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# What is a fact family in arithmetic?

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A fact family is a group of three numbers, where two of them add up to the third. Fact families are used in the study of primary arithmetic to introduce students to the relationship between addition and subtraction.

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Fact families illustrate number relationships and the conceptual relationship between addition and subtractions which can be demonstrated in four different equations. Using 3, 5 and 8 as examples, the equations are:

• 3 + 5 = 8 and 5 + 3 = 8. The numbers can be added up in either order and the sum remains the same
• 8 - 5 = 3 and 8 - 3 = 5. Subtracting one of the original numbers from the sum results in the third number

Given two numbers, two fact families can be built. Using 5 and 7 as an example, the third number can be found by either addition or subtraction.

• 5 + 7 = 12 or 7 + 5 = 12, resulting in the fact family of 5, 7 and 12
• 7 - 5 = 2, resulting in the fact family of 7, 5 and 2

In the case of subtraction, as above, the smaller number should be subtracted from the larger number or a negative number will result.

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