Division and Multiplication: Inverse Operations

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What is the relationship between division and multiplication?

They are 'inverse operations,' which means they are opposites and can 'undo' each other.

If you know that \(6 \times 4 = 24\), what are the two related division facts you also know?

You also know that \(24 \div 4 = 6\) and \(24 \div 6 = 4\).

What is a 'fact family' in math?

A fact family is a set of related math facts that use the same three numbers. For multiplication and division, it typically includes two multiplication facts and two division facts.

Write the complete fact family for the numbers \(5\), \(8\), and \(40\).

\(5 \times 8 = 40\) \(8 \times 5 = 40\) \(40 \div 5 = 8\) \(40 \div 8 = 5\)

How can you use multiplication to check the answer to \(35 \div 7 = 5\)?

Multiply the quotient (\(5\)) by the divisor (\(7\)). If the result is the dividend (\(35\)), the answer is correct. \(5 \times 7 = 35\).

Use multiplication to find the missing number: \(? \div 3 = 9\).

To find the dividend, multiply the quotient by the divisor: \(9 \times 3 = 27\). The missing number is \(27\).

Use your knowledge of fact families to find the missing number: \(54 \div ? = 6\).

Ask yourself, "\(6\) times what number equals \(54\)?" Since \(6 \times 9 = 54\), the missing number is \(9\).

Solve for \(n\): \(n \times 7 = 42\). Now, write a related division fact.

The value of \(n\) is \(6\). A related division fact is \(42 \div 7 = 6\) (or \(42 \div 6 = 7\)).

True or False: The fact family for \(9\), \(9\), and \(81\) has four different facts.

False. Because two of the numbers are the same, it only has two unique facts: \(9 \times 9 = 81\) and \(81 \div 9 = 9\).