6th Grade operations with integers: Adding, Subtracting, Multiplying, and Dividing

Do you know what integers are? Do you also know why they are important? Let’s find out together!

Integers are numbers that do not have fractions or decimals. They can be written as ... (1) or ... (-1). The symbol ℤ denotes the set of integers, and it includes all the positive and negative whole numbers and zero. For example, 5, -3, 0, 12, and -8 are all integers.

Integers are useful for representing situations that involve changes or differences. For example, if the temperature rises by 5 degrees Celsius, we can write this as +5. If the temperature drops by 3 degrees Celsius, we can write this as -3. If the temperature stays the same, we can write this as 0. Similarly, if we gain $10, we can write this as +10. If we lose $7, we can write this as -7. If we have no change in money, we can write this as 0.

In Grade 6, children are expected to learn to add, subtract, multiply, and divide integers using various methods and tools. They should also be able to apply the order of operations with integers and solve word problems involving operations with integers. Some of the specific skills that children should master by the end of Grade 6 are:

• Identify and compare integers using a number line
• Use a number line to model addition and subtraction of integers
• Use rules of signs to multiply and divide integers
• Use parentheses and brackets to group expressions with integers
• Apply the order of operations (PEMDAS) with integers
• Solve word problems involving operations with integers
• Use integers worksheets for practice and assessment

A number line is a horizontal line with numbers marked at equal intervals. It can help us visualize and perform addition and subtraction of integers. To add or subtract integers using a number line, we follow these steps:

• Locate the first integer on the number line
• Move to the right if the second integer is positive or to the left if the second integer is negative
• The distance and direction of the movement is determined by the absolute value of the second integer
• The final position on the number line is the sum or difference of the two integers

For example:

• To add 4 + (-2), we start at 4 on the number line and move 2 units to the left because -2 is negative. The final position is 2, which is the sum of 4 and -2.

   

  

   

• To subtract 4 - (-2), we start at 4 on the number line and move 2 units to the right because -(-2) is positive. The final position is 6, which is the difference of 4 and -2.

   

  

   

To multiply or divide integers, we do not need a number line. We can use rules of signs to determine the sign of the product or quotient. The rules of signs are:

• The product or quotient of two positive integers is positive
• The product or quotient of two negative integers is positive
• The product or quotient of a positive integer and a negative integer is negative
• The product or quotient of zero and any integer is zero

For example:

• To multiply 4 x (-3), we use the rule that the product of a positive integer and a negative integer is negative. Therefore, 4 x (-3) = -12.
• To divide -12 / (-3), we use the rule that the quotient of two negative integers is positive. Therefore, -12 / (-3) = 4.

The order of operations is a set of rules that tells us which operation to perform first when there is more than one operation in an expression. The order of operations is:

• Parentheses (or brackets)
• Exponents (or powers)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

The acronym PEMDAS can help us remember the order of operations.

For example, to simplify the expression 2 + (3 x -4) - (-5) / 5, we follow these steps:

• Simplify the parentheses first: 2 + (-12) - (-5) / 5
• Simplify the division next: 2 + (-12) - (-1)
• Simplify the addition and subtraction from left to right: -10 - (-1) = -9

Word problems are problems that use words to describe a situation that involves mathematics. To solve word problems involving operations with integers, we follow these steps:

• Read the problem carefully and identify the question
• Identify the given information and the unknowns
• Choose a variable to represent the unknowns
• Write an equation or expression that models the situation using the given information and the variable
• Solve the equation or expression using the appropriate operations and methods
• Check the solution by plugging it back into the equation or expression
• Write the answer in a complete sentence

For example, solve this word problem:

A submarine is at a depth of -200 meters below sea level. It ascends 50 meters and then descends 75 meters. What is its final depth?

• The question is: What is its final depth?
• The given information is: The submarine is at a depth of -200 meters below sea level. It ascends 50 meters and then descends 75 meters.
• The unknown is: The final depth of the submarine
• Let x be the variable that represents the final depth of the submarine
• Write an equation that models the situation: x = -200 + 50 - 75
• Solve the equation using addition and subtraction: x = -225
• Check the solution by plugging it back into the equation: -225 = -200 + 50 - 75
• Write the answer in a complete sentence: The final depth of the submarine is -225 meters below sea level.