QuestionAdd without a calculator: $\frac{2}{3}+\frac{1}{15}$ . Enter your answer as a mixed number (e.g., 11/2).

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions $\frac{}{3}$ and $\frac{1}{15}$ . . We are not using a calculator.
3. The result should be expressed as a mixed number.

STEP 2

To add fractions, we need to have the same denominator. The common denominator is the least common multiple (LCM) of the two denominators.

STEP 3

Find the LCM of3 and15. Since15 is a multiple of3, the LCM is15.

STEP 4

Now, we need to convert each fraction to an equivalent fraction with the denominator of15. The first fraction $\frac{2}{3}$ needs to be converted.

STEP 5

To convert $\frac{2}{3}$ to a fraction with a denominator of15, we multiply both the numerator and the denominator by5.
$\frac{2}{3} = \frac{2 \times5}{3 \times5} = \frac{10}{15}$

STEP 6

Now, we have two fractions with the same denominator $\frac{10}{15}$ and $\frac{1}{15}$ .

STEP 7

We can now add these two fractions by adding the numerators and keeping the denominator the same.
$\frac{10}{15} + \frac{1}{15} = \frac{10+1}{15}$

STEP 8

Perform the addition in the numerator.
$\frac{10+1}{15} = \frac{11}{15}$

STEP 9

The fraction $\frac{11}{15}$ is already in its simplest form and it's not a mixed number, so we are done.
The result of adding $\frac{2}{3}$ and $\frac{}{15}$ is $\frac{11}{15}$ .

Was this helpful?

QuestionAdd without a calculator: $\frac{2}{3}+\frac{1}{15}$ . Enter your answer as a mixed number (e.g., 11/2).

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions $\frac{}{3}$ and $\frac{1}{15}$ . . We are not using a calculator.
3. The result should be expressed as a mixed number.

STEP 2

To add fractions, we need to have the same denominator. The common denominator is the least common multiple (LCM) of the two denominators.

STEP 3

Find the LCM of3 and15. Since15 is a multiple of3, the LCM is15.

STEP 4

Now, we need to convert each fraction to an equivalent fraction with the denominator of15. The first fraction $\frac{2}{3}$ needs to be converted.

STEP 5

To convert $\frac{2}{3}$ to a fraction with a denominator of15, we multiply both the numerator and the denominator by5.
$\frac{2}{3} = \frac{2 \times5}{3 \times5} = \frac{10}{15}$

STEP 6

Now, we have two fractions with the same denominator $\frac{10}{15}$ and $\frac{1}{15}$ .

STEP 7

We can now add these two fractions by adding the numerators and keeping the denominator the same.
$\frac{10}{15} + \frac{1}{15} = \frac{10+1}{15}$

STEP 8

Perform the addition in the numerator.
$\frac{10+1}{15} = \frac{11}{15}$

STEP 9

The fraction $\frac{11}{15}$ is already in its simplest form and it's not a mixed number, so we are done.
The result of adding $\frac{2}{3}$ and $\frac{}{15}$ is $\frac{11}{15}$ .

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionAdd without a calculator: 23+115\frac{2}{3}+\frac{1}{15}32​+151​. Enter your answer as a mixed number (e.g., 11/2).

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions 3\frac{}{3}3​ and 115\frac{1}{15}151​. . We are not using a calculator.3. The result should be expressed as a mixed number.

STEP 2

To add fractions, we need to have the same denominator. The common denominator is the least common multiple (LCM) of the two denominators.

STEP 3

Find the LCM of3 and15. Since15 is a multiple of3, the LCM is15.

STEP 4

Now, we need to convert each fraction to an equivalent fraction with the denominator of15. The first fraction 23\frac{2}{3}32​ needs to be converted.

STEP 5

To convert 23\frac{2}{3}32​ to a fraction with a denominator of15, we multiply both the numerator and the denominator by5.23=2×53×5=1015\frac{2}{3} = \frac{2 \times5}{3 \times5} = \frac{10}{15}32​=3×52×5​=1510​

STEP 6

Now, we have two fractions with the same denominator 1015\frac{10}{15}1510​ and 115\frac{1}{15}151​.

STEP 7

We can now add these two fractions by adding the numerators and keeping the denominator the same.1015+115=10+115\frac{10}{15} + \frac{1}{15} = \frac{10+1}{15}1510​+151​=1510+1​

STEP 8

Perform the addition in the numerator.10+115=1115\frac{10+1}{15} = \frac{11}{15}1510+1​=1511​

STEP 9

The fraction 1115\frac{11}{15}1511​ is already in its simplest form and it's not a mixed number, so we are done.The result of adding 23\frac{2}{3}32​ and 15\frac{}{15}15​ is 1115\frac{11}{15}1511​.

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionAdd without a calculator: $\frac{2}{3}+\frac{1}{15}$ . Enter your answer as a mixed number (e.g., 11/2).

Assumptions1. We are adding two fractions $\frac{}{3}$ and $\frac{1}{15}$ . . We are not using a calculator.
3. The result should be expressed as a mixed number.

Now, we need to convert each fraction to an equivalent fraction with the denominator of15. The first fraction $\frac{2}{3}$ needs to be converted.

To convert $\frac{2}{3}$ to a fraction with a denominator of15, we multiply both the numerator and the denominator by5.
$\frac{2}{3} = \frac{2 \times5}{3 \times5} = \frac{10}{15}$

Now, we have two fractions with the same denominator $\frac{10}{15}$ and $\frac{1}{15}$ .

We can now add these two fractions by adding the numerators and keeping the denominator the same.
$\frac{10}{15} + \frac{1}{15} = \frac{10+1}{15}$

Perform the addition in the numerator.
$\frac{10+1}{15} = \frac{11}{15}$

The fraction $\frac{11}{15}$ is already in its simplest form and it's not a mixed number, so we are done.
The result of adding $\frac{2}{3}$ and $\frac{}{15}$ is $\frac{11}{15}$ .