How to Do Grade 9 Mathematical Processes
Do Operations with fractions., Do Operations with Integers., Follow the Order of Operations (B.E.M.D.A.S., Focus on Problem Solving When you solve problems in mathematics, or in other subjects, a specific process helps you to organize your...
Step-by-Step Guide
-
Step 1: Do Operations with fractions.
Add and Subtract.
Fractions can only be added, or subtracted, if they have the same denominator, otherwise the answer is incorrect.
For example, 2/5 + 1/5 = 3/5.
To add or subtract fractions with different denominators, the first step is to find the lowest common denominator.
For example, 3/4 + 1/2 = 3/4 + 1X2/2X2 = 3/4 + 2/4 = 5/4 or 1 1/4 3/4
- 1/3 = 3X3/4X3
- 1X4/3X4 = 9/12
- 4/12 = 5/12 Multiply.
To multiply fractions, divide the numerator and the denominator by any common factors.
Any mixed numbers should first be converted to improper fractions.
To divide by a fraction, multiply by its reciprocal. /9 X 3/4 = 8/9 X 3/4 = 2/3 X 1/1 = 2/3 1/2 \ 6/7 = 7/2 \ 6/7 = 7/2 \ 7/6 the reciprocal of 6/7 is 7/6.* = 49/12 12 \ 49 = 4 R
1.* = 4 1/12 -
Step 2: Do Operations with Integers.
an integer number line and integer chips are tools that can help you understand operations with integers.
You may also think in terms of profit and loss.
Add Integers:
-2 + 5 = 3 OR 2 + (-6) =
-4 Subtract Integers:
-4
-9 =
-4 + (-9) OR 3
-10 = 3 + (-10) =
-13 =
-7 OR
-2
- (-4) =
-2 + 4 = 2 Multiply or Divide Integers:
X (-5) =
-45 OR
-6 X (-7) = 42 OR 20 \ (-4) =
-5 OR
-16 \ (-2) = 8 , or P.E.M.D.A.S.) B
-- Brackets (parentheses) E
-- Exponents D
-- Division and M
-- Multiplication, in order from left to right.
A
-- Addition and S
-- Subtraction, in order from left to right. (15
- 18) = 2(-3) =
-6
- 3(4² + 10) = 7
- 3(16 + 10) = 7
- 3(26) = 7
- 78 =
-71 , This way, you can clearly understand the problem, devise a strategy, carry out the strategy, and reflect on the results. , You may use other strategies too.
Make an Organized List Look for a Pattern Work Backward Draw a Diagram Select a Tool Use Systematic Trial Use Logic or Reasoning ,, Pennies are laid out in a triangular pattern; the first triangular pattern has two on the base, 1 on top.
The second has three on the base, 2 in the middle, 1 on top.
The third has four on the bottom, three on the next line, two on the next one, and one on top.
How many pennies do you need to form a triangle with 10 pennies in its base? , Read it again.
Express it in your own words.
A possible strategy is to identify and continue the pattern started in the diagram.
Copy the diagram into your notebook. , Describe how the pattern develops.
Use your description to extend it to a triangle with a base of 10 pennies.
Record your numbers in a table with the following headings: "Diagram Number" and "Number of Pennies". , Can you find another pattern that could help you solve this problem? , identify and describing a pattern is a strategy that can be use when a sequence of operations or diagrams occurs.
When solving a problem, you will often use more than strategy.
Here are some problems solving strategies:
Draw a diagram.
Work backward.
Make a model.
Make an organized list.
Look for a pattern.
Find needed information.
Act it out. ,, Solve a similar but simpler problem. , We currently represent numbers using the numerals 0, 1, 2, and so on.
Ancient civilizations used different symbols to represent numbers. , How can you represent numbers with ancient symbols? about 5000 years ago, the ancient Egyptians used symbols to represent numbers. (See image.) How would the Egyptians represent the numbers 13, 126, and 1291? EXAMPLE Use a Diagram to Communicate ,, Communication can take the form of words, diagrams, and symbols. ,,,,, You can make connecting mathematics to real life easier by drawing a diagram to illustrate the situation.
You can then use the diagram to help you solve the problem.
You can also use other strategies, such as making an organized list or looking for a pattern. , For example, to find the amount of paint needed, you would use measurement, geometry, and number skills. ,,, =P) -
Step 3: Follow the Order of Operations (B.E.M.D.A.S.
-
Step 4: Focus on Problem Solving When you solve problems in mathematics
-
Step 5: or in other subjects
-
Step 6: a specific process helps you to organize your thoughts.
-
Step 7: Consider the following strategies when you are developing mathematical solutions to problems.
-
Step 8: Investigate How can a pattern help you solve a problem?
-
Step 9: Make an organized list or table.
-
Step 10: read the problem above.
-
Step 11: Extend the pattern.
-
Step 12: Explain how you used the pattern to solve the problem.
-
Step 13: Find the Key Concepts Making an organized list or chart is a strategy that helps you to organize your thoughts and to see the information in an organized way.
-
Step 14: Use systematic trial.
-
Step 15: Use a formula.
-
Step 16: Focus on Communicating People have been communicating for thousands of years--that includes communicating mathematically.
-
Step 17: Investigate.
-
Step 18: Key Concepts
-
Step 19: -It is important to be able to communicate clearly in mathematics.
-
Step 20: Use mathematical vocabulary when explaining your strategies.
-
Step 21: -Use correct mathematical form when using symbols and simplifying expressions.
-
Step 22: -Draw neat
-
Step 23: fully labeled diagrams to illustrate a situation.
-
Step 24: Focus on Connecting
-
Step 25: Situations in real life often involves problems that you can solve using mathematical processes.
-
Step 26: in solving problems
-
Step 27: you need to make connections among different areas of mathematics.
-
Step 28: Investigate
-
Step 29: how can you represent different representations of a problem?
-
Step 30: (Not finished yet.
Detailed Guide
Add and Subtract.
Fractions can only be added, or subtracted, if they have the same denominator, otherwise the answer is incorrect.
For example, 2/5 + 1/5 = 3/5.
To add or subtract fractions with different denominators, the first step is to find the lowest common denominator.
For example, 3/4 + 1/2 = 3/4 + 1X2/2X2 = 3/4 + 2/4 = 5/4 or 1 1/4 3/4
- 1/3 = 3X3/4X3
- 1X4/3X4 = 9/12
- 4/12 = 5/12 Multiply.
To multiply fractions, divide the numerator and the denominator by any common factors.
Any mixed numbers should first be converted to improper fractions.
To divide by a fraction, multiply by its reciprocal. /9 X 3/4 = 8/9 X 3/4 = 2/3 X 1/1 = 2/3 1/2 \ 6/7 = 7/2 \ 6/7 = 7/2 \ 7/6 the reciprocal of 6/7 is 7/6.* = 49/12 12 \ 49 = 4 R
1.* = 4 1/12
an integer number line and integer chips are tools that can help you understand operations with integers.
You may also think in terms of profit and loss.
Add Integers:
-2 + 5 = 3 OR 2 + (-6) =
-4 Subtract Integers:
-4
-9 =
-4 + (-9) OR 3
-10 = 3 + (-10) =
-13 =
-7 OR
-2
- (-4) =
-2 + 4 = 2 Multiply or Divide Integers:
X (-5) =
-45 OR
-6 X (-7) = 42 OR 20 \ (-4) =
-5 OR
-16 \ (-2) = 8 , or P.E.M.D.A.S.) B
-- Brackets (parentheses) E
-- Exponents D
-- Division and M
-- Multiplication, in order from left to right.
A
-- Addition and S
-- Subtraction, in order from left to right. (15
- 18) = 2(-3) =
-6
- 3(4² + 10) = 7
- 3(16 + 10) = 7
- 3(26) = 7
- 78 =
-71 , This way, you can clearly understand the problem, devise a strategy, carry out the strategy, and reflect on the results. , You may use other strategies too.
Make an Organized List Look for a Pattern Work Backward Draw a Diagram Select a Tool Use Systematic Trial Use Logic or Reasoning ,, Pennies are laid out in a triangular pattern; the first triangular pattern has two on the base, 1 on top.
The second has three on the base, 2 in the middle, 1 on top.
The third has four on the bottom, three on the next line, two on the next one, and one on top.
How many pennies do you need to form a triangle with 10 pennies in its base? , Read it again.
Express it in your own words.
A possible strategy is to identify and continue the pattern started in the diagram.
Copy the diagram into your notebook. , Describe how the pattern develops.
Use your description to extend it to a triangle with a base of 10 pennies.
Record your numbers in a table with the following headings: "Diagram Number" and "Number of Pennies". , Can you find another pattern that could help you solve this problem? , identify and describing a pattern is a strategy that can be use when a sequence of operations or diagrams occurs.
When solving a problem, you will often use more than strategy.
Here are some problems solving strategies:
Draw a diagram.
Work backward.
Make a model.
Make an organized list.
Look for a pattern.
Find needed information.
Act it out. ,, Solve a similar but simpler problem. , We currently represent numbers using the numerals 0, 1, 2, and so on.
Ancient civilizations used different symbols to represent numbers. , How can you represent numbers with ancient symbols? about 5000 years ago, the ancient Egyptians used symbols to represent numbers. (See image.) How would the Egyptians represent the numbers 13, 126, and 1291? EXAMPLE Use a Diagram to Communicate ,, Communication can take the form of words, diagrams, and symbols. ,,,,, You can make connecting mathematics to real life easier by drawing a diagram to illustrate the situation.
You can then use the diagram to help you solve the problem.
You can also use other strategies, such as making an organized list or looking for a pattern. , For example, to find the amount of paint needed, you would use measurement, geometry, and number skills. ,,, =P)
About the Author
Ryan Tucker
Specializes in breaking down complex crafts topics into simple steps.
Rate This Guide
How helpful was this guide? Click to rate: