Math / Numbers & Operations

QuestionDivide. Enter your answer as a fraction in simplest form. $\frac{1}{5}+\frac{11}{15}$
The solution is

Studdy Solution

STEP 1

1. We are adding two fractions: $\frac{1}{5}$ and $\frac{11}{15}$ .
2. The goal is to find the sum and express it as a fraction in simplest form.

STEP 2

1. Find a common denominator.
2. Convert each fraction to have the common denominator.
3. Add the fractions.
4. Simplify the resulting fraction.

STEP 3

Identify the least common denominator (LCD) for the fractions $\frac{1}{5}$ and $\frac{11}{15}$ .
The denominators are $5$ and $15$ . The least common multiple of $5$ and $15$ is $15$ .

STEP 4

Convert $\frac{1}{5}$ to an equivalent fraction with a denominator of $15$ .
Multiply both the numerator and the denominator of $\frac{1}{5}$ by $3$ :
$\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$

STEP 5

Add the fractions $\frac{3}{15}$ and $\frac{11}{15}$ .
$\frac{3}{15} + \frac{11}{15} = \frac{3 + 11}{15} = \frac{14}{15}$

STEP 6

Simplify the fraction $\frac{14}{15}$ .
Since $14$ and $15$ have no common factors other than $1$ , $\frac{14}{15}$ is already in simplest form.
The sum of the fractions in simplest form is:
$\boxed{\frac{14}{15}}$

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QuestionDivide. Enter your answer as a fraction in simplest form. $\frac{1}{5}+\frac{11}{15}$
The solution is

Studdy Solution

STEP 1

1. We are adding two fractions: $\frac{1}{5}$ and $\frac{11}{15}$ .
2. The goal is to find the sum and express it as a fraction in simplest form.

STEP 2

1. Find a common denominator.
2. Convert each fraction to have the common denominator.
3. Add the fractions.
4. Simplify the resulting fraction.

STEP 3

Identify the least common denominator (LCD) for the fractions $\frac{1}{5}$ and $\frac{11}{15}$ .
The denominators are $5$ and $15$ . The least common multiple of $5$ and $15$ is $15$ .

STEP 4

Convert $\frac{1}{5}$ to an equivalent fraction with a denominator of $15$ .
Multiply both the numerator and the denominator of $\frac{1}{5}$ by $3$ :
$\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$

STEP 5

Add the fractions $\frac{3}{15}$ and $\frac{11}{15}$ .
$\frac{3}{15} + \frac{11}{15} = \frac{3 + 11}{15} = \frac{14}{15}$

STEP 6

Simplify the fraction $\frac{14}{15}$ .
Since $14$ and $15$ have no common factors other than $1$ , $\frac{14}{15}$ is already in simplest form.
The sum of the fractions in simplest form is:
$\boxed{\frac{14}{15}}$

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QuestionDivide. Enter your answer as a fraction in simplest form. 15+1115\frac{1}{5}+\frac{11}{15}51​+1511​The solution is

Studdy Solution

STEP 1

1. We are adding two fractions: 15\frac{1}{5}51​ and 1115\frac{11}{15}1511​.2. The goal is to find the sum and express it as a fraction in simplest form.

STEP 2

1. Find a common denominator.2. Convert each fraction to have the common denominator.3. Add the fractions.4. Simplify the resulting fraction.

STEP 3

Identify the least common denominator (LCD) for the fractions 15\frac{1}{5}51​ and 1115\frac{11}{15}1511​.The denominators are 555 and 151515. The least common multiple of 555 and 151515 is 151515.

STEP 4

Convert 15\frac{1}{5}51​ to an equivalent fraction with a denominator of 151515.Multiply both the numerator and the denominator of 15\frac{1}{5}51​ by 333:15=1×35×3=315\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}51​=5×31×3​=153​

STEP 5

Add the fractions 315\frac{3}{15}153​ and 1115\frac{11}{15}1511​.315+1115=3+1115=1415\frac{3}{15} + \frac{11}{15} = \frac{3 + 11}{15} = \frac{14}{15}153​+1511​=153+11​=1514​

STEP 6

Simplify the fraction 1415\frac{14}{15}1514​.Since 141414 and 151515 have no common factors other than 111, 1415\frac{14}{15}1514​ is already in simplest form. The sum of the fractions in simplest form is:1415\boxed{\frac{14}{15}}1514​​

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionDivide. Enter your answer as a fraction in simplest form. $\frac{1}{5}+\frac{11}{15}$
The solution is

1. We are adding two fractions: $\frac{1}{5}$ and $\frac{11}{15}$ .
2. The goal is to find the sum and express it as a fraction in simplest form.

1. Find a common denominator.
2. Convert each fraction to have the common denominator.
3. Add the fractions.
4. Simplify the resulting fraction.

Identify the least common denominator (LCD) for the fractions $\frac{1}{5}$ and $\frac{11}{15}$ .
The denominators are $5$ and $15$ . The least common multiple of $5$ and $15$ is $15$ .

Convert $\frac{1}{5}$ to an equivalent fraction with a denominator of $15$ .
Multiply both the numerator and the denominator of $\frac{1}{5}$ by $3$ :
$\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$

Add the fractions $\frac{3}{15}$ and $\frac{11}{15}$ .
$\frac{3}{15} + \frac{11}{15} = \frac{3 + 11}{15} = \frac{14}{15}$

Simplify the fraction $\frac{14}{15}$ .
Since $14$ and $15$ have no common factors other than $1$ , $\frac{14}{15}$ is already in simplest form.
The sum of the fractions in simplest form is:
$\boxed{\frac{14}{15}}$