Noah says that dividing a number by 2 is the same as multiplying it by 1/2. He wants to know if he is right, and if so, why? How do you respond?
yes.
when dividing, it is the same as multiplying by the reciprocal.
Noah is correct. Dividing a number by 2 is the same as multiplying it by 1/2. This is because division is the inverse operation of multiplication. When you divide a number by 2, you are essentially splitting it into two equal parts. Multiplying the number by 1/2 accomplishes the same thing, as multiplying by 1/2 means you are taking half of the original number and leaving the other half behind. So, both operations result in the original number being divided into two equal parts, making them equivalent.
To determine if Noah is right, let's examine the basic principles of division and multiplication. Division is the process of splitting a number into equal parts, while multiplication involves combining a number with itself a certain number of times.
Now, let's analyze Noah's statement that dividing a number by 2 is the same as multiplying it by 1/2.
To verify Noah's claim, we can use a specific number. Let's consider the number 10 for our demonstration.
1. Dividing by 2: When we divide 10 by 2, we get 10 ÷ 2 = 5.
2. Multiplying by 1/2: When we multiply 10 by 1/2, we get 10 × 1/2 = 5.
As we can see, both dividing 10 by 2 and multiplying 10 by 1/2 result in the same answer of 5. Therefore, Noah is correct.
Now, let's understand why dividing a number by 2 is the same as multiplying it by 1/2.
When we divide a number by 2, we essentially split it into two equal parts. Similarly, when we multiply a number by 1/2, we are effectively calculating half of that number.
Mathematically, dividing a number x by 2 can be represented as x ÷ 2, and multiplying a number x by 1/2 can be expressed as x × (1/2).
To perform the division, we can rewrite it as x ÷ 2 = x × (1/2). By canceling out the denominator of 2, we have x ÷ 2 = x × 1/2.
Ultimately, the multiplication equation x × 1/2 is equivalent to the division equation x ÷ 2, meaning dividing a number by 2 is indeed the same as multiplying it by 1/2.