Question Simplify the expression $\frac{7}{8} \div \frac{5}{4}$ and express the result as a simplified fraction.

Studdy Solution

STEP 1

Assumptions1. We are dividing two fractions, $\frac{7}{8}$ and $\frac{5}{4}$ . . The division of fractions is done by multiplying the first fraction by the reciprocal of the second fraction.
3. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
4. The simplest form of a fraction is achieved when the numerator and the denominator are coprime, i.e., their greatest common divisor (GCD) is1.

STEP 2

First, we need to find the reciprocal of the second fraction, $\frac{5}{4}$ .
$Reciprocal\, of\, \frac{5}{4} = \frac{4}{5}$

STEP 3

Now, we perform the division by multiplying the first fraction by the reciprocal of the second fraction.
$\frac{7}{8} \div \frac{5}{} = \frac{7}{8} \times \frac{}{5}$

STEP 4

To multiply two fractions, we multiply the numerators together to get the new numerator, and the denominators together to get the new denominator.
$\frac{7}{8} \times \frac{4}{} = \frac{7 \times4}{8 \times}$

STEP 5

Perform the multiplication in the numerator and the denominator.
$\frac{7 \times4}{8 \times5} = \frac{28}{40}$

STEP 6

Now, we simplify the fraction to its simplest form. We do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of28 and40 is4.
$\frac{28}{40} = \frac{28 \div4}{40 \div4}$

STEP 7

Perform the division in the numerator and the denominator.
$\frac{28 \div4}{40 \div4} = \frac{7}{10}$ So, $\frac{7}{} \div \frac{5}{4}$ simplifies to $\frac{7}{10}$ in its simplest form.

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Question Simplify the expression $\frac{7}{8} \div \frac{5}{4}$ and express the result as a simplified fraction.

Studdy Solution

STEP 1

STEP 2

First, we need to find the reciprocal of the second fraction, $\frac{5}{4}$ .
$Reciprocal\, of\, \frac{5}{4} = \frac{4}{5}$

STEP 3

Now, we perform the division by multiplying the first fraction by the reciprocal of the second fraction.
$\frac{7}{8} \div \frac{5}{} = \frac{7}{8} \times \frac{}{5}$

STEP 4

To multiply two fractions, we multiply the numerators together to get the new numerator, and the denominators together to get the new denominator.
$\frac{7}{8} \times \frac{4}{} = \frac{7 \times4}{8 \times}$

STEP 5

Perform the multiplication in the numerator and the denominator.
$\frac{7 \times4}{8 \times5} = \frac{28}{40}$

STEP 6

Now, we simplify the fraction to its simplest form. We do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of28 and40 is4.
$\frac{28}{40} = \frac{28 \div4}{40 \div4}$

STEP 7

Perform the division in the numerator and the denominator.
$\frac{28 \div4}{40 \div4} = \frac{7}{10}$ So, $\frac{7}{} \div \frac{5}{4}$ simplifies to $\frac{7}{10}$ in its simplest form.

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Question Simplify the expression 78÷54\frac{7}{8} \div \frac{5}{4}87​÷45​ and express the result as a simplified fraction.

Studdy Solution

STEP 1

STEP 2

First, we need to find the reciprocal of the second fraction, 54\frac{5}{4}45​.Reciprocal of 54=45Reciprocal\, of\, \frac{5}{4} = \frac{4}{5}Reciprocalof45​=54​

STEP 3

Now, we perform the division by multiplying the first fraction by the reciprocal of the second fraction.78÷5=78×5\frac{7}{8} \div \frac{5}{} = \frac{7}{8} \times \frac{}{5}87​÷5​=87​×5​

STEP 4

To multiply two fractions, we multiply the numerators together to get the new numerator, and the denominators together to get the new denominator.78×4=7×48×\frac{7}{8} \times \frac{4}{} = \frac{7 \times4}{8 \times}87​×4​=8×7×4​

STEP 5

Perform the multiplication in the numerator and the denominator.7×48×5=2840\frac{7 \times4}{8 \times5} = \frac{28}{40}8×57×4​=4028​

STEP 6

Now, we simplify the fraction to its simplest form. We do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of28 and40 is4.2840=28÷440÷4\frac{28}{40} = \frac{28 \div4}{40 \div4}4028​=40÷428÷4​

STEP 7

Perform the division in the numerator and the denominator.28÷440÷4=710\frac{28 \div4}{40 \div4} = \frac{7}{10}40÷428÷4​=107​So, 7÷54\frac{7}{} \div \frac{5}{4}7​÷45​ simplifies to 710\frac{7}{10}107​ in its simplest form.

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Question Simplify the expression $\frac{7}{8} \div \frac{5}{4}$ and express the result as a simplified fraction.

First, we need to find the reciprocal of the second fraction, $\frac{5}{4}$ .
$Reciprocal\, of\, \frac{5}{4} = \frac{4}{5}$

Now, we perform the division by multiplying the first fraction by the reciprocal of the second fraction.
$\frac{7}{8} \div \frac{5}{} = \frac{7}{8} \times \frac{}{5}$

To multiply two fractions, we multiply the numerators together to get the new numerator, and the denominators together to get the new denominator.
$\frac{7}{8} \times \frac{4}{} = \frac{7 \times4}{8 \times}$

Perform the multiplication in the numerator and the denominator.
$\frac{7 \times4}{8 \times5} = \frac{28}{40}$

Now, we simplify the fraction to its simplest form. We do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of28 and40 is4.
$\frac{28}{40} = \frac{28 \div4}{40 \div4}$

Perform the division in the numerator and the denominator.
$\frac{28 \div4}{40 \div4} = \frac{7}{10}$ So, $\frac{7}{} \div \frac{5}{4}$ simplifies to $\frac{7}{10}$ in its simplest form.