Which of the following is true?
A. 8 multiplied by 4 is equal to 4 divided by [tex]$8 (8 \times 4 = 4 \div 8)$[/tex]
B. 8 multiplied by 4 is equal to 4 multiplied by [tex]$8 (8 \times 4 = 4 \times 8)$[/tex]
C. 8 divided by 4 is equal to 4 multiplied by [tex]$8 (8 \div 4 = 4 \times 8)$[/tex]
D. 8 divided by 4 is equal to 4 divided by [tex]$8 (8 \div 4 = 4 \div 8)$[/tex]
Answer (1)
Evaluate 8 t im es 4 = 32 and 4 d i v 8 = 0.5 . Since 32 e q 0.5 , the first statement is false.
Evaluate 8 t im es 4 = 32 and 4 t im es 8 = 32 . Since 32 = 32 , the second statement is true.
Evaluate 8 d i v 4 = 2 and 4 t im es 8 = 32 . Since 2 e q 32 , the third statement is false.
Evaluate 8 d i v 4 = 2 and 4 d i v 8 = 0.5 . Since 2 e q 0.5 , the fourth statement is false.
The true statement is: 8 t im es 4 = 4 t im es 8 .
Explanation
Problem Analysis We are given four statements and we need to determine which one is true. We will evaluate both sides of each equation to check for equality.
Evaluating Statement 1 Statement 1: 8 × 4 = 4 ÷ 8 . We know that 8 × 4 = 32 and 4 ÷ 8 = 0.5 . Since 32 = 0.5 , this statement is false.
Evaluating Statement 2 Statement 2: 8 × 4 = 4 × 8 . We know that 8 × 4 = 32 and 4 × 8 = 32 . Since 32 = 32 , this statement is true.
Evaluating Statement 3 Statement 3: 8 ÷ 4 = 4 × 8 . We know that 8 ÷ 4 = 2 and 4 × 8 = 32 . Since 2 = 32 , this statement is false.
Evaluating Statement 4 Statement 4: 8 ÷ 4 = 4 ÷ 8 . We know that 8 ÷ 4 = 2 and 4 ÷ 8 = 0.5 . Since 2 = 0.5 , this statement is false.
Conclusion Therefore, the only true statement is 8 × 4 = 4 × 8 .
Examples
Understanding the commutative property of multiplication is useful in everyday situations. For example, if you're arranging chairs in rows and columns, whether you have 8 rows of 4 chairs or 4 rows of 8 chairs, the total number of chairs remains the same. This concept simplifies calculations and helps in planning and organizing tasks efficiently.
