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 (2)
Evaluate 8 × 4 = 32 and 4 ÷ 8 = 0.5 , so 8 × 4 = 4 ÷ 8 .
Evaluate 8 × 4 = 32 and 4 × 8 = 32 , so 8 × 4 = 4 × 8 .
Evaluate 8 ÷ 4 = 2 and 4 × 8 = 32 , so 8 ÷ 4 = 4 × 8 .
Evaluate 8 ÷ 4 = 2 and 4 ÷ 8 = 0.5 , so 8 ÷ 4 = 4 ÷ 8 .
The true statement is: 8 × 4 = 4 × 8
Explanation
Analyzing the Problem We are given four statements and we need to determine which one is true. Each statement compares two arithmetic expressions involving multiplication and division of the numbers 8 and 4. We will evaluate each side of the equations in the statements and check for equality.
Evaluating Statement 1 Let's analyze the first statement: 8 × 4 = 4 ÷ 8 . We know that 8 × 4 = 32 and 4 ÷ 8 = 0.5 . Since 32 = 0.5 , the first statement is false.
Evaluating Statement 2 Now, let's analyze the second statement: 8 × 4 = 4 × 8 . We know that 8 × 4 = 32 and 4 × 8 = 32 . Since 32 = 32 , the second statement is true.
Evaluating Statement 3 Next, let's analyze the third statement: 8 ÷ 4 = 4 × 8 . We know that 8 ÷ 4 = 2 and 4 × 8 = 32 . Since 2 = 32 , the third statement is false.
Evaluating Statement 4 Finally, let's analyze the fourth statement: 8 ÷ 4 = 4 ÷ 8 . We know that 8 ÷ 4 = 2 and 4 ÷ 8 = 0.5 . Since 2 = 0.5 , the fourth statement is false.
Conclusion Therefore, the only true statement is the second one: 8 × 4 = 4 × 8 .
Examples
Understanding the commutative property of multiplication, as demonstrated in this problem, is crucial in various real-life scenarios. For instance, when calculating the area of a rectangle, whether you multiply length by width or width by length, the result remains the same. This principle applies to numerous situations, from calculating total costs (number of items times price per item) to understanding proportions in recipes or scaling quantities in manufacturing. Recognizing that the order of multiplication doesn't affect the outcome simplifies calculations and enhances problem-solving skills in everyday tasks.
The true statement among the options is B: 8 multiplied by 4 is equal to 4 multiplied by 8. This is verified by the calculations showing both equal 32. The other statements are false due to unequal results.
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