An expression equal to \(7 \times 8\) could be:
1. Repeated addition:
\[7 + 7 + ... ( \text { eight times} ) \] 2. Using commutative property:
\[8 \times 7\]
3. Using distributive property:
- Example with breaking down one factor: \[( 5+ 2) \times 8= 5\times 8+ 2\times 8= 40+ 16= 56\]
- Example with breaking down both factors:
\[4\times 14= ( 4\times 10) + ( 4\times 4) = 40+ 16= 56\]
Supplemental Knowledge:
In mathematics, expressing a multiplication operation can be done in various ways while maintaining the equality. The expression \(7 \times 8\) can be represented using different arithmetic operations or properties of multiplication.
Examples of Equivalent Expressions:
1. Using Addition:
\(7 \times 8\) can be expressed as repeated addition: \[7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56\]
2. Using Commutative Property:
The commutative property of multiplication states that changing the order of factors does not change the product: \[8 \times 7 = 56\]
3. Using Distributive Property:
The distributive property allows you to break down numbers into simpler parts: \[( 5 + 2) \times 8 = ( 5 \times 8) + ( 2 \times 8) = 40 + 16 = 56\] Alternatively: \[7 \times ( 5 + 3) = ( 7 \times 5) + ( 7 \times 3) = 35 + 21 = 56\]
4. Using Known Multiplication Facts:
If you know that:\[4 \times 14 = ( 4 \times ( 10+ 4) ) = 40+ 16= 56\]then: \[4 \times ( 14) = 56\]
Knowledge in Action:
Understanding different approaches to multiplication can prove essential in many real-life settings, from budgeting and cooking to construction and more. When calculating total costs or area measurements of multiple items or areas in a space, being able to manipulate expressions efficiently makes such tasks much less daunting.
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