Review of Basic Operations
Review of Basic Operations: Sharpening Your Math Skills
This chapter serves as a refresher on the fundamental mathematical operations of addition, subtraction, multiplication, and division with whole numbers. It also delves into the order of operations (PEMDAS/BODMAS) and explores estimation techniques to enhance your problem-solving skills.
Refreshing Addition, Subtraction, Multiplication, and Division with Whole Numbers
These basic operations form the building blocks of mathematics. Let’s revisit each one:
i. Addition ( + ): Combines two or more whole numbers to find their total sum.
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- Example: 3 + 5 = 8 (Three plus five equals eight)
ii. Subtraction ( – ): Takes away a whole number (subtrahend) from another whole number (minuend) to find the difference.
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- Example: 10 – 4 = 6 (Ten minus four equals six)
iii. Multiplication ( x ): Repeated addition of the same whole number (multiplicand) a specific number of times (multiplier) to find the product.
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- Example: 2 x 3 = 6 (Two multiplied by three equals six)
iv. Division ( ÷ ): Separates a whole number (dividend) into equal groups (the size of each group is the divisor) and finds the number of groups.
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- Example: 12 ÷ 3 = 4 (Twelve divided by three equals four)
Properties of Operations:
Understanding these properties can simplify calculations:
- Commutative Property: The order of numbers in addition and multiplication does not affect the result. (e.g., 3 + 5 = 5 + 3; 2 x 4 = 4 x 2)
- Associative Property: Grouping does not affect the result in addition and multiplication. (e.g., (2 + 3) + 4 = 2 + (3 + 4); (2 x 3) x 4 = 2 x (3 x 4))
Practice Problems:
Solve the following problems to test your understanding:
- 7 + 8 = ( )
- 15 – 6 = ( )
- 4 x 5 = ( )
- 20 ÷ 5 = ( )
Order of Operations (PEMDAS/BODMAS)
PEMDAS (Parentheses, Exponents, Multiplication and Division from Left to Right, Addition and Subtraction from Left to Right) or BODMAS (Brackets, Orders, Multiplication and Division from Left to Right, Addition and Subtraction from Left to Right) is a set of rules that determines the order in which mathematical operations should be performed within a single expression. Following this order ensures you get the correct answer.
Example:
3 + 2 x 4 = ?
According to PEMDAS, we perform multiplication first:
3 + (2 x 4) = 3 + 8
Then, we perform addition:
3 + 8 = 11
Therefore, 3 + 2 x 4 = 11
Practice Problems:
Solve the following problems using PEMDAS:
- (5 + 3) x 2 = ( )
- 10 – 2 x 3 = ( )
- 8 ÷ 2 + 4 = ( )
- 12 + 3 ^ 2 = ( ) (Remember: Exponents come before multiplication)
Estimating Calculations and Rounding Techniques
Estimation helps approximate answers before performing exact calculations. It can save time and identify potential errors in calculations. Here are some rounding techniques for estimation:
- Rounding to the nearest ten: Look at the tens digit. If the ones digit is 5 or greater, round up the tens digit by 1. If the ones digit is less than 5, round down the tens digit.
- Rounding to the nearest hundred: Look at the tens and ones digits. If the tens and ones digits are both 5 or greater, round up the hundreds digit by 1. Otherwise, round down the hundreds digit.
Example:
Estimate the sum: 345 + 278
- Round 345 to 350 (nearest ten)
- Round 278 to 300 (nearest hundred)
- Estimate: 350 + 300 = 650
Practice Problems:
Estimate the following:
- 721 – 189 (Round to nearest hundred)
- 4 x 13 (Round to nearest ten)
- 87 ÷ 6 (Round to nearest ten)
By revisiting these fundamental operations, understanding the order of operations, and utilizing estimation techniques, you’ll be well-equipped to tackle more complex math problems on the H.