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Operations: Parenthesis

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Operations: Parenthesis
CCSS.MATH.CONTENT.3.OA.B.5

Basics on the topic Operations: Parenthesis

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Operations in Math – Parentheses

Have you ever heard of parentheses in math and why they are important? If you want to find out the answer to this question, continue reading. This text teaches you everything you need to know about the importance, meaning and definition of math parentheses as well as the rules for applying them.

What Do the Parentheses Mean in Math?

So what are parentheses used for in math? Parentheses in math tell you to solve inside the parentheses first. It is important to follow the rules of parentheses in math because your solution can be incorrect if you don’t!

The steps to solve problems with numbers in parentheses in math are:

  • Solve inside the parentheses.
  • Rewrite the equation.
  • Repeat until all parentheses are solved.
  • Solve the equation.

Parentheses in Math – Example

Now you know the definition of parentheses in math, we can work through an example. Below is a problem which we will first solve by ignoring the parentheses rule. Afterwards, we will be following the parentheses rule to show how the solution is affected by parentheses.

Parentheses example

For the left side, we will ignore the parentheses. We would first solve 8 subtract 2, which gives us 6. From here, we move down the plus 6, and solve 6 + 6. This gives us a solution of 12.

Solution with ignoring parentheses

For the right side however, we will solve inside the parentheses. What does parentheses around a number mean again in math? Remember, it means we must solve it first! Two plus 6 is inside the parentheses, which is 8. We move this down, and move our 8 down too. This gives us 8 subtract 8 to find the solution, which is 0.

Solution inside parantheses

Now comparing both, we see that the left side solution is incorrect because we ignored the parentheses rule. The right side solution is correct because we did follow the rules for parentheses. This is why it is important to always solve inside the parentheses first!

Incorrect and correct solution

Parentheses in Math – Summary

Do Don’t
solve inside the parentheses first → correct solution of equation ignore the parentheses → incorrect solution of equation

Next to this text you will find parentheses math worksheets and practice problems to support your learning. They can help you memorize to always solve inside the parentheses first before you solve anything else.

Transcript Operations: Parenthesis

Mr. Squeaks is working on some blueprints for a hot air balloon and Imani has already gathered the materials needed. To know how many pieces of cardboard and how many balloons are needed Mr. Squeaks needs to solve problems with parentheses. Operations: Parentheses. Parentheses are rounded brackets. They show what needs to be solved first in an equation. Let's look at the steps to follow when solving equations with parentheses. First, solve inside the parentheses. Second, rewrite the equation. Repeat step one and two until all parentheses are solved. Finally, solve the equation. Parentheses are mostly used in multi-step problems like this. Parentheses are important, because if you don't solve them first, the solution will be wrong. Let me show you why it is important to solve parentheses first. Let's solve this equation first, ignoring the parentheses. If you ignore these parentheses, we solve eight minus two, which is six. Then solve six plus six, which gives a sum of twelve. Now let's look at this equation, following the rules for parentheses. This time, we look at the parentheses here. Inside here we need to find the sum of two plus six which is eight. Now we can leave the parentheses out, and rewrite the equation. Next, find eight subtract eight which equals zero. What do you notice? This solution is incorrect, because we didn't solve inside the parentheses first. This solution is correct, because we followed the steps for solving parentheses first. This is why solving inside the parentheses first is very important. Now you can solve problems with parentheses, let's help Mr. Squeaks calculate the number of cardboard pieces needed. The equation we need to solve is fifteen divided by one plus two, with one plus two in parentheses. What is your first step? Solve inside the parentheses first, so find the sum of one and two. The sum is three, and we rewrite the equation below. Do you know what fifteen divided by three equals? Fifteen divided by three is five. Mr. Squeaks needs five pieces of cardboard to make the basket. Now let's help Mr. Squeaks calculate how many balloons are needed. However, the balloons equation has multiple steps, which is why solving all parentheses first is important. The equation given is ten plus two divided by three minus one, with ten plus two in parentheses, and three minus one in parentheses. What is your first step? First you solve inside the left parentheses, which is ten plus two. What is the sum of ten plus two? The sum is twelve, so rewrite the equation below. What is your next step? Solve the remaining parentheses. Do you know what three minus one is? Three minus one equals two. What should you do next? You need to rewrite your equation underneath. There are no more parentheses, so you can find the solution. Do you know what twelve divided by two is? Twelve divided by two is six, so Mr. Squeaks needs six balloons for the hot air balloon. Remember, when solving equations with parentheses, first solve inside the parentheses. Second, rewrite the equation. Repeat step one and two until all parentheses are solved, and finally, solve the equation. Wow, it looks like Mr. Squeaks has his hot air balloon built and ready to go. The hot air balloon looks like it's a great success. Uh oh, is that a swarm of wasps? This doesn't look like it will end well. Phew, it sure is a good job Imani can fly!

Operations: Parenthesis exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Operations: Parenthesis.
  • What's the correct order?

    Hints

    When an expression includes parentheses, that is the first step.

    After solving inside the parentheses, rewrite the new equation.

    Sometimes, there are more than one set of parentheses to solve.

    Solution

    First, solve inside the parentheses

    Then, rewrite the equation

    Next, repeat until all parentheses solved

    Finally, solve to get the final answer

  • Complete the steps to solve the problem.

    Hints

    When an expression contains parentheses, first solve the expression in the parentheses.

    Then, rewrite the expression.

    Finally, solve the rest of the expression.

    Solution

    3 x ( 1 + 4):

    First, add the numbers 1 and 4. Now the expression reads 3 x 5. Then, multiply to get a final value of 15.

  • Solve the equations.

    Hints

    First, find the expression in the parentheses and solve it.

    After solving the expression in the parentheses, solve the rest of the expression from left to right.

    Solution

    Solve each equation by completing the parenthesis first.

    6 $\div$ (7 - 5) = 3

    First, subtract 5 from 7 since that is in the parentheses: 6 $\div$ 2. Then, divide 6 by 2 to complete solving the expression: 3.

    3 x (9 - 6) + 4 = 13

    First, subtract 6 from 9 since that is in the parentheses: 3 x 3 + 4. Next, multiply 3 and 3 to start solving the rest of the expression: 9 + 4. Finally, add 9 and 4 to complete solving the expression: 13.

    19 - (3 + 2) + (5 + 3) = 22 First, add 3 and 2 since that is in the parentheses: 3 + 2 = 5. Next, add 5 and 3 since that is also in parentheses: 5 + 3 = 8. Then, subtract 5 from 19 to start solving the rest of the expression: 19 - 5 = 14. Finally, add 14 and 8 to complete solving the rest of the expression: 14 + 8 = 22.

    (8 + 2) $\div$ (14 - 9) = 2 First, add 8 and 2 since that is in parentheses: 8 + 2 = 10. Next, subtract 9 from 14 since that is also in parentheses: 14 - 9 = 5. Finally, divide 10 by 5 to complete solving the rest of the expression: 10 $\div$ 5 = 2.

  • Solve each problem.

    Hints

    First, solve the expression inside the parentheses.

    Then, solve the rest of the expression from left to right.

    Solution

    18 $\div$ (6 + 3)

    • (6 + 3) = 9
    • 18 $\div$ 9 = 2
    • So, 18 $\div$ (6 + 3) = 2
    (18 $\div$ 6) + 3
    • (18 $\div$ 6) = 3
    • 3 + 3 = 6
    • So, (18 $\div$ 6) + 3 = 6
    (11 - 9) x (10 - 7)
    • (11 - 9) = 2
    • (10 - 7) = 3
    • 2 x 3 = 6
    • So, (11 - 9) x (10 - 7) = 6
    (11 - 9) x 10 - 7
    • (11 - 9) = 2
    • 2 x 10 = 20
    • 20 - 7 = 13
    • So, (11-9) x 10 - 7 = 13

  • Highlight the first step to solve each problem.

    Hints

    Make sure to highlight both numbers and the operation that is completed first.

    For example, in 5 - (3 + 1), the 3, +, and 1 should all be highlighted.

    When an expression includes parentheses, the first step is to solve inside the parentheses.

    Solution

    For each problem, find the expression that is in the parentheses. Then, highlight the numbers and operation in the expression in the parentheses.

  • Solve each problem.

    Hints

    First, solve the expression inside the parentheses.

    Then, rewrite the equation and solve any other expressions in parentheses.

    After rewriting the equation with no parentheses, solve the rest from left to right to get your final answer.

    Solution

    2 x (6 + 4)

    • (6 + 4) = 10
    • 2 x 10 = 20
    • So, 2 x (6 + 4) = 20
    9 $\div$ (10 - 7) + 1
    • (10 - 7) = 3
    • 9 $\div$ 3 = 3
    • 3 + 1 = 4
    • So, 9 $\div$ (10 - 7) + 1= 4
    (8 + 6) $\div$ 2
    • (8 + 6) =14
    • 14 $\div$ 2 = 7
    • So, (8 + 6) $\div$ 2 = 7
    (3 + 5) $\div$ (15 - 13)
    • (3 + 5) = 8
    • (15 - 13) = 2
    • 8 $\div$ 2 = 4
    • So, (3 + 5) $\div$ (15 - 13) = 4