QuestionDetermine if the sum $\frac{2}{9}+\frac{9}{11}$ is rational or irrational.

Studdy Solution

STEP 1

Assumptions1. We have two fractions, $\frac{}{9}$ and $\frac{9}{11}$ . . We are asked to determine if the sum of these two fractions is a rational or an irrational number.

STEP 2

First, let's add the two fractions. To add fractions, we need to find a common denominator. The common denominator of9 and11 is their product, which is99.
$\frac{2}{9}+\frac{9}{11} = \frac{2 \times11}{9 \times11} + \frac{9 \times9}{11 \times9}$

STEP 3

Now, calculate the numerator and denominator for each fraction.
$\frac{2 \times11}{9 \times11} + \frac{9 \times9}{11 \times9} = \frac{22}{99} + \frac{81}{99}$

STEP 4

Since the denominators are the same, we can add the numerators directly.
$\frac{22}{99} + \frac{81}{99} = \frac{22 +81}{99}$

STEP 5

Calculate the sum in the numerator.
$\frac{22 +81}{99} = \frac{103}{99}$

STEP 6

The sum of the two fractions is $\frac{103}{99}$ , which is a fraction. A fraction is a type of rational number, as it can be expressed as the quotient of two integers. Therefore, the sum of the two fractions is a rational number.

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QuestionDetermine if the sum $\frac{2}{9}+\frac{9}{11}$ is rational or irrational.

Studdy Solution

STEP 1

Assumptions1. We have two fractions, $\frac{}{9}$ and $\frac{9}{11}$ . . We are asked to determine if the sum of these two fractions is a rational or an irrational number.

STEP 2

First, let's add the two fractions. To add fractions, we need to find a common denominator. The common denominator of9 and11 is their product, which is99.
$\frac{2}{9}+\frac{9}{11} = \frac{2 \times11}{9 \times11} + \frac{9 \times9}{11 \times9}$

STEP 3

Now, calculate the numerator and denominator for each fraction.
$\frac{2 \times11}{9 \times11} + \frac{9 \times9}{11 \times9} = \frac{22}{99} + \frac{81}{99}$

STEP 4

Since the denominators are the same, we can add the numerators directly.
$\frac{22}{99} + \frac{81}{99} = \frac{22 +81}{99}$

STEP 5

Calculate the sum in the numerator.
$\frac{22 +81}{99} = \frac{103}{99}$

STEP 6

The sum of the two fractions is $\frac{103}{99}$ , which is a fraction. A fraction is a type of rational number, as it can be expressed as the quotient of two integers. Therefore, the sum of the two fractions is a rational number.

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QuestionDetermine if the sum 29+911\frac{2}{9}+\frac{9}{11}92​+119​ is rational or irrational.

Studdy Solution

STEP 1

Assumptions1. We have two fractions, 9\frac{}{9}9​ and 911\frac{9}{11}119​. . We are asked to determine if the sum of these two fractions is a rational or an irrational number.

STEP 2

STEP 3

Now, calculate the numerator and denominator for each fraction.2×119×11+9×911×9=2299+8199\frac{2 \times11}{9 \times11} + \frac{9 \times9}{11 \times9} = \frac{22}{99} + \frac{81}{99} 9×112×11​+11×99×9​=9922​+9981​

STEP 4

Since the denominators are the same, we can add the numerators directly.2299+8199=22+8199\frac{22}{99} + \frac{81}{99} = \frac{22 +81}{99} 9922​+9981​=9922+81​

STEP 5

Calculate the sum in the numerator.22+8199=10399\frac{22 +81}{99} = \frac{103}{99} 9922+81​=99103​

STEP 6

The sum of the two fractions is 10399\frac{103}{99}99103​, which is a fraction. A fraction is a type of rational number, as it can be expressed as the quotient of two integers. Therefore, the sum of the two fractions is a rational number.

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QuestionDetermine if the sum $\frac{2}{9}+\frac{9}{11}$ is rational or irrational.

Assumptions1. We have two fractions, $\frac{}{9}$ and $\frac{9}{11}$ . . We are asked to determine if the sum of these two fractions is a rational or an irrational number.

Now, calculate the numerator and denominator for each fraction.
$\frac{2 \times11}{9 \times11} + \frac{9 \times9}{11 \times9} = \frac{22}{99} + \frac{81}{99}$

Since the denominators are the same, we can add the numerators directly.
$\frac{22}{99} + \frac{81}{99} = \frac{22 +81}{99}$

Calculate the sum in the numerator.
$\frac{22 +81}{99} = \frac{103}{99}$

The sum of the two fractions is $\frac{103}{99}$ , which is a fraction. A fraction is a type of rational number, as it can be expressed as the quotient of two integers. Therefore, the sum of the two fractions is a rational number.