QuestionDetermine if the product is rational or irrational: $-\frac{1}{5} \times \frac{1}{3}$ .

Studdy Solution

STEP 1

Assumptions1. We are given two fractions $-\frac{1}{5}$ and $\frac{1}{3}$ . . We need to find the product of these two fractions.
3. We need to determine whether the result is a rational or an irrational number.

STEP 2

First, let's find the product of the two fractions. The product of two fractions is obtained by multiplying the numerators together to get the new numerator and the denominators together to get the new denominator.
$Product = \left(-\frac{1}{5}\right) \times \frac{1}{}$

STEP 3

Now, multiply the numerators and the denominators.
$Product = \frac{-1 \times1}{5 \times3}$

STEP 4

Calculate the product.
$Product = \frac{-1}{15}$

STEP 5

Now, we need to determine whether the result is a rational or an irrational number. A rational number can be expressed as a fraction where both the numerator and the denominator are integers and the denominator is not zero. An irrational number cannot be expressed as a simple fraction.

STEP 6

Looking at our result, $-\frac{1}{15}$ , we see that it is a fraction where both the numerator and the denominator are integers and the denominator is not zero. Therefore, $-\frac{1}{15}$ is a rational number.
The product $-\frac{1}{15}$ is a rational number.

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QuestionDetermine if the product is rational or irrational: $-\frac{1}{5} \times \frac{1}{3}$ .

Studdy Solution

STEP 1

Assumptions1. We are given two fractions $-\frac{1}{5}$ and $\frac{1}{3}$ . . We need to find the product of these two fractions.
3. We need to determine whether the result is a rational or an irrational number.

STEP 2

First, let's find the product of the two fractions. The product of two fractions is obtained by multiplying the numerators together to get the new numerator and the denominators together to get the new denominator.
$Product = \left(-\frac{1}{5}\right) \times \frac{1}{}$

STEP 3

Now, multiply the numerators and the denominators.
$Product = \frac{-1 \times1}{5 \times3}$

STEP 4

Calculate the product.
$Product = \frac{-1}{15}$

STEP 5

Now, we need to determine whether the result is a rational or an irrational number. A rational number can be expressed as a fraction where both the numerator and the denominator are integers and the denominator is not zero. An irrational number cannot be expressed as a simple fraction.

STEP 6

Looking at our result, $-\frac{1}{15}$ , we see that it is a fraction where both the numerator and the denominator are integers and the denominator is not zero. Therefore, $-\frac{1}{15}$ is a rational number.
The product $-\frac{1}{15}$ is a rational number.

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QuestionDetermine if the product is rational or irrational: −15×13-\frac{1}{5} \times \frac{1}{3}−51​×31​.

Studdy Solution

STEP 1

Assumptions1. We are given two fractions −15-\frac{1}{5}−51​ and 13\frac{1}{3}31​. . We need to find the product of these two fractions.3. We need to determine whether the result is a rational or an irrational number.

STEP 2

STEP 3

Now, multiply the numerators and the denominators.Product=−1×15×3Product = \frac{-1 \times1}{5 \times3}Product=5×3−1×1​

STEP 4

Calculate the product.Product=−115Product = \frac{-1}{15}Product=15−1​

STEP 5

Now, we need to determine whether the result is a rational or an irrational number. A rational number can be expressed as a fraction where both the numerator and the denominator are integers and the denominator is not zero. An irrational number cannot be expressed as a simple fraction.

STEP 6

Looking at our result, −115-\frac{1}{15}−151​, we see that it is a fraction where both the numerator and the denominator are integers and the denominator is not zero. Therefore, −115-\frac{1}{15}−151​ is a rational number.The product −115-\frac{1}{15}−151​ is a rational number.

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QuestionDetermine if the product is rational or irrational: $-\frac{1}{5} \times \frac{1}{3}$ .

Assumptions1. We are given two fractions $-\frac{1}{5}$ and $\frac{1}{3}$ . . We need to find the product of these two fractions.
3. We need to determine whether the result is a rational or an irrational number.

Now, multiply the numerators and the denominators.
$Product = \frac{-1 \times1}{5 \times3}$

Calculate the product.
$Product = \frac{-1}{15}$

Looking at our result, $-\frac{1}{15}$ , we see that it is a fraction where both the numerator and the denominator are integers and the denominator is not zero. Therefore, $-\frac{1}{15}$ is a rational number.
The product $-\frac{1}{15}$ is a rational number.