Solved on Sep 18, 2023

Add or subtract $\frac{2}{3} - \left(-\frac{1}{7}\right)$ .

STEP 1

Assumptions1. We are dealing with two fractions $\frac{}{3}$ and $-\frac{1}{7}$ . . We need to add or subtract these fractions.
3. The operation between these fractions is subtraction, but there is a negative sign before the second fraction.

STEP 2

We can simplify the expression by applying the rule of signs. In this case, subtracting a negative value is the same as adding a positive value.
$\frac{2}{}-\left(-\frac{1}{7}\right) = \frac{2}{} + \frac{1}{7}$

STEP 3

To add fractions, we need to have a common denominator. The least common multiple (LCM) of3 and7 is21.

STEP 4

We rewrite the fractions with the common denominator of21.
$\frac{2}{3} + \frac{1}{7} = \frac{2 \times7}{3 \times7} + \frac{1 \times3}{7 \times3}$

STEP 5

We calculate the numerators and denominators of the fractions.
$\frac{2 \times7}{3 \times7} + \frac{1 \times3}{7 \times3} = \frac{14}{21} + \frac{3}{21}$

STEP 6

We add the fractions.
$\frac{14}{21} + \frac{3}{21} = \frac{14 +3}{21}$

STEP 7

We calculate the numerator of the resulting fraction.
$\frac{14 +3}{21} = \frac{17}{21}$ So, $\frac{2}{3}-\left(-\frac{1}{7}\right) = \frac{17}{21}$ .

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Add or subtract $\frac{2}{3} - \left(-\frac{1}{7}\right)$ .

STEP 1

Assumptions1. We are dealing with two fractions $\frac{}{3}$ and $-\frac{1}{7}$ . . We need to add or subtract these fractions.
3. The operation between these fractions is subtraction, but there is a negative sign before the second fraction.

STEP 2

We can simplify the expression by applying the rule of signs. In this case, subtracting a negative value is the same as adding a positive value.
$\frac{2}{}-\left(-\frac{1}{7}\right) = \frac{2}{} + \frac{1}{7}$

STEP 3

To add fractions, we need to have a common denominator. The least common multiple (LCM) of3 and7 is21.

STEP 4

We rewrite the fractions with the common denominator of21.
$\frac{2}{3} + \frac{1}{7} = \frac{2 \times7}{3 \times7} + \frac{1 \times3}{7 \times3}$

STEP 5

We calculate the numerators and denominators of the fractions.
$\frac{2 \times7}{3 \times7} + \frac{1 \times3}{7 \times3} = \frac{14}{21} + \frac{3}{21}$

STEP 6

We add the fractions.
$\frac{14}{21} + \frac{3}{21} = \frac{14 +3}{21}$

STEP 7

We calculate the numerator of the resulting fraction.
$\frac{14 +3}{21} = \frac{17}{21}$ So, $\frac{2}{3}-\left(-\frac{1}{7}\right) = \frac{17}{21}$ .

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Add or subtract 23−(−17)\frac{2}{3} - \left(-\frac{1}{7}\right)32​−(−71​).

STEP 1

Assumptions1. We are dealing with two fractions 3\frac{}{3}3​ and −17-\frac{1}{7}−71​. . We need to add or subtract these fractions.3. The operation between these fractions is subtraction, but there is a negative sign before the second fraction.

STEP 2

We can simplify the expression by applying the rule of signs. In this case, subtracting a negative value is the same as adding a positive value.2−(−17)=2+17\frac{2}{}-\left(-\frac{1}{7}\right) = \frac{2}{} + \frac{1}{7}2​−(−71​)=2​+71​

STEP 3

To add fractions, we need to have a common denominator. The least common multiple (LCM) of3 and7 is21.

STEP 4

We rewrite the fractions with the common denominator of21.23+17=2×73×7+1×37×3\frac{2}{3} + \frac{1}{7} = \frac{2 \times7}{3 \times7} + \frac{1 \times3}{7 \times3}32​+71​=3×72×7​+7×31×3​

STEP 5

We calculate the numerators and denominators of the fractions.2×73×7+1×37×3=1421+321\frac{2 \times7}{3 \times7} + \frac{1 \times3}{7 \times3} = \frac{14}{21} + \frac{3}{21}3×72×7​+7×31×3​=2114​+213​

STEP 6

We add the fractions.1421+321=14+321\frac{14}{21} + \frac{3}{21} = \frac{14 +3}{21}2114​+213​=2114+3​

STEP 7

We calculate the numerator of the resulting fraction.14+321=1721\frac{14 +3}{21} = \frac{17}{21}2114+3​=2117​So, 23−(−17)=1721\frac{2}{3}-\left(-\frac{1}{7}\right) = \frac{17}{21}32​−(−71​)=2117​.

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Add or subtract $\frac{2}{3} - \left(-\frac{1}{7}\right)$ .

Assumptions1. We are dealing with two fractions $\frac{}{3}$ and $-\frac{1}{7}$ . . We need to add or subtract these fractions.
3. The operation between these fractions is subtraction, but there is a negative sign before the second fraction.

We can simplify the expression by applying the rule of signs. In this case, subtracting a negative value is the same as adding a positive value.
$\frac{2}{}-\left(-\frac{1}{7}\right) = \frac{2}{} + \frac{1}{7}$

We rewrite the fractions with the common denominator of21.
$\frac{2}{3} + \frac{1}{7} = \frac{2 \times7}{3 \times7} + \frac{1 \times3}{7 \times3}$

We calculate the numerators and denominators of the fractions.
$\frac{2 \times7}{3 \times7} + \frac{1 \times3}{7 \times3} = \frac{14}{21} + \frac{3}{21}$

We add the fractions.
$\frac{14}{21} + \frac{3}{21} = \frac{14 +3}{21}$

We calculate the numerator of the resulting fraction.
$\frac{14 +3}{21} = \frac{17}{21}$ So, $\frac{2}{3}-\left(-\frac{1}{7}\right) = \frac{17}{21}$ .