Solved on Jan 26, 2024

Evaluate $8 \frac{5}{12}-6 \frac{1}{3}+4 \frac{5}{6}$ and write the answer as a mixed number in simplest form.

STEP 1

Assumptions
1. We are working with mixed numbers.
2. The operation involves subtraction and addition of these mixed numbers.
3. The mixed numbers need to be simplified after the operations.
4. The final answer should be in the form of a mixed number in simplest form.

STEP 2

First, we need to convert the mixed numbers into improper fractions to make the calculations easier.
$8 \frac{5}{12} = \frac{12 \times 8 + 5}{12} = \frac{96 + 5}{12} = \frac{101}{12}$
$6 \frac{1}{3} = \frac{3 \times 6 + 1}{3} = \frac{18 + 1}{3} = \frac{19}{3}$
$4 \frac{5}{6} = \frac{6 \times 4 + 5}{6} = \frac{24 + 5}{6} = \frac{29}{6}$

STEP 3

Now, we need to find a common denominator for the fractions to perform the addition and subtraction. The common denominator for 12, 3, and 6 is 12.

STEP 4

Convert the fractions to have the common denominator of 12.
$\frac{101}{12} \text{ already has a denominator of } 12.$
$\frac{19}{3} = \frac{19 \times 4}{3 \times 4} = \frac{76}{12}$
$\frac{29}{6} = \frac{29 \times 2}{6 \times 2} = \frac{58}{12}$

STEP 5

Now we can perform the subtraction and addition with the common denominator.
$\frac{101}{12} - \frac{76}{12} + \frac{58}{12}$

STEP 6

Combine the numerators over the common denominator.
$\frac{101 - 76 + 58}{12}$

STEP 7

Perform the arithmetic in the numerator.
$\frac{101 - 76 + 58}{12} = \frac{25 + 58}{12} = \frac{83}{12}$

STEP 8

Now, we need to convert the improper fraction back into a mixed number.
$\frac{83}{12} = 6 \frac{11}{12} \text{ (since } 83 = 6 \times 12 + 11 \text{)}$

STEP 9

The mixed number is already in its simplest form because the numerator and the denominator have no common factors other than 1.
The final answer is: $6 \frac{11}{12}$

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Evaluate $8 \frac{5}{12}-6 \frac{1}{3}+4 \frac{5}{6}$ and write the answer as a mixed number in simplest form.

STEP 1

Assumptions
1. We are working with mixed numbers.
2. The operation involves subtraction and addition of these mixed numbers.
3. The mixed numbers need to be simplified after the operations.
4. The final answer should be in the form of a mixed number in simplest form.

STEP 2

STEP 3

Now, we need to find a common denominator for the fractions to perform the addition and subtraction. The common denominator for 12, 3, and 6 is 12.

STEP 4

Convert the fractions to have the common denominator of 12.
$\frac{101}{12} \text{ already has a denominator of } 12.$
$\frac{19}{3} = \frac{19 \times 4}{3 \times 4} = \frac{76}{12}$
$\frac{29}{6} = \frac{29 \times 2}{6 \times 2} = \frac{58}{12}$

STEP 5

Now we can perform the subtraction and addition with the common denominator.
$\frac{101}{12} - \frac{76}{12} + \frac{58}{12}$

STEP 6

Combine the numerators over the common denominator.
$\frac{101 - 76 + 58}{12}$

STEP 7

Perform the arithmetic in the numerator.
$\frac{101 - 76 + 58}{12} = \frac{25 + 58}{12} = \frac{83}{12}$

STEP 8

Now, we need to convert the improper fraction back into a mixed number.
$\frac{83}{12} = 6 \frac{11}{12} \text{ (since } 83 = 6 \times 12 + 11 \text{)}$

STEP 9

The mixed number is already in its simplest form because the numerator and the denominator have no common factors other than 1.
The final answer is: $6 \frac{11}{12}$

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Evaluate 8512−613+4568 \frac{5}{12}-6 \frac{1}{3}+4 \frac{5}{6}8125​−631​+465​ and write the answer as a mixed number in simplest form.

STEP 1

Assumptions1. We are working with mixed numbers.2. The operation involves subtraction and addition of these mixed numbers.3. The mixed numbers need to be simplified after the operations.4. The final answer should be in the form of a mixed number in simplest form.

STEP 2

STEP 3

Now, we need to find a common denominator for the fractions to perform the addition and subtraction. The common denominator for 12, 3, and 6 is 12.

STEP 4

STEP 5

Now we can perform the subtraction and addition with the common denominator.10112−7612+5812 \frac{101}{12} - \frac{76}{12} + \frac{58}{12} 12101​−1276​+1258​

STEP 6

Combine the numerators over the common denominator.101−76+5812 \frac{101 - 76 + 58}{12} 12101−76+58​

STEP 7

Perform the arithmetic in the numerator.101−76+5812=25+5812=8312 \frac{101 - 76 + 58}{12} = \frac{25 + 58}{12} = \frac{83}{12} 12101−76+58​=1225+58​=1283​

STEP 8

Now, we need to convert the improper fraction back into a mixed number.8312=61112 (since 83=6×12+11) \frac{83}{12} = 6 \frac{11}{12} \text{ (since } 83 = 6 \times 12 + 11 \text{)} 1283​=61211​ (since 83=6×12+11)

STEP 9

The mixed number is already in its simplest form because the numerator and the denominator have no common factors other than 1.The final answer is: 61112 6 \frac{11}{12} 61211​

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Evaluate $8 \frac{5}{12}-6 \frac{1}{3}+4 \frac{5}{6}$ and write the answer as a mixed number in simplest form.

Assumptions
1. We are working with mixed numbers.
2. The operation involves subtraction and addition of these mixed numbers.
3. The mixed numbers need to be simplified after the operations.
4. The final answer should be in the form of a mixed number in simplest form.

Now we can perform the subtraction and addition with the common denominator.
$\frac{101}{12} - \frac{76}{12} + \frac{58}{12}$

Combine the numerators over the common denominator.
$\frac{101 - 76 + 58}{12}$

Perform the arithmetic in the numerator.
$\frac{101 - 76 + 58}{12} = \frac{25 + 58}{12} = \frac{83}{12}$

Now, we need to convert the improper fraction back into a mixed number.
$\frac{83}{12} = 6 \frac{11}{12} \text{ (since } 83 = 6 \times 12 + 11 \text{)}$

The mixed number is already in its simplest form because the numerator and the denominator have no common factors other than 1.
The final answer is: $6 \frac{11}{12}$