Solved on Jan 10, 2024

Évaluez l'expression fractionnaire $\frac{5}{9} \div \frac{4}{9}+\frac{1}{3}$ .

STEP 1

Assumptions
1. We are performing arithmetic operations with fractions.
2. The division and addition operations must follow the order of operations, which means we perform the division first and then the addition.

STEP 2

First, we need to perform the division of the two fractions. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{5}{9} \div \frac{4}{9} = \frac{5}{9} \times \frac{9}{4}$

STEP 3

Now, multiply the numerators and the denominators separately.
$\frac{5}{9} \times \frac{9}{4} = \frac{5 \times 9}{9 \times 4}$

STEP 4

Simplify the multiplication.
$\frac{5 \times 9}{9 \times 4} = \frac{45}{36}$

STEP 5

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9.
$\frac{45}{36} = \frac{45 \div 9}{36 \div 9}$

STEP 6

Calculate the simplified fraction.
$\frac{45 \div 9}{36 \div 9} = \frac{5}{4}$

STEP 7

Now that we have the result of the division, we need to add the fraction $\frac{1}{3}$ to it.
$\frac{5}{4} + \frac{1}{3}$

STEP 8

To add fractions, they must have a common denominator. The least common denominator (LCD) for 4 and 3 is 12.

STEP 9

Convert both fractions to have the common denominator of 12.
$\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}$
$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

STEP 10

Now, add the two fractions with the common denominator.
$\frac{15}{12} + \frac{4}{12} = \frac{15 + 4}{12}$

STEP 11

Calculate the sum of the numerators.
$\frac{15 + 4}{12} = \frac{19}{12}$

STEP 12

The fraction $\frac{19}{12}$ is an improper fraction, and it can be left as is, or it can be converted to a mixed number. To convert it to a mixed number, divide 19 by 12.
$19 \div 12 = 1 \text{ remainder } 7$

STEP 13

Write the result as a mixed number.
$\frac{19}{12} = 1 \frac{7}{12}$
The solution to the problem $\frac{5}{9} \div \frac{4}{9}+\frac{1}{3}$ is $1 \frac{7}{12}$ .

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Évaluez l'expression fractionnaire $\frac{5}{9} \div \frac{4}{9}+\frac{1}{3}$ .

STEP 1

Assumptions
1. We are performing arithmetic operations with fractions.
2. The division and addition operations must follow the order of operations, which means we perform the division first and then the addition.

STEP 2

First, we need to perform the division of the two fractions. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{5}{9} \div \frac{4}{9} = \frac{5}{9} \times \frac{9}{4}$

STEP 3

Now, multiply the numerators and the denominators separately.
$\frac{5}{9} \times \frac{9}{4} = \frac{5 \times 9}{9 \times 4}$

STEP 4

Simplify the multiplication.
$\frac{5 \times 9}{9 \times 4} = \frac{45}{36}$

STEP 5

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9.
$\frac{45}{36} = \frac{45 \div 9}{36 \div 9}$

STEP 6

Calculate the simplified fraction.
$\frac{45 \div 9}{36 \div 9} = \frac{5}{4}$

STEP 7

Now that we have the result of the division, we need to add the fraction $\frac{1}{3}$ to it.
$\frac{5}{4} + \frac{1}{3}$

STEP 8

To add fractions, they must have a common denominator. The least common denominator (LCD) for 4 and 3 is 12.

STEP 9

Convert both fractions to have the common denominator of 12.
$\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}$
$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

STEP 10

Now, add the two fractions with the common denominator.
$\frac{15}{12} + \frac{4}{12} = \frac{15 + 4}{12}$

STEP 11

Calculate the sum of the numerators.
$\frac{15 + 4}{12} = \frac{19}{12}$

STEP 12

The fraction $\frac{19}{12}$ is an improper fraction, and it can be left as is, or it can be converted to a mixed number. To convert it to a mixed number, divide 19 by 12.
$19 \div 12 = 1 \text{ remainder } 7$

STEP 13

Write the result as a mixed number.
$\frac{19}{12} = 1 \frac{7}{12}$
The solution to the problem $\frac{5}{9} \div \frac{4}{9}+\frac{1}{3}$ is $1 \frac{7}{12}$ .

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Évaluez l'expression fractionnaire 59÷49+13\frac{5}{9} \div \frac{4}{9}+\frac{1}{3}95​÷94​+31​.

STEP 1

Assumptions1. We are performing arithmetic operations with fractions.2. The division and addition operations must follow the order of operations, which means we perform the division first and then the addition.

STEP 2

First, we need to perform the division of the two fractions. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.59÷49=59×94\frac{5}{9} \div \frac{4}{9} = \frac{5}{9} \times \frac{9}{4}95​÷94​=95​×49​

STEP 3

Now, multiply the numerators and the denominators separately.59×94=5×99×4\frac{5}{9} \times \frac{9}{4} = \frac{5 \times 9}{9 \times 4}95​×49​=9×45×9​

STEP 4

Simplify the multiplication.5×99×4=4536\frac{5 \times 9}{9 \times 4} = \frac{45}{36}9×45×9​=3645​

STEP 5

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9.4536=45÷936÷9\frac{45}{36} = \frac{45 \div 9}{36 \div 9}3645​=36÷945÷9​

STEP 6

Calculate the simplified fraction.45÷936÷9=54\frac{45 \div 9}{36 \div 9} = \frac{5}{4}36÷945÷9​=45​

STEP 7

Now that we have the result of the division, we need to add the fraction 13\frac{1}{3}31​ to it.54+13\frac{5}{4} + \frac{1}{3}45​+31​

STEP 8

To add fractions, they must have a common denominator. The least common denominator (LCD) for 4 and 3 is 12.

STEP 9

Convert both fractions to have the common denominator of 12.54=5×34×3=1512\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}45​=4×35×3​=1215​13=1×43×4=412\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}31​=3×41×4​=124​

STEP 10

Now, add the two fractions with the common denominator.1512+412=15+412\frac{15}{12} + \frac{4}{12} = \frac{15 + 4}{12}1215​+124​=1215+4​

STEP 11

Calculate the sum of the numerators.15+412=1912\frac{15 + 4}{12} = \frac{19}{12}1215+4​=1219​

STEP 12

The fraction 1912\frac{19}{12}1219​ is an improper fraction, and it can be left as is, or it can be converted to a mixed number. To convert it to a mixed number, divide 19 by 12.19÷12=1 remainder 719 \div 12 = 1 \text{ remainder } 719÷12=1 remainder 7

STEP 13

Write the result as a mixed number.1912=1712\frac{19}{12} = 1 \frac{7}{12}1219​=1127​The solution to the problem 59÷49+13\frac{5}{9} \div \frac{4}{9}+\frac{1}{3}95​÷94​+31​ is 17121 \frac{7}{12}1127​.

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Évaluez l'expression fractionnaire $\frac{5}{9} \div \frac{4}{9}+\frac{1}{3}$ .

Assumptions
1. We are performing arithmetic operations with fractions.
2. The division and addition operations must follow the order of operations, which means we perform the division first and then the addition.

First, we need to perform the division of the two fractions. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{5}{9} \div \frac{4}{9} = \frac{5}{9} \times \frac{9}{4}$

Now, multiply the numerators and the denominators separately.
$\frac{5}{9} \times \frac{9}{4} = \frac{5 \times 9}{9 \times 4}$

Simplify the multiplication.
$\frac{5 \times 9}{9 \times 4} = \frac{45}{36}$

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9.
$\frac{45}{36} = \frac{45 \div 9}{36 \div 9}$

Calculate the simplified fraction.
$\frac{45 \div 9}{36 \div 9} = \frac{5}{4}$

Now that we have the result of the division, we need to add the fraction $\frac{1}{3}$ to it.
$\frac{5}{4} + \frac{1}{3}$

Convert both fractions to have the common denominator of 12.
$\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}$
$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

Now, add the two fractions with the common denominator.
$\frac{15}{12} + \frac{4}{12} = \frac{15 + 4}{12}$

Calculate the sum of the numerators.
$\frac{15 + 4}{12} = \frac{19}{12}$

The fraction $\frac{19}{12}$ is an improper fraction, and it can be left as is, or it can be converted to a mixed number. To convert it to a mixed number, divide 19 by 12.
$19 \div 12 = 1 \text{ remainder } 7$

Write the result as a mixed number.
$\frac{19}{12} = 1 \frac{7}{12}$
The solution to the problem $\frac{5}{9} \div \frac{4}{9}+\frac{1}{3}$ is $1 \frac{7}{12}$ .