Lesson 3: Generate Equivalent Fractions: Multiplication

Property

The product of any number and 1 is the number. 1 is called the multiplicative identity.

Examples

• To calculate $1 \cdot 63$, remember that the product of any number and one is the number itself. So, $1 \cdot 63 = 63$.
• To find $(250)1$, multiplying by one does not change the value. The result is $250$.
• The product $1 \times 7,654$ is simply $7,654$ because 1 is the multiplicative identity.

Explanation

Multiplying a number by 1 means you have exactly one group of that number, so its value (or identity) doesn't change. It's like the number is looking in a mirror; it stays the same.

Property

A fraction is equal to the whole number 1 when its numerator (the top number) and its denominator (the bottom number) are the same.

(where $n$ is any whole number except 0)

Examples

Property

To find an equivalent fraction, multiply the numerator and the denominator by the same whole number, $n$, where $n > 1$.
This process corresponds to visually decomposing each part of an area model into $n$ smaller, equal parts.

Examples