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Quick introduction to Algebra 1


Order of Operations - BODMAS

There is another article written on BODMAS available on SubjectCoach, which you can find here  

Operations means things like addition, subtraction, multiplication, division, squaring etc. but when you evaluate an expression like below

3 + (6 x 22 +3)

What part should you calculate first?

If you calculate them in wrong order, you may end up with a wrong answer. There are some rules set, when doing calculations.

 

1. Do things in brackets first.

2 x (6+1) = 2 x 7 = 14 Right
2 x (6+1) = 12 + 1 = 13 Wrong

2. Exponents (Powers and roots) are calculated next.

3 x 22 = 3 x 4 =12 Right
3 x 22 = 62 = 36 Wrong

3. Division and Multiplication are calculated next ( from left to right).

1 + 4 x 2 = 1 + 8 = 9 Right
1 + 4 x 2 = 5 x 2 = 10 Wrong

Order should be left to right as in the example below.

30 / 5 x 2 = 6 x 2 = 12 Right
30 / 5 x 2 = 30 / 10 =3 Wrong

4. Last but not least, Addition and Subtraction is calculated (from left to right).

Obey these simple rules and you will always calculate the correct answer. How do we remember all these rules? There’s an easy way to remember this.

B Brackets first
O Orders (ie Powers and Square Roots etc.)
DM Division and Multiplication (left-to-right)
AS Addition and Subtraction (left-to-right)

 

Eg1:

2 x 6 + 3 – 4 / 2 – 5 + 20 / 5 x 3 + 50

 

2 x 6 + 3 – 4 / 2 – 5 + 20 / 5 x 3 + 50 
first all multiplications and divisions from left to right 
12 + 3 – 2 – 5 + 4 x 3 + 50 
now all additions and subtractions from left to right  
12 + 3 – 2 – 5 + 12 + 50 
70 Done, 
 
you got the right answer

 

Eg2: (3 + 3 - 5) x (15 - 5) x 10-99

 

(3+3-5) x (15-5) x 10-99 
Start performing the operations inside the brackets 
1 x 10 x 10 -99 
then all the multiplications 
100 – 99 
finally subtraction.
The answer is 1.

 

Eg3: 50 / 5 – 7 x 2 + 11 + 3 x 10 / 2 – 2 + 6 x 5

 

10 – 14 + 11 + 15 – 2 + 30 
50


In next chapter onwards we will explore expressions

Description

In this tutorial we will cover Algebra 1 with examples. This is really a quick introduction to Algebra 1. This tutorial will suit students who want to check out what Algebra is all about or for students who wants to quickly brush up their Algebra knowledge

Topics for this tutorial includes

  1. Quick background on Algebra
  2. Variables and expressions
  3. Algebraic multiplication
  4. Expressions
  5. Order of operations
  6. Algebra basic definitions
  7. Commutative, Associative and Distributive Laws
  8. Manipulating Expressions
  9. Writing and interpreting expressions.
  10. Expressions adding fractions
  11. What next

This quiz is followed up with a BODMAS based quiz, which is absolutely free to take and test your knowledge.

I hope that you will enjoy this tutorial. Please leave your feedback and improvement suggestions



Prerequisites

Mathematics knowledge including pre algrebra, multiplication, subtraction, additions etc is essential

Audience

Students starting with Algebra 1 or students looking to quickly brush up their Algebra 1 knowledge.

Learning Objectives

Learn Algebra 1

Author: Subject Coach
Added on: 27th Jan 2015

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