BODMAS in Algebra

Use of BODMAS in Algebra

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BODMAS is an acronym that stands for "Brackets, Orders/Of, Division, Multiplication, Addition, Subtraction". In this regard, it's tell us what operation to solve first in an algebraic expression containing various operations.

Below are the steps to follow when solving operations in algebra through BODMAS:

1. Solve brackets first.

2. Solve power/roots next.

3. Solve division or multiplication from left to right. In essence, when an algebraic question has division and multiplication in it, solve the operation that comes first (left) before that which comes last (right.)

4. Solve addition or subtraction from left to right. In essence, when an algebraic question has addition and subtraction in it, solve the operation that comes first (left) before that which comes last (right.)

Please read on addition and subtraction in algebra here.

 

Below is a summarized application of the rule of BODMAS:

• Step 1: First simplify inside brackets: Consider this expression: 5 (x + 3). According to BODMAS, you are to first simplify the x + 3 (inside the bracket) before multiplying the simplified product by 5.

• Step 2: Simplify powers/roots: For example, in the expression 5x² + 3; first calculate for x² before multiplying by 5.

• Step 3: Simplify division or multiplication (from left to right) before addition or subtraction. For example, In 8 + 4 × 6 ÷ 2, first simplify 4 × 6 (because multiplication appears left), then divide the result by 2 before adding your answer to 8. This makes our final answer is 20

• Step 4: Simplify addition or subtraction (from left to right). For example, In 8 - 4 + 6, first simplify 8 - 4 (because subtraction appears left), then add 6 to the result. This gives us our final answer, and that's 10.

Please read on multiplication and division in algebra here.

The image below shows the rule of BODMAS:

Please read on word problems in fractions here.

 

The following terminologies are crucial when solving algebraic expressions.

• Variables: These are alphabets like 'x, y, z' that represent unknown numbers, and are manipulated to solve for unknown values.

•  Like Terms: These are terms with identical variable(s) raised to the same power. For example, in the expression 4x + 4x² - 2x ÷ 5 × 2x² + 3; the like terms are: (4x and 2x), (4x² and 2x²), (5 and 3) respectively. An understanding of this is very important. Also, take note of the 'plus or minus' sign present in front of the the variable or coefficient when collecting like terms.

• Coefficients: These are numbers in front of the variables. For example 2 is the coefficient in the expression 2x².

Please read on multiplication and division in fractions here.

 

It is also very important to understand how the various operations work in algebra. These are summarized below:

• Addition:

a + a = 2a

2a + 2a = 4a

2a + a = 3a

3a + 1 = 3a + 1

3a + 3b = 3a + 3b

 

• Subtraction

a - a = 0

5a - 2a = 3a

2a - a = a

3a - 1 = 3a - 1

3a - 3b = 3a - 3b

 

• Multiplication 

a × a = a²

2a × 2a = 4a²

2a × a = 2a²

3a × 2 = 6a

3a × 3b = 9ab

 

• Division

a ÷ a

Answer = 1

 

4a ÷ 2a

Answer = 2a

 

3a ÷ 3b

Answer = a/b

Please read on expressing one quantity as a percentage of another here.

You can read on types of angle pairs here.

 

Finally, the following multiplication outcomes on the addition and subtraction operations are important, especially when opening brackets: These are:

• (Plus × Plus) + × + = +

• (Plus × Minus) + × - = -

• (Minus × Plus) - × + = -

• (Minus × Minus) - × - = +

Please read on angles based on degree measurements here.

 

Note: When a negative sign (minus) or a positive sign (plus) appears before a bracket, we would multiply the specific sign with the contents of the bracket. The multiplication rule had been stated in the above paragraph.

• Once again, it is noteworthy to state that BODMAS is a rule in mathematics that helps us consistently solve multiple operations, alongside variables in complex algebraic expressions by simplifying the expression; thus ensuring everyone arrives at the same correct answer. 

Please read on linear equation in mathematics here.

 

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Worked Examples on Algebra through BODMAS

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Note: All the examples below were solved by the application of the BODMAS rules as explained above. So make sure to understand these rules.

 

Example 1

• Simplify 16a × 2 - 3 + 14a ÷ 7

Solution 

• Solve for multiplication 

32a - 3 + 14a ÷ 7

• Solve for division

32a - 3 + 2a

• Simplify like terms

32a + 2a - 3

• Answer: 34a - 3

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Example 2

• Simplify 7 × 3q - (3a + 5a) × 2

Solution 

• Simplify inside bracket

7 × 3a - (8a) × 2

• Open simplified bracket by multiplying with the minus sign

7 × 3a -  8a × 2

• Solve for multiplication 

21a - 16a

• Simplify like terms 

• Answer: 5a

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Example 3

• Simplify 11x + 24x ÷ 3

Solution 

• Solve for division 

11x + 8x

• Simplify like terms

• Answer = 19x

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Example 4

• Simplify 18y ÷ 9 - 5y + 3 × 4y

Solution 

• Solve for division 

2y - 5y + 3 × 4y

• Solve for multiplication 

2y - 5y + 12y

• Subtract like terms

-3y + 12y

• Simplify like terms

• Answer = 9y

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Example 5

• Simplify 9 + (5 - 2)

Solution 

• Simplify inside bracket 

9 + (3)

• Open simplified bracket by multiplying with the plus sign

9 + 3

• Simplify like terms

• Answer = 12

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Example 6

• Simplify 2a + (3a + 2b)

Solution 

• Open bracket by multiplying its contents with the plus sign

2a + 3a + 2b

• Simplify like terms

• Answer = 5a + 2b

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Example 7

• Simplify 11x + (13x - 9y)

Solution 

• Open the bracket by multipling its content with the plus sign

11x + 13x - 9y

• Simplify like terms

• Answer = 24x - 9y or 3(8x - 3y)

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Example 8

• Simplify (6x + 5y) + (3y + 4x)

Solution 

• Open both brackets by multiplying their contents with the signs before them

6x + 5y + 3y + 4x

• Collect like terms and simplify

6x + 4x + 5y + 3y

• Answer = 10x + 8y or 2(5x + 4y)

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Example 9

• Simplify 7x - (3x + 4)

Solution 

• Open bracket by multiplying its content with the minus sign before it

7x - 3x - 4

• Simplify like terms 

• Answer = 4x - 4 or 4(x - 1)

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Example 10

• Simplify 11a - (7b - 3a)

Solution 

• Open bracket by multiplying its content with the minus sign before it

11a - 7b + 3a

• Collect like terms and simplify

11a + 3a - 7b

• Answer = 14a - 7b or 7(2a - b)

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Example 11

• Simplify (6x - y) - (7x - 2y)

Solution 

• Open brackets by multiplying its content with the signs before them

6x - y - 7x + 2y

• Collect like terms and simplify

6x - 7x - y + 2y

• Answer = -x + y or y - x

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Example 12

• Simplify (6x + 5y) - (3y + 4x)

Solution 

• Open brackets by multiplying its content with the signs before them

6x + 5y - 3y - 4x

• Collect like terms and simplify

6x - 4x + 5y - 3y

• Answer = 2x + 2y or 2(x + y)

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Example 13

• Simplify - (2a - b) + (a + b)

Solution 

• Open brackets by multiplying its content with the signs before them

-2a + b + a + b

• Collect like terms and simplify

-2a + a + b + b

• Answer = -a + 2b or 2b - a

You can read on the conversion of percentages to fractions here.

Please read on prime factors and index notation here.

You can read on number base conversion here.

 

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Assignment on Algebra using BODMAS

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Simplify the following:

• 18 - 6 × 2

• 12 ÷ 4 + 2

• 6 - 8 ÷ 13

• 4 × 5 + 8 ÷ 4

• 16 ÷ 2 - 3 × 2

• 1 - y × 0

• 6a × 4 - 2a × 7

• 3 × 5x + 4x - 2

• 4 × 8x + 7x × 3

• 6u × 5 - 3 × 4u - 2u

• 24x ÷ 6 + x + 1 × 5x

• 7x - 3 × 4x + 5x × 2

• 8v × 2 + 5v ÷ 5 - 12v

• 7a × 2 × 5 × 8a - 6a × 9

• 5 × 6x - 4x × 0 - 7x × 4

• 6a + (3a - 2b)

• (3a + 8b) + 8a

• 2 + (5a - 9)

• (4x - 5y) + 11y

• (2p - 6q) - q

• (3a + 2) + (5a + a)

• (7 + 3n) + (1 - n)

• (2x + 4) + (1 - x)

• (x - 3y) + (x - 3y)

• (13x - 4y) + (5x - 8y)

• 6x - (x + 11y)

• 2 - (4n - 5)

• 7n - (m + n)

• 4a - (3 - a)

• (8x + 3y) - (4x + y)

• a - 2a - (4 + 3a)

• (14x + 5y) - 7x - 6y

• (6x - y) - (4x - 5y)

• (4x - 2) - (3x - 2)

• (13a - 5b) - (7a + 10b)

Please read on mathematics week 10 topic for jss1 first term here.

Please read on mathematics scheme of work for jss1 first term here.