Fact Family Calculator

Work out fact family instantly with clear inputs, formula shown and shareable results.

About Fact Family Calculator

A fact family takes two numbers and their product (or sum) and writes all four related facts, using commutativity and the inverse operation. Children who see 6 x 7 and 42 / 7 as the same fact family halve the number of facts they need to memorise.

Formulas

Multiplicative family

a x b = p, b x a = p, p / a = b, p / b = a

Additive family

a + b = s, b + a = s, s - a = b, s - b = a

Worked example

With the default values below, Fact Family Calculator returns Product of 42. Change any input above and every figure here is recalculated in your browser.

Inputs used

First numberminimum 1: 6
Second numberminimum 1: 7

Results

Product: 42
Sum: 13
Multiplication and division family: 6 x 7 = 42; 7 x 6 = 42; 42 / 6 = 7; 42 / 7 = 6
Addition and subtraction family: 6 + 7 = 13; 13 - 6 = 7

Step by step

1Values used
2Multiplicative family
3Additive family
4Product= 42
5Sum= 13
6Multiplication and division family= 6 x 7 = 42; 7 x 6 = 42; 42 / 6 = 7; 42 / 7 = 6
7Addition and subtraction family= 6 + 7 = 13; 13 - 6 = 7

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Fact Family figure worked out?

a x b = p, b x a = p, p / a = b, p / b = a. A fact family takes two numbers and their product (or sum) and writes all four related facts, using commutativity and the inverse operation.

Why does this matter?

Children who see 6 x 7 and 42 / 7 as the same fact family halve the number of facts they need to memorise.

What do I need to enter?

Enter first number, second number. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.