Why is 3x 1/10 less then 3x10

The value of 1 ten is less than the value of 3 tens.
The value of 1 tenth is less then the value of 3 tenths.
The value of 1 tenth is less then the value of 1 ten.
The value of 1 tne is less than the value of 1 tenth.

3 answers

Let's break down the statements to clarify the concepts of tens and tenths and why \(3 \times \frac{1}{10}\) is less than \(3 \times 10\).

  1. Understanding the terms:

    • "Ten" refers to the whole number 10.
    • "Tenth" refers to one part out of ten parts, which is represented as \(\frac{1}{10}\) or 0.1.
  2. Calculating values:

    • \(3 \times 10 = 30\).
    • \(3 \times \frac{1}{10} = 3 \times 0.1 = 0.3\).
  3. Comparison:

    • \(30\) (which is \(3 \times 10\)) is far greater than \(0.3\) (which is \(3 \times \frac{1}{10}\)).

Now, let's analyze the statements:

  1. "The value of 1 ten is less than the value of 3 tens."

    • This statement is true, as \(10\) is less than \(30\).
  2. "The value of 1 tenth is less than the value of 3 tenths."

    • This is also true, since \(0.1\) (1 tenth) is less than \(0.3\) (3 tenths).
  3. "The value of 1 tenth is less than the value of 1 ten."

    • This statement is true, as \(0.1\) (1 tenth) is indeed less than \(10\) (1 ten).
  4. "The value of 1 ten is less than the value of 1 tenth."

    • This statement is false; \(10\) (1 ten) is not less than \(0.1\) (1 tenth). In fact, it's much greater.

Summary:

The comparison \(3 \times \frac{1}{10}\) is less than \(3 \times 10\) because the individual values of a tenth (0.1) are drastically lower than that of a ten (10). Therefore, when you multiply each by 3, you maintain that relationship.

Pick one

The correct statement is: "The value of 1 tenth is less than the value of 1 ten."