QuestionDivide and simplify: $\frac{5}{6} \div \frac{25}{9}$ . Choose A for a number or fraction, B if undefined.

Studdy Solution

STEP 1

Assumptions1. We are dividing two fractions, $\frac{5}{6}$ and $\frac{25}{9}$ . . The division of fractions is defined as multiplication by the reciprocal of the divisor.

STEP 2

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
$\frac{5}{6} \div \frac{25}{9} = \frac{5}{6} \times \frac{9}{25}$

STEP 3

Now, we multiply the numerators together and the denominators together.
$\frac{5}{6} \times \frac{9}{25} = \frac{5 \times9}{6 \times25}$

STEP 4

Calculate the multiplication in the numerator and the denominator.
$\frac{ \times9}{6 \times25} = \frac{45}{150}$

STEP 5

Now, we simplify the fraction to its simplest form. We can do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of45 and150 is15.
$\frac{45}{150} = \frac{45 \div15}{150 \div15}$

STEP 6

Calculate the division in the numerator and the denominator.
$\frac{45 \div15}{150 \div15} = \frac{3}{10}$ So, $\frac{5}{6} \div \frac{25}{9} = \frac{3}{10}$ .

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QuestionDivide and simplify: $\frac{5}{6} \div \frac{25}{9}$ . Choose A for a number or fraction, B if undefined.

Studdy Solution

STEP 1

Assumptions1. We are dividing two fractions, $\frac{5}{6}$ and $\frac{25}{9}$ . . The division of fractions is defined as multiplication by the reciprocal of the divisor.

STEP 2

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
$\frac{5}{6} \div \frac{25}{9} = \frac{5}{6} \times \frac{9}{25}$

STEP 3

Now, we multiply the numerators together and the denominators together.
$\frac{5}{6} \times \frac{9}{25} = \frac{5 \times9}{6 \times25}$

STEP 4

Calculate the multiplication in the numerator and the denominator.
$\frac{ \times9}{6 \times25} = \frac{45}{150}$

STEP 5

Now, we simplify the fraction to its simplest form. We can do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of45 and150 is15.
$\frac{45}{150} = \frac{45 \div15}{150 \div15}$

STEP 6

Calculate the division in the numerator and the denominator.
$\frac{45 \div15}{150 \div15} = \frac{3}{10}$ So, $\frac{5}{6} \div \frac{25}{9} = \frac{3}{10}$ .

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QuestionDivide and simplify: 56÷259\frac{5}{6} \div \frac{25}{9}65​÷925​. Choose A for a number or fraction, B if undefined.

Studdy Solution

STEP 1

Assumptions1. We are dividing two fractions, 56\frac{5}{6}65​ and 259\frac{25}{9}925​. . The division of fractions is defined as multiplication by the reciprocal of the divisor.

STEP 2

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.56÷259=56×925\frac{5}{6} \div \frac{25}{9} = \frac{5}{6} \times \frac{9}{25} 65​÷925​=65​×259​

STEP 3

Now, we multiply the numerators together and the denominators together.56×925=5×96×25\frac{5}{6} \times \frac{9}{25} = \frac{5 \times9}{6 \times25} 65​×259​=6×255×9​

STEP 4

Calculate the multiplication in the numerator and the denominator.×96×25=45150\frac{ \times9}{6 \times25} = \frac{45}{150} 6×25×9​=15045​

STEP 5

Now, we simplify the fraction to its simplest form. We can do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of45 and150 is15.45150=45÷15150÷15\frac{45}{150} = \frac{45 \div15}{150 \div15} 15045​=150÷1545÷15​

STEP 6

Calculate the division in the numerator and the denominator.45÷15150÷15=310\frac{45 \div15}{150 \div15} = \frac{3}{10} 150÷1545÷15​=103​So, 56÷259=310\frac{5}{6} \div \frac{25}{9} = \frac{3}{10}65​÷925​=103​.

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QuestionDivide and simplify: $\frac{5}{6} \div \frac{25}{9}$ . Choose A for a number or fraction, B if undefined.

Assumptions1. We are dividing two fractions, $\frac{5}{6}$ and $\frac{25}{9}$ . . The division of fractions is defined as multiplication by the reciprocal of the divisor.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
$\frac{5}{6} \div \frac{25}{9} = \frac{5}{6} \times \frac{9}{25}$

Now, we multiply the numerators together and the denominators together.
$\frac{5}{6} \times \frac{9}{25} = \frac{5 \times9}{6 \times25}$

Calculate the multiplication in the numerator and the denominator.
$\frac{ \times9}{6 \times25} = \frac{45}{150}$

Now, we simplify the fraction to its simplest form. We can do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of45 and150 is15.
$\frac{45}{150} = \frac{45 \div15}{150 \div15}$

Calculate the division in the numerator and the denominator.
$\frac{45 \div15}{150 \div15} = \frac{3}{10}$ So, $\frac{5}{6} \div \frac{25}{9} = \frac{3}{10}$ .