Question
Explain the distributive property
Answers
GPT-4o mini
The distributive property is a fundamental principle in arithmetic and algebra that describes how multiplication interacts with addition (or subtraction). It states that when you multiply a number (or expression) by a sum (or difference), you can distribute the multiplication across each term within the parentheses.
In mathematical terms, the distributive property can be expressed as:
\[ a(b + c) = ab + ac \]
and
\[ a(b - c) = ab - ac \]
Here:
- \( a \) is the number (or expression) being multiplied,
- \( b \) and \( c \) are the numbers (or expressions) being added (or subtracted).
### Example:
If you want to evaluate \( 3(4 + 5) \) using the distributive property:
1. Apply the distributive property:
\[ 3(4 + 5) = 3 \times 4 + 3 \times 5 \]
2. Calculate each term:
\[ 3 \times 4 = 12 \]
\[ 3 \times 5 = 15 \]
3. Add the results:
\[ 12 + 15 = 27 \]
So, \( 3(4 + 5) = 27 \).
### Summary
The distributive property allows you to simplify expressions and perform calculations more easily, making it a crucial tool in both basic arithmetic and more advanced algebra.
In mathematical terms, the distributive property can be expressed as:
\[ a(b + c) = ab + ac \]
and
\[ a(b - c) = ab - ac \]
Here:
- \( a \) is the number (or expression) being multiplied,
- \( b \) and \( c \) are the numbers (or expressions) being added (or subtracted).
### Example:
If you want to evaluate \( 3(4 + 5) \) using the distributive property:
1. Apply the distributive property:
\[ 3(4 + 5) = 3 \times 4 + 3 \times 5 \]
2. Calculate each term:
\[ 3 \times 4 = 12 \]
\[ 3 \times 5 = 15 \]
3. Add the results:
\[ 12 + 15 = 27 \]
So, \( 3(4 + 5) = 27 \).
### Summary
The distributive property allows you to simplify expressions and perform calculations more easily, making it a crucial tool in both basic arithmetic and more advanced algebra.