Mathematics
Grade 6
15 min
Add and subtract whole numbers
Add and subtract whole numbers
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1
Introduction & Learning Objectives
Learning Objectives
Add whole numbers up to 6 digits using the standard algorithm.
Subtract whole numbers up to 6 digits using the standard algorithm.
Accurately perform addition and subtraction with regrouping (carrying and borrowing).
Solve multi-step word problems involving addition and subtraction of whole numbers.
Estimate sums and differences of whole numbers to check for reasonableness.
Identify and correct common errors in addition and subtraction calculations.
Ever wonder how stores calculate your total bill or how much change you should get back? 💰 It all starts with adding and subtracting whole numbers!
In this lesson, you'll learn how to confidently add and subtract large whole numbers using efficient strategies. Mastering these fundamental skills is cruci...
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Key Concepts & Vocabulary
TermDefinitionExample
Whole NumbersThe set of non-negative integers (0, 1, 2, 3, ...). They do not include fractions, decimals, or negative numbers.The numbers 15, 0, 2,345, and 1,000,000 are all whole numbers.
SumThe result obtained when two or more numbers are added together.In the equation 5 + 3 = 8, the sum is 8.
DifferenceThe result obtained when one number is subtracted from another.In the equation 10 - 4 = 6, the difference is 6.
AddendA number that is added to another number to form a sum.In the equation 12 + 7 = 19, both 12 and 7 are addends.
MinuendThe number from which another number is subtracted.In the equation 25 - 10 = 15, the minuend is 25.
SubtrahendThe number that is subtracted from the minuend.In the equation 25 - 10 = 15, the subtrahend is 10.
Regrouping (Carrying/Borr...
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Core Formulas
Commutative Property of Addition
$a + b = b + a$
The order in which you add two whole numbers does not change their sum. This property does NOT apply to subtraction.
Associative Property of Addition
$(a + b) + c = a + (b + c)$
The way in which whole numbers are grouped when adding three or more numbers does not change their sum. This property does NOT apply to subtraction.
Identity Property of Addition
$a + 0 = a$
Adding zero to any whole number results in the original number. Zero is the additive identity.
Standard Algorithm for Addition/Subtraction
Align numbers by place value (ones under ones, tens under tens, etc.) and perform operations column by column, starting from the rightmost column (ones place), regrouping as needed.
This is the most common method...
5 more steps in this tutorial
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Challenging
What is the correct result of 700,030 - 123,456?
A.576,574
B.576,574
C.587,684
D.676,574
Challenging
A student was asked to solve this problem: 'A factory produced 150,000 widgets. It sold 85,500 and then produced 25,000 more. How many widgets does it have now?' The student's answer was 180,500. What was the student's error?
A.They subtracted $75,000 instead of adding it.
B.They added $120,000 instead of subtracting it.
C.They performed the operations in the wrong order.
D.They made a calculation error.
Challenging
A city is planning a new park. The budget for landscaping is $125,000 and the budget for a new playground is $85,000. The city has 5 full-time park employees. Last year, the city spent $45,000 on park maintenance. What is the total combined budget for the new landscaping and playground?
A.165,000
B.255,000
C.210,000
D.210,000
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