Number Sense and Operations - Grade 7
Number Sense and Operations are fundamental concepts in mathematics that help you understand how numbers work and how to manipulate them. This webpage will guide you through key concepts such as place value, operations with integers, and the order of operations.
1. Place Value
Place value is the value of each digit in a number based on its position. For example, in the number 345, the digit 3 is in the hundreds place, the digit 4 is in the tens place, and the digit 5 is in the ones place.
Example: The number 789 can be broken down as follows:
- 7 is in the hundreds place, so it represents 700.
- 8 is in the tens place, so it represents 80.
- 9 is in the ones place, so it represents 9.
Therefore, 789 = 700 + 80 + 9.
2. Operations with Integers
Integers are whole numbers that can be positive, negative, or zero. Operations with integers include addition, subtraction, multiplication, and division. Understanding these operations is crucial for solving various mathematical problems.
Example: Adding and subtracting integers:
- 5 + (-3) = 2 (Think of it as moving 3 steps backward from 5, which lands you at 2.)
- 7 - (-4) = 11 (Subtracting a negative is the same as adding a positive, so 7 + 4 = 11.)
3. Order of Operations
The order of operations is a rule that tells you the correct sequence of steps to solve a mathematical expression. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) is often used to remember this order.
Example: Solve the expression 3 + 6 × 2 ÷ (1 − 5)².
Step-by-step solution:
- Parentheses: (1 − 5) = -4
- Exponents: (-4)² = 16
- Multiplication and Division: 6 × 2 ÷ 16 = 12 ÷ 16 = 0.75
- Addition: 3 + 0.75 = 3.75
So, the answer is 3.75.
4. Rational Numbers
Rational numbers are numbers that can be expressed as a fraction of two integers. This includes all integers, fractions, and terminating or repeating decimals.
Example: Identify if the following numbers are rational:
- 0.75 (Rational, as it can be written as 3/4)
- √2 (Not rational, as it cannot be expressed as a fraction of two integers)
- -3/5 (Rational, as it is a fraction of two integers)
By mastering these concepts, you will gain a strong foundation in Number Sense and Operations, enabling you to tackle more complex mathematical problems with confidence.