODMAS and PEMDAS have the same rules to follow but vary in names. Specially, we use parentheses in applying these rules while performing arithmetic operations. Parentheses are represented by [ ], ( ), { }.

In this free printable parentheses worksheet, you will get more problems to understand about the concept of Parentheses and how to use the numbers while grouping them with parentheses and the order of solving.

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## Parentheses Worksheets with Answers

1. Find the answers for the following numbers using Parentheses.

(i) ( 15 + 5 ) – ( 8 + 3 ) = ___

(ii) ( 6 – 2) + ( 4 – 2) = ___

(iii) ( 14 + 12 ) – ( 9 – 5 ) = ___

(iv) ( 2 + 4 ) + ( 6 + 5) = ___

(v) ( 13 – 5 ) – ( 4 + 3 ) = ___

**Solution:**

To get the correct solution for the given numbers. We have to use the BODMAS rule.

By applying the BODMAS rule, first, we perform the arithmetic operation on numbers in parentheses.

(i) 20 – 11 = **9**

(ii) 4 + 2 = **6**

(iii) 26 – 4 = **22**

(iv) 6 + 11 = **17**

(v) 8 – 7 = **1**

2. Apply the arithmetic operations for the following expressions

(i) (2 × 3) + (4 × 5) = ___

(ii) (12 × 2) – (3 × 6) = ___

(iii) (7 × 3) × (2 × 7) = ___

(iv) (6 × 4) + (4 × 3) = ___

**Solution:**

Here, we perform the operations which are in parentheses for first.

To calculate the numbers in parentheses, we should follow some rules to get the correct value of the expression.

Now, let’s see the correct solution for the given expressions using the BODMAS rule.

(i) 6 + 20 = **26**

(ii) 24 – 18 = **6**

(iii) 21 × 14 = **294**

(iv) 24 + 12 = **36**

3. Use the parentheses to make the answer true for the given problems

(i) 45 – 8 × 3 = 21

(ii) 10 – 6 + 5 = 9

(iii) 36÷9 + 12 = 16

(iv) 7 – 3 + 4 = 8

(v) 6 – 4 × 6 = 12

**Solution:**

Now, to make the given answer true we have to add the brackets or parentheses.

If we add brackets to the numbers, should apply the BODMAS rule and do the arithmetic operation for the numbers in brackets.

So, let’s apply the brackets for the numbers & find the answer is true or not.

(i) 45 – (8×3) = 45 – 24 = 21

(ii) (10-6) + 5 = 4 + 5 = 9

(iii) (36÷9) + 12 = 4 + 12 = 16

(iv) (7-3) + 4 = 4 + 4 = 8

(v) (6-4) × 6 = 2 × 6 = 12

4. From the following numbers first make number 8 and then add to the remaining numbers to get the given correct answer.

(i) 4 + 2 + 2 + 1 = 9

(ii) 3 + 2 + 4 + 2 = 11

(iii) 1 + 4 + 2 + 6= 13

(iv) 5 + 3 + 2 = 10

(v) 3 + 2 + 3 + 3 + 7 =18

**Solution:**

Let’s apply the parentheses to the given numbers

(i) { 4 + 2+ 2 } + 1 = 8 + 1 = 9

(ii) 3 + { 2 + 4 + 2 } = 3 + 8 = 11

(iii) 1 + 4 + { 2 + 6 } = 1 + 4 + 8 = 13

(iv) { 5 + 3 } + 2 = 8 + 2 = 10

(v) 3 + { 2 + 3 + 3 } + 7 = 3 + 8 + 7 = 18

5. Simplify the expression 5^{2} + ( 4 × 3 ) – 8

**Solution:**

The given expression is 5^{2} + ( 4 × 3 ) – 8.

To solve the numbers in parentheses we use the PEMDAS rule. So, apply the rule

First, we calculate the numbers in parentheses and then exponent operation.

5^{2} + ( 4 × 3 ) – 8 = 12 and 5^{2} + 12 – 8 = 25 + 12 – 8

Now, perform the addition

25 + 12 – 8 = 37 – 8

And finally, perform the subtraction

i.e., 37 – 8 = 29.

Thus, 5^{2} + ( 4 × 3 ) – 8 = **29**.

6. Solve 78÷(6×3)+15.

**Solution:**

Given 78÷(6×3)+15

We apply the BODMAS rule.

First, we need to perform the operation in brackets

i.e., 78÷(18)+15

Now, perform the division rule

i.e., 78÷18+15 = 4.33 +15

Then, perform the addition operation

4.33 +15 = 19.33

Hence, the answer for the given expression 78÷(6×3)+15 is **19.33**.

7. Calculate the expression in parentheses [54+(20-14)×(6×7)-34]

**Solution:**

Given expression is [54+(20-14)×(6×7)-34]

Here, we solve the expression using the PEMDAS. By applying this rule, first, we perform the operations that are in brackets and calculate the numbers.

Let’s see the expression, we have two parentheses here. So, perform the operation one after the other.

[54+(20-14)×(6×7)-34] = [54+(6)×(6×7)-34] = [54+6×(42)-34]

Now, perform the multiplication operation

Then, [54+6×(42)-34] = [54+252-34]

Next, do the addition

[54+252-34] = [306-34]

Lastly, do the subtraction to get the exact solution

i.e., [306-34] = [272] = 272.

Hence, the solution for the given number in parentheses is **272**.