Mathematics
Grade 6
15 min
Related subtraction facts
Related subtraction facts
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1
Introduction & Learning Objectives
Learning Objectives
Define 'related subtraction facts' and 'fact families'.
Identify the inverse relationship between addition and subtraction.
Generate all related subtraction facts from a given addition fact.
Generate all related addition and subtraction facts from a given subtraction fact.
Apply related facts to solve missing number problems.
Explain how related facts can be used to check subtraction answers.
Extend the concept of related facts to larger numbers and decimals.
Ever wonder how knowing one math problem can instantly help you solve two others? 🤔 It's like having a secret math superpower!
In this lesson, you'll discover the fascinating connection between addition and subtraction, learning how to create 'fact families'...
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Key Concepts & Vocabulary
TermDefinitionExample
Fact FamilyA set of three numbers that are related by addition and subtraction. These three numbers can be used to create two addition facts and two subtraction facts (unless two of the numbers are identical).The numbers 3, 5, and 8 form a fact family: 3 + 5 = 8, 5 + 3 = 8, 8 - 3 = 5, 8 - 5 = 3.
Inverse OperationsOperations that undo each other. Addition and subtraction are inverse operations because one can reverse the effect of the other.If you add 5 to a number, you can undo it by subtracting 5 from the result. (x + 5) - 5 = x.
MinuendIn a subtraction problem, the minuend is the number from which another number is subtracted. It is the 'whole' amount.In the problem 15 - 7 = 8, the minuend is 15.
SubtrahendIn a subtraction problem, the subtrahend is the n...
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Core Formulas
Addition-Subtraction Inverse Property
If $a + b = c$, then $c - a = b$ and $c - b = a$.
This rule shows how an addition fact directly leads to two related subtraction facts. The sum (c) becomes the minuend, and the addends (a and b) become the subtrahend and difference in the subtraction facts.
Subtraction-Addition Inverse Property
If $c - b = a$, then $a + b = c$.
This rule demonstrates how a subtraction fact can be 'checked' or related back to an addition fact. The difference (a) and the subtrahend (b) add up to the original minuend (c).
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Challenging
You are given two numbers from a fact family: 21.5 and 30. The third number is less than 21.5. What is the complete set of related subtraction facts for this family?
A.30 - 21.5 = 8.5 and 30 - 8.5 = 21.5
B.21.5 - 8.5 = 13 and 30 - 13 = 17
C.51.5 - 30 = 21.5 and 51.5 - 21.5 = 30
D.30 - 21.5 = 8.5 and 21.5 - 8.5 = 13
Challenging
If the variables a, b, and c represent positive numbers and form the addition fact a + b = c, which equation correctly represents the relationship to find the value of 'a'?
A.a = b - c
B.a = c - b
C.a = c + b
D.a = b + c
Challenging
Consider the fact family for 8 + 8 = 16. Why is there only one related subtraction fact (16 - 8 = 8) instead of two?
A.Because 16 is an even number.
B.Because the number 8 is a single digit.
C.This is an exception to the rule of inverse operations.
D.Because the two addends are identical, swapping them in the subtraction fact c - a = b results in the same equation.
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