Many teachers do not emphasize “order of operation”, but “order of operations” is very important. Without knowing order of operations well, you do not know how to solve a math problem.
Some examples are given in the following, There are also worksheets for you to work on after you understand the examples.
Order of operations ( in order to make the explanation easy to understand, simple numbers are used)
Without any other operations in an expression: Addition and subtraction are equal operations in the way that is “first come, first served” from left to right:
Without any other operations in an expression: multiplication and division are equal operations in the way that is “first come, first served” from left to right:
= 2 ×3
When an expression has addition and (or) subtractions with multiplication and (or) divisions in it, multiplications and ( or divisions) should be done first; additions and (or) subtractions should be done afterwards.
2+ 4 ×5 – 3×7
=2+ 20- 21
When an expression has parenthesis first, the operations in the parenthesis should be done first and other operations need to follow the rules above.
2+ 4 × (5 – 3) ×7 (operation in the parenthesis is done first)
=2+4 × 2×7 (multiplication is done before addition)
=2+ 8 × 7 (first multiplication is done , now let’s do the second multiplication)
Worksheets for you to work on
Can you solve this problem?
1/8 of a stick is cut off. If If another stick that is 15 inches long is glued to the remaining part of the first stick, the first stick will be 1/2 longer than its original length. What is the original length of the first stick?
In this problem, you need to find the match between the fractional part and the amount in it ( if you do not know about these terms, please go to Word Problem: Detailed Explanations of Reasoning and Solving Strategies Volumes 11-A, 11-B and 12)
15 inches not only has covered 1/8 of the stick that is cut off but also makes the the stick 1/2 longer so we can say that 15 inches match the sum of the fractional parts: 1/8 and 1/2.
We divide the sum of the fractional parts: 1/8+1/2=5/8 into the amount that matches it: 15 inches to find the amount in 1, which is the length of the original stick: ( please go to the books Word Problem: Detailed Explanations of Reasoning and Solving Strategies Volumes 11-A, 11-B and 12 for more detailed explanation):
The original stick is 24 inches.
Look at the following equations:
1. 70 x 4=280
2. 70 x 40=2,800
3. 700 x 4=2,800
4. 700 x 40=28,000
5. 7,000 x 40=280,000
What can we learn from the above equations?
All the equations have four numbers in common: 7 , 4 , their products, 28 and 0’s.
Here is the trick: when you try to get the answer of 7,000 x 40, you only need to take two steps:
First: Find the product of 7 and 4, which is 28;
Secondly: count the number of 0’s in both 7,000 and 40, which is 4; put the four 0’s after 28.
Therefore, the product of 7,000 and 40 is 280,000
The last thing that you want to do is to multiply 0’s by 0’s in the numbers.