QuestionCalculate the sum: $-\frac{1}{15} + \left(-\frac{5}{12}\right)$

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions $-\frac{1}{15}$ and $-\frac{5}{12}$ . . The operation to be performed is addition.
3. The fractions are in the form $\frac{a}{b}$ , where $a$ is the numerator and $b$ is the denominator.

STEP 2

To add fractions, we need to have the same denominator for both fractions. This is called the least common denominator (LCD). The LCD of15 and12 is60.

STEP 3

We convert each fraction to an equivalent fraction with the LCD as the denominator. For the first fraction, we multiply both the numerator and the denominator by.
$-\frac{1}{15} = -\frac{1 \times}{15 \times} = -\frac{}{60}$

STEP 4

For the second fraction, we multiply both the numerator and the denominator by.
$-\frac{}{12} = -\frac{ \times}{12 \times} = -\frac{25}{60}$

STEP 5

Now that both fractions have the same denominator, we can add the fractions by adding the numerators.
$-\frac{4}{60} + -\frac{25}{60} = -\frac{4 +25}{60}$

STEP 6

Perform the addition in the numerator.
$-\frac{4 +25}{60} = -\frac{29}{60}$ So, $-\frac{1}{15}+\left(-\frac{5}{12}\right) = -\frac{29}{60}$ .

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QuestionCalculate the sum: $-\frac{1}{15} + \left(-\frac{5}{12}\right)$

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions $-\frac{1}{15}$ and $-\frac{5}{12}$ . . The operation to be performed is addition.
3. The fractions are in the form $\frac{a}{b}$ , where $a$ is the numerator and $b$ is the denominator.

STEP 2

To add fractions, we need to have the same denominator for both fractions. This is called the least common denominator (LCD). The LCD of15 and12 is60.

STEP 3

We convert each fraction to an equivalent fraction with the LCD as the denominator. For the first fraction, we multiply both the numerator and the denominator by.
$-\frac{1}{15} = -\frac{1 \times}{15 \times} = -\frac{}{60}$

STEP 4

For the second fraction, we multiply both the numerator and the denominator by.
$-\frac{}{12} = -\frac{ \times}{12 \times} = -\frac{25}{60}$

STEP 5

Now that both fractions have the same denominator, we can add the fractions by adding the numerators.
$-\frac{4}{60} + -\frac{25}{60} = -\frac{4 +25}{60}$

STEP 6

Perform the addition in the numerator.
$-\frac{4 +25}{60} = -\frac{29}{60}$ So, $-\frac{1}{15}+\left(-\frac{5}{12}\right) = -\frac{29}{60}$ .

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QuestionCalculate the sum: −115+(−512)-\frac{1}{15} + \left(-\frac{5}{12}\right)−151​+(−125​)

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions −115-\frac{1}{15}−151​ and −512-\frac{5}{12}−125​. . The operation to be performed is addition.3. The fractions are in the form ab\frac{a}{b}ba​, where aaa is the numerator and bbb is the denominator.

STEP 2

To add fractions, we need to have the same denominator for both fractions. This is called the least common denominator (LCD). The LCD of15 and12 is60.

STEP 3

We convert each fraction to an equivalent fraction with the LCD as the denominator. For the first fraction, we multiply both the numerator and the denominator by.−115=−1×15×=−60-\frac{1}{15} = -\frac{1 \times}{15 \times} = -\frac{}{60}−151​=−15×1×​=−60​

STEP 4

For the second fraction, we multiply both the numerator and the denominator by.−12=−×12×=−2560-\frac{}{12} = -\frac{ \times}{12 \times} = -\frac{25}{60}−12​=−12××​=−6025​

STEP 5

Now that both fractions have the same denominator, we can add the fractions by adding the numerators.−460+−2560=−4+2560-\frac{4}{60} + -\frac{25}{60} = -\frac{4 +25}{60}−604​+−6025​=−604+25​

STEP 6

Perform the addition in the numerator.−4+2560=−2960-\frac{4 +25}{60} = -\frac{29}{60}−604+25​=−6029​So, −115+(−512)=−2960-\frac{1}{15}+\left(-\frac{5}{12}\right) = -\frac{29}{60}−151​+(−125​)=−6029​.

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QuestionCalculate the sum: $-\frac{1}{15} + \left(-\frac{5}{12}\right)$

Assumptions1. We are adding two fractions $-\frac{1}{15}$ and $-\frac{5}{12}$ . . The operation to be performed is addition.
3. The fractions are in the form $\frac{a}{b}$ , where $a$ is the numerator and $b$ is the denominator.

We convert each fraction to an equivalent fraction with the LCD as the denominator. For the first fraction, we multiply both the numerator and the denominator by.
$-\frac{1}{15} = -\frac{1 \times}{15 \times} = -\frac{}{60}$

For the second fraction, we multiply both the numerator and the denominator by.
$-\frac{}{12} = -\frac{ \times}{12 \times} = -\frac{25}{60}$

Now that both fractions have the same denominator, we can add the fractions by adding the numerators.
$-\frac{4}{60} + -\frac{25}{60} = -\frac{4 +25}{60}$

Perform the addition in the numerator.
$-\frac{4 +25}{60} = -\frac{29}{60}$ So, $-\frac{1}{15}+\left(-\frac{5}{12}\right) = -\frac{29}{60}$ .