Math / Numbers & Operations

QuestionEvaluate. Write your answer as a fraction. $\frac{3}{10} + \frac{1}{8} + \frac{3}{4}$

Studdy Solution

STEP 1

1. We are given three fractions: $\frac{3}{10}$ , $\frac{1}{8}$ , and $\frac{3}{4}$ .
2. We need to find the sum of these fractions and express the result as a single fraction.

STEP 2

1. Find a common denominator.
2. Convert each fraction to an equivalent fraction with the common denominator.
3. Add the fractions.
4. Simplify the resulting fraction if necessary.

STEP 3

Identify the least common denominator (LCD) for the fractions $\frac{3}{10}$ , $\frac{1}{8}$ , and $\frac{3}{4}$ .
- The denominators are $10$ , $8$ , and $4$ . - The least common multiple of $10$ , $8$ , and $4$ is $40$ .

STEP 4

Convert each fraction to an equivalent fraction with the common denominator $40$ .
- Convert $\frac{3}{10}$ to an equivalent fraction with denominator $40$ : $ \frac{3}{10} = \frac{3 \times 4}{10 \times 4} = \frac{12}{40} \]
- Convert $\frac{1}{8}$ to an equivalent fraction with denominator $40$ : $ \frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40} \]
- Convert $\frac{3}{4}$ to an equivalent fraction with denominator $40$ : $ \frac{3}{4} = \frac{3 \times 10}{4 \times 10} = \frac{30}{40} \]

STEP 5

Add the fractions $\frac{12}{40}$ , $\frac{5}{40}$ , and $\frac{30}{40}$ .
$\frac{12}{40} + \frac{5}{40} + \frac{30}{40} = \frac{12 + 5 + 30}{40} = \frac{47}{40}$

STEP 6

Simplify the fraction $\frac{47}{40}$ if necessary.
- Since $47$ and $40$ have no common factors other than $1$ , $\frac{47}{40}$ is already in its simplest form.
The sum of the fractions is:
$\boxed{\frac{47}{40}}$

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QuestionEvaluate. Write your answer as a fraction. $\frac{3}{10} + \frac{1}{8} + \frac{3}{4}$

Studdy Solution

STEP 1

1. We are given three fractions: $\frac{3}{10}$ , $\frac{1}{8}$ , and $\frac{3}{4}$ .
2. We need to find the sum of these fractions and express the result as a single fraction.

STEP 2

1. Find a common denominator.
2. Convert each fraction to an equivalent fraction with the common denominator.
3. Add the fractions.
4. Simplify the resulting fraction if necessary.

STEP 3

Identify the least common denominator (LCD) for the fractions $\frac{3}{10}$ , $\frac{1}{8}$ , and $\frac{3}{4}$ .
- The denominators are $10$ , $8$ , and $4$ . - The least common multiple of $10$ , $8$ , and $4$ is $40$ .

STEP 4

STEP 5

Add the fractions $\frac{12}{40}$ , $\frac{5}{40}$ , and $\frac{30}{40}$ .
$\frac{12}{40} + \frac{5}{40} + \frac{30}{40} = \frac{12 + 5 + 30}{40} = \frac{47}{40}$

STEP 6

Simplify the fraction $\frac{47}{40}$ if necessary.
- Since $47$ and $40$ have no common factors other than $1$ , $\frac{47}{40}$ is already in its simplest form.
The sum of the fractions is:
$\boxed{\frac{47}{40}}$

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QuestionEvaluate. Write your answer as a fraction. 310+18+34\frac{3}{10} + \frac{1}{8} + \frac{3}{4}103​+81​+43​

Studdy Solution

STEP 1

1. We are given three fractions: 310\frac{3}{10}103​, 18\frac{1}{8}81​, and 34\frac{3}{4}43​.2. We need to find the sum of these fractions and express the result as a single fraction.

STEP 2

1. Find a common denominator.2. Convert each fraction to an equivalent fraction with the common denominator.3. Add the fractions.4. Simplify the resulting fraction if necessary.

STEP 3

Identify the least common denominator (LCD) for the fractions 310\frac{3}{10}103​, 18\frac{1}{8}81​, and 34\frac{3}{4}43​.- The denominators are 101010, 888, and 444. - The least common multiple of 101010, 888, and 444 is 404040.

STEP 4

STEP 5

Add the fractions 1240\frac{12}{40}4012​, 540\frac{5}{40}405​, and 3040\frac{30}{40}4030​.1240+540+3040=12+5+3040=4740\frac{12}{40} + \frac{5}{40} + \frac{30}{40} = \frac{12 + 5 + 30}{40} = \frac{47}{40}4012​+405​+4030​=4012+5+30​=4047​

STEP 6

Simplify the fraction 4740\frac{47}{40}4047​ if necessary.- Since 474747 and 404040 have no common factors other than 111, 4740\frac{47}{40}4047​ is already in its simplest form. The sum of the fractions is:4740\boxed{\frac{47}{40}}4047​​

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QuestionEvaluate. Write your answer as a fraction. $\frac{3}{10} + \frac{1}{8} + \frac{3}{4}$

1. We are given three fractions: $\frac{3}{10}$ , $\frac{1}{8}$ , and $\frac{3}{4}$ .
2. We need to find the sum of these fractions and express the result as a single fraction.

1. Find a common denominator.
2. Convert each fraction to an equivalent fraction with the common denominator.
3. Add the fractions.
4. Simplify the resulting fraction if necessary.

Identify the least common denominator (LCD) for the fractions $\frac{3}{10}$ , $\frac{1}{8}$ , and $\frac{3}{4}$ .
- The denominators are $10$ , $8$ , and $4$ . - The least common multiple of $10$ , $8$ , and $4$ is $40$ .

Add the fractions $\frac{12}{40}$ , $\frac{5}{40}$ , and $\frac{30}{40}$ .
$\frac{12}{40} + \frac{5}{40} + \frac{30}{40} = \frac{12 + 5 + 30}{40} = \frac{47}{40}$

Simplify the fraction $\frac{47}{40}$ if necessary.
- Since $47$ and $40$ have no common factors other than $1$ , $\frac{47}{40}$ is already in its simplest form.
The sum of the fractions is:
$\boxed{\frac{47}{40}}$