QuestionAdd: $\frac{3}{7}+\frac{2}{3}=$

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions $\frac{3}{7}$ and $\frac{}{3}$ . . The fractions are in the form $\frac{a}{b}$ , where $a$ is the numerator and $b$ is the denominator.

STEP 2

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

STEP 3

Let's find the LCM of7 and3. The LCM of two numbers is the smallest number that is a multiple of both numbers. In this case, the LCM of7 and3 is21.

STEP 4

Now that we have the common denominator, we can rewrite the fractions with this new denominator. We do this by multiplying the numerator and denominator of each fraction by the factor that makes the denominator equal to the LCM.
$\frac{3}{7} = \frac{3 \times3}{7 \times3} = \frac{9}{21}$ $\frac{2}{3} = \frac{2 \times7}{3 \times7} = \frac{14}{21}$

STEP 5

Now we can add the two fractions, since they have the same denominator.
$\frac{9}{21} + \frac{14}{21} = \frac{9+14}{21}$

STEP 6

Perform the addition in the numerator.
$\frac{9+14}{21} = \frac{23}{21}$

STEP 7

The fraction $\frac{23}{21}$ is an improper fraction, because the numerator is larger than the denominator. We can convert this to a mixed number by dividing the numerator by the denominator.
$\frac{23}{21} =1\frac{2}{21}$ So, $\frac{3}{7}+\frac{2}{3}=1\frac{2}{21}$ .

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QuestionAdd: $\frac{3}{7}+\frac{2}{3}=$

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions $\frac{3}{7}$ and $\frac{}{3}$ . . The fractions are in the form $\frac{a}{b}$ , where $a$ is the numerator and $b$ is the denominator.

STEP 2

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

STEP 3

Let's find the LCM of7 and3. The LCM of two numbers is the smallest number that is a multiple of both numbers. In this case, the LCM of7 and3 is21.

STEP 4

STEP 5

Now we can add the two fractions, since they have the same denominator.
$\frac{9}{21} + \frac{14}{21} = \frac{9+14}{21}$

STEP 6

Perform the addition in the numerator.
$\frac{9+14}{21} = \frac{23}{21}$

STEP 7

The fraction $\frac{23}{21}$ is an improper fraction, because the numerator is larger than the denominator. We can convert this to a mixed number by dividing the numerator by the denominator.
$\frac{23}{21} =1\frac{2}{21}$ So, $\frac{3}{7}+\frac{2}{3}=1\frac{2}{21}$ .

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QuestionAdd: 37+23=\frac{3}{7}+\frac{2}{3}=73​+32​=

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions 37\frac{3}{7}73​ and 3\frac{}{3}3​. . The fractions are in the form ab\frac{a}{b}ba​, where aaa is the numerator and bbb is the denominator.

STEP 2

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

STEP 3

Let's find the LCM of7 and3. The LCM of two numbers is the smallest number that is a multiple of both numbers. In this case, the LCM of7 and3 is21.

STEP 4

STEP 5

Now we can add the two fractions, since they have the same denominator.921+1421=9+1421\frac{9}{21} + \frac{14}{21} = \frac{9+14}{21}219​+2114​=219+14​

STEP 6

Perform the addition in the numerator.9+1421=2321\frac{9+14}{21} = \frac{23}{21}219+14​=2123​

STEP 7

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QuestionAdd: $\frac{3}{7}+\frac{2}{3}=$

Assumptions1. We are adding two fractions $\frac{3}{7}$ and $\frac{}{3}$ . . The fractions are in the form $\frac{a}{b}$ , where $a$ is the numerator and $b$ is the denominator.

Now we can add the two fractions, since they have the same denominator.
$\frac{9}{21} + \frac{14}{21} = \frac{9+14}{21}$

Perform the addition in the numerator.
$\frac{9+14}{21} = \frac{23}{21}$