Operations: Brackets
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Basics on the topic Operations: Brackets
Operations: Brackets in Maths
In this video, Mr. Squeaks is working on some blueprints for a hot air balloon. His equations include the use of brackets in maths. First, Mr. Squeaks learns how to use brackets in maths, brackets in maths rules, and learns the answer to the question what do brackets mean in maths? After following the rules of brackets in maths, Mr. Squeaks is able to successfully build his hot air balloon and takes a flight with Imani!
Using Brackets in Maths
What are brackets in maths? Brackets in maths are used so you know you need to solve inside the brackets FIRST. This is what the definition of brackets in maths teaches us. It is important to follow the rules of brackets in maths because your solution can be incorrect if you don’t!
The steps to solve problems with numbers in brackets in maths are:
- Solve inside the brackets.
- Rewrite the equation.
- Repeat until all brackets are solved.
- Solve the equation.
Brackets in Maths Equations
Now you know the definition of brackets in maths, we can work through an example! Below is a problem which we will solve by ignoring the brackets rule, and then following the brackets rule, to show how the solution is affected by brackets.
For the left side, we will ignore the brackets. 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.
For the right side, we will solve inside the brackets first. What does brackets around an equation mean in maths? Remember, it means we must solve it first! 2 plus 6 is inside the brackets, which is 8. We move this down, and also move our 8 down too. This gives us 8 subtract 8 to find the solution, which is 0.
Now comparing both, we see that the left side solution is INCORRECT because we ignored the brackets rule. The right side solution is CORRECT because we did follow the rules for brackets. This is why it is important to ALWAYS solve inside the brackets first!
Brackets in Maths Summary
Remember, when thinking about how to work out brackets in maths, ask yourself ‘What do brackets mean in maths?’ It is important to always solve inside the brackets FIRST before you solve anything else.
Below you will find practice problems and using brackets in maths KS2 worksheets to support your learning.
Transcript Operations: Brackets
Mr. Squeaks is working on some plans 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 brackets. "Operations: Brackets"
Brackets or parentheses look like this. They show what needs to be solved FIRST in an equation. Let's look at the steps to follow when solving equations with brackets. First, "solve inside the brackets". Second, "rewrite the equation". "Repeat" step one and two "until ALL brackets are solved". Finally, "Solve the equation". Brackets are mostly used in multi-step problems like THIS. Brackets 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 brackets first! Let's solve THIS equation first, ignoring the brackets. If you ignore THESE brackets, 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 brackets. This time, we look at the brackets HERE. Inside here we need to find the sum of TWO plus SIX, which is EIGHT. Now we can leave the brackets 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 brackets first. THIS solution is CORRECT because we followed the steps for solving brackets first. This is why solving inside the brackets FIRST is very important. Now that you can solve problems with brackets, 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 brackets. What is your first step? Solve inside the brackets 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 brackets first is important. The equation given is ten plus two divided by three minus one with ten plus two in brackets AND three minus one in brackets. What is your first step?
First you solve inside the LEFT brackets, 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 brackets! 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 brackets, 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 brackets, first, "solve inside the brackets". Second, "rewrite the equation". "Repeat" step one and two "until all brackets 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's definitely a good job Imani can fly!
Operations: Brackets exercise
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What is the correct order?
HintsWhen an expression includes brackets, that is the first step.
After solving inside the brackets, rewrite the new equation.
Sometimes, there are more than one set of brackets to solve.
SolutionFirst, solve inside the brackets.
Then, rewrite the equation.
Next, repeat for all parts within brackets.
Finally, solve to get the final answer.
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Complete the steps to solve the problem.
HintsWhen an expression contains brackets, first solve the expression inside the brackets.
Then, rewrite the expression.
Finally, solve the rest of the expression.
Solution3 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.
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Solve the equations.
HintsFirst, find the expression in the brackets and solve it.
After solving the expression in the brackets, solve the rest of the expression from left to right.
SolutionSolve each equation by completing what is inside the brackets first.
6 $\div$ (7 - 5) = 3
First, subtract 5 from 7 since that is inside brackets: 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 inside brackets: 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 brackets: 3 + 2 = 5. Next, add 5 and 3 since that is also in brackets: 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 brackets: 8 + 2 = 10. Next, subtract 9 from 14 since that is also in brackets: 14 - 9 = 5. Finally, divide 10 by 5 to complete solving the rest of the expression: 10 $\div$ 5 = 2.
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Solve each problem.
HintsFirst, solve the expression inside the brackets.
Then, solve the rest of the expression from left to right.
Solution18 $\div$ (6 + 3)
- (6 + 3) = 9
- 18 $\div$ 9 = 2
- So, 18 $\div$ (6 + 3) = 2
- (18 $\div$ 6) = 3
- 3 + 3 = 6
- So, (18 $\div$ 6) + 3 = 6
- (11 - 9) = 2
- (10 - 7) = 3
- 2 x 3 = 6
- So, (11 - 9) x (10 - 7) = 6
- (11 - 9) = 2
- 2 x 10 = 20
- 20 - 7 = 13
- So, (11-9) x 10 - 7 = 13
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Highlight the first step to solve each problem.
HintsMake 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 brackets, the first step is to solve inside the brackets.
SolutionFor each problem, find the expression that is within brackets. Then, highlight the numbers and operation within the brackets.
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Solve each problem.
HintsFirst, solve the expression inside the brackets.
Then, rewrite the equation and solve any other expressions in brackets.
After rewriting the equation without brackets, solve the rest from left to right to get your final answer.
Solution2 x (6 + 4)
- (6 + 4) = 10
- 2 x 10 = 20
- So, 2 x (6 + 4) = 20
- (10 - 7) = 3
- 9 $\div$ 3 = 3
- 3 + 1 = 4
- So, 9 $\div$ (10 - 7) + 1= 4
- (8 + 6) =14
- 14 $\div$ 2 = 7
- So, (8 + 6) $\div$ 2 = 7
- (3 + 5) = 8
- (15 - 13) = 2
- 8 $\div$ 2 = 4
- So, (3 + 5) $\div$ (15 - 13) = 4
This was VERY easy and helpful👌👍