QuestionFind the sum of $\frac{3}{4}$ and $\frac{1}{7}$ and select the simplified form from the options: a. $\frac{25}{28}$ , b. 56, c. 28, d. $\frac{50}{56}$ .

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions $\frac{3}{4}$ and $\frac{1}{7}$ . . We need to find the least common denominator (LCD) to add these fractions.
3. The result should be simplified to its lowest terms.

STEP 2

First, we need to find the least common denominator (LCD) of the two fractions. The LCD is the least common multiple (LCM) of the denominators of the fractions.
$LCD = LCM(4,7)$

STEP 3

Since and7 are both prime numbers, their least common multiple is simply their product.
$LCD = \times7$

STEP 4

Calculate the LCD.
$LCD =4 \times7 =28$

STEP 5

Now that we have the LCD, we can rewrite each fraction with this new denominator. To do this, we multiply the numerator and denominator of each fraction by the factor that makes the denominator equal to the LCD.
$\frac{3}{4} = \frac{3 \times7}{4 \times7}$ $\frac{1}{7} = \frac{1 \times4}{7 \times4}$

STEP 6

Calculate the new fractions.
$\frac{3}{4} = \frac{21}{28}$ $\frac{1}{} = \frac{4}{28}$

STEP 7

Now we can add the two fractions.
$\frac{21}{28} + \frac{4}{28}$

STEP 8

Add the numerators of the fractions.
$\frac{21 +4}{28}$

STEP 9

Calculate the sum.
$\frac{25}{28}$ The simplified sum of $\frac{3}{4}$ and $\frac{}{7}$ is $\frac{25}{28}$ .

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QuestionFind the sum of $\frac{3}{4}$ and $\frac{1}{7}$ and select the simplified form from the options: a. $\frac{25}{28}$ , b. 56, c. 28, d. $\frac{50}{56}$ .

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions $\frac{3}{4}$ and $\frac{1}{7}$ . . We need to find the least common denominator (LCD) to add these fractions.
3. The result should be simplified to its lowest terms.

STEP 2

First, we need to find the least common denominator (LCD) of the two fractions. The LCD is the least common multiple (LCM) of the denominators of the fractions.
$LCD = LCM(4,7)$

STEP 3

Since and7 are both prime numbers, their least common multiple is simply their product.
$LCD = \times7$

STEP 4

Calculate the LCD.
$LCD =4 \times7 =28$

STEP 5

Now that we have the LCD, we can rewrite each fraction with this new denominator. To do this, we multiply the numerator and denominator of each fraction by the factor that makes the denominator equal to the LCD.
$\frac{3}{4} = \frac{3 \times7}{4 \times7}$ $\frac{1}{7} = \frac{1 \times4}{7 \times4}$

STEP 6

Calculate the new fractions.
$\frac{3}{4} = \frac{21}{28}$ $\frac{1}{} = \frac{4}{28}$

STEP 7

Now we can add the two fractions.
$\frac{21}{28} + \frac{4}{28}$

STEP 8

Add the numerators of the fractions.
$\frac{21 +4}{28}$

STEP 9

Calculate the sum.
$\frac{25}{28}$ The simplified sum of $\frac{3}{4}$ and $\frac{}{7}$ is $\frac{25}{28}$ .

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QuestionFind the sum of 34\frac{3}{4}43​ and 17\frac{1}{7}71​ and select the simplified form from the options: a. 2528\frac{25}{28}2825​, b. 56, c. 28, d. 5056\frac{50}{56}5650​.

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions 34\frac{3}{4}43​ and 17\frac{1}{7}71​. . We need to find the least common denominator (LCD) to add these fractions.3. The result should be simplified to its lowest terms.

STEP 2

First, we need to find the least common denominator (LCD) of the two fractions. The LCD is the least common multiple (LCM) of the denominators of the fractions.LCD=LCM(4,7)LCD = LCM(4,7)LCD=LCM(4,7)

STEP 3

Since and7 are both prime numbers, their least common multiple is simply their product.LCD=×7LCD = \times7LCD=×7

STEP 4

Calculate the LCD.LCD=4×7=28LCD =4 \times7 =28LCD=4×7=28

STEP 5

STEP 6

Calculate the new fractions.34=2128\frac{3}{4} = \frac{21}{28}43​=2821​1=428\frac{1}{} = \frac{4}{28}1​=284​

STEP 7

Now we can add the two fractions.2128+428\frac{21}{28} + \frac{4}{28}2821​+284​

STEP 8

Add the numerators of the fractions.21+428\frac{21 +4}{28}2821+4​

STEP 9

Calculate the sum.2528\frac{25}{28}2825​The simplified sum of 34\frac{3}{4}43​ and 7\frac{}{7}7​ is 2528\frac{25}{28}2825​.

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QuestionFind the sum of $\frac{3}{4}$ and $\frac{1}{7}$ and select the simplified form from the options: a. $\frac{25}{28}$ , b. 56, c. 28, d. $\frac{50}{56}$ .

Assumptions1. We are adding two fractions $\frac{3}{4}$ and $\frac{1}{7}$ . . We need to find the least common denominator (LCD) to add these fractions.
3. The result should be simplified to its lowest terms.

First, we need to find the least common denominator (LCD) of the two fractions. The LCD is the least common multiple (LCM) of the denominators of the fractions.
$LCD = LCM(4,7)$

Since and7 are both prime numbers, their least common multiple is simply their product.
$LCD = \times7$

Calculate the LCD.
$LCD =4 \times7 =28$

Calculate the new fractions.
$\frac{3}{4} = \frac{21}{28}$ $\frac{1}{} = \frac{4}{28}$

Now we can add the two fractions.
$\frac{21}{28} + \frac{4}{28}$

Add the numerators of the fractions.
$\frac{21 +4}{28}$

Calculate the sum.
$\frac{25}{28}$ The simplified sum of $\frac{3}{4}$ and $\frac{}{7}$ is $\frac{25}{28}$ .