What does it mean?
A fact family uses one whole and its two parts. If the parts are 127 and 346 and the whole is 473, adding joins the parts, while subtracting either part from the whole leaves the other. The numbers keep their roles even when the equation is written in a different order.
Addition and subtraction are inverse relationships on the same whole and parts. Use one operation to undo or check the other.
Learning goal: Use inverse addition/subtraction relationships to check calculations and solve missing-value equations. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Number sense and multiplication if an earlier idea needs revisiting.
See the idea
Read each diagram with its labels, then follow the worked examples. Practice questions include their own measurements and information.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Choose a method and explain why it works
Label the whole and the known part before choosing an operation. A missing part is whole minus known part. A missing starting whole is the sum of the removed part and the remaining part. Use the inverse operation to put the answer back into the original story or equation.
Key rule and when to use it
For a + b = c, the inverse checks are c − a = b and c − b = a. Use the actual sum and parts in the check.
Worked examples, step by step
Example 1: Use an inverse fact to check 346 + 127 = 473.
- 473 is the whole.
- 127 is one part.
- Subtract 127 from 473.
- The result is 346, the other part.
Answer: 473 - 127 = 346
Example 2: Find the missing value in 730 - __ = 268.
- 730 is the whole.
- 268 is the remaining part.
- The missing removed part is 730 - 268.
- That equals 462.
Answer: 462
Example 3: Find the missing number in □ − 245 = 318.
- The missing number is the starting whole.
- Rebuild it by adding the removed part and the remainder: 245 + 318 = 563.
- Check in the original equation: 563 − 245 = 318.
Common mistakes and important boundaries
The same three numbers do not make every arrangement true. From 487 + 156 = 643, subtracting 487 from 643 leaves 156, not 487. Equal parts create repeated-looking facts, and zero is allowed: 6 + 0 = 6 and 6 − 0 = 6 still follow the whole–part relationship.
A point to explain
The learner may create a check that changes the whole-part relationship or simply repeats the original operation.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Addition and Subtraction Fact Families — practice
Work on paper first. Open each answer afterwards and compare the reasoning. Print the questions with or without the separate answer key; no account is required.
Name: ____________________ Date: __________
If 346 + 127 = 473, which subtraction checks it?
Show answer
473 - 127 = 346
Which addition checks 601 - 274 = 327?
Show answer
327 + 274 = 601
Find the missing value: 285 + __ = 640.
Show answer
355
Find the missing value: 730 - __ = 268.
Show answer
462
Find the missing start: __ - 189 = 406.
Show answer
595
Why can addition check a subtraction answer?
Show answer
Addition can recombine the difference and removed part to rebuild the starting amount.
A child says 487 + 156 = 643, so the check is 643 - 487 = 487. Is the check correct?
Show answer
no
Use an inverse fact to find __ in 824 - __ = 357.
Show answer
467
Addition and Subtraction Fact Families — answer key
473 - 127 = 346
327 + 274 = 601
355
462
595
Addition can recombine the difference and removed part to rebuild the starting amount.
no
467
Questions students and parents ask
Does checking by addition always catch a copied mistake?
Only if you calculate the check independently. Repeating the same incorrect number without working it out does not verify the answer.
Can subtraction check an addition answer?
Yes. Subtract one original addend from the proposed total. The result should be the other addend; use the original numbers, not accidentally copied wrong ones.
Is this a complete set of textbook exercise solutions?
No. This guide adapts BananaLearn’s own teaching examples and practice. It is not official NCERT material or a promise of the exact chapter sequence in a particular board, country or textbook edition.
What if the examples are still difficult?
Revisit Number sense and multiplication. Try the first example with its model, then attempt one fresh question independently. A correct copied answer is not evidence that the method can be used without support.
Help at home
Draw a bar with one whole and two parts. Move the missing box between the whole and a part so your child explains why the operation changes.
Keep one example of the learner’s own working. A repeated difficulty across fresh questions can guide a discussion with their teacher; one short practice sheet does not establish a diagnosis or a full mastery profile.
Connect this idea to the next skill
- Number sense and multiplication
- Grade 3 Estimating Sums and Differences
- Grade 3 Odd and Even Numbers: Pairs and Patterns
- Grade 3 Mental Addition: Bridge Tens and Compensate
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About this guide
Based on BananaLearn’s Grade 3 course lesson “Related Addition and Subtraction Facts”. The explanations have been adapted for independent reading; course diagrams are reused where they fit the idea, and missing classroom givens are made explicit in questions.
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