Solved on Sep 06, 2023

Simplify the division problem $\frac{7}{4} \div 1 \frac{3}{4}$ and select the correct answer.

STEP 1

Assumptions1. We are given a fraction divided by a mixed number. . We need to simplify the expression.

STEP 2

First, we need to convert the mixed number into an improper fraction. The formula to convert a mixed number to an improper fraction is $\text{Improper Fraction} = \text{Whole Number} \times \text{Denominator} + \text{umerator}$

STEP 3

Now, plug in the values for the whole number, denominator, and numerator from the mixed number $1 \frac{3}{}$ to calculate the improper fraction.
$\text{Improper Fraction} =1 \times +3$

STEP 4

Calculate the improper fraction.
$\text{Improper Fraction} =1 \times4 +3 =7$ So, $1 \frac{3}{4}$ is equivalent to $\frac{7}{4}$ .

STEP 5

Now, we can rewrite the original expression using the improper fraction instead of the mixed number.
$\frac{7}{4} \div \frac{7}{4}$

STEP 6

The division of two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
So, we rewrite the expression as $\frac{}{4} \times \frac{4}{}$

STEP 7

Now, we can multiply the fractions. When multiplying fractions, we multiply the numerators together and the denominators together.
$\frac{7 \times4}{4 \times7}$

STEP 8

Calculate the multiplication.
$\frac{7 \times4}{4 \times7} = \frac{28}{28}$

STEP 9

implify the fraction.
$\frac{28}{28} =$ So, the simplified form of $\frac{7}{4} \div \frac{3}{4}$ is $$.

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Simplify the division problem $\frac{7}{4} \div 1 \frac{3}{4}$ and select the correct answer.

STEP 1

Assumptions1. We are given a fraction divided by a mixed number. . We need to simplify the expression.

STEP 2

First, we need to convert the mixed number into an improper fraction. The formula to convert a mixed number to an improper fraction is $\text{Improper Fraction} = \text{Whole Number} \times \text{Denominator} + \text{umerator}$

STEP 3

Now, plug in the values for the whole number, denominator, and numerator from the mixed number $1 \frac{3}{}$ to calculate the improper fraction.
$\text{Improper Fraction} =1 \times +3$

STEP 4

Calculate the improper fraction.
$\text{Improper Fraction} =1 \times4 +3 =7$ So, $1 \frac{3}{4}$ is equivalent to $\frac{7}{4}$ .

STEP 5

Now, we can rewrite the original expression using the improper fraction instead of the mixed number.
$\frac{7}{4} \div \frac{7}{4}$

STEP 6

The division of two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
So, we rewrite the expression as $\frac{}{4} \times \frac{4}{}$

STEP 7

Now, we can multiply the fractions. When multiplying fractions, we multiply the numerators together and the denominators together.
$\frac{7 \times4}{4 \times7}$

STEP 8

Calculate the multiplication.
$\frac{7 \times4}{4 \times7} = \frac{28}{28}$

STEP 9

implify the fraction.
$\frac{28}{28} =$ So, the simplified form of $\frac{7}{4} \div \frac{3}{4}$ is $$.

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Simplify the division problem 74÷134\frac{7}{4} \div 1 \frac{3}{4}47​÷143​ and select the correct answer.

STEP 1

Assumptions1. We are given a fraction divided by a mixed number. . We need to simplify the expression.

STEP 2

STEP 3

Now, plug in the values for the whole number, denominator, and numerator from the mixed number 131 \frac{3}{}13​ to calculate the improper fraction.Improper Fraction=1×+3\text{Improper Fraction} =1 \times +3Improper Fraction=1×+3

STEP 4

Calculate the improper fraction.Improper Fraction=1×4+3=7\text{Improper Fraction} =1 \times4 +3 =7Improper Fraction=1×4+3=7So, 1341 \frac{3}{4}143​ is equivalent to 74\frac{7}{4}47​.

STEP 5

Now, we can rewrite the original expression using the improper fraction instead of the mixed number.74÷74\frac{7}{4} \div \frac{7}{4}47​÷47​

STEP 6

The division of two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.So, we rewrite the expression as4×4\frac{}{4} \times \frac{4}{}4​×4​

STEP 7

Now, we can multiply the fractions. When multiplying fractions, we multiply the numerators together and the denominators together.7×44×7\frac{7 \times4}{4 \times7}4×77×4​

STEP 8

Calculate the multiplication.7×44×7=2828\frac{7 \times4}{4 \times7} = \frac{28}{28}4×77×4​=2828​

STEP 9

implify the fraction.2828=\frac{28}{28} =2828​=So, the simplified form of 74÷34\frac{7}{4} \div \frac{3}{4}47​÷43​ is $$.

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Simplify the division problem $\frac{7}{4} \div 1 \frac{3}{4}$ and select the correct answer.

Now, plug in the values for the whole number, denominator, and numerator from the mixed number $1 \frac{3}{}$ to calculate the improper fraction.
$\text{Improper Fraction} =1 \times +3$

Calculate the improper fraction.
$\text{Improper Fraction} =1 \times4 +3 =7$ So, $1 \frac{3}{4}$ is equivalent to $\frac{7}{4}$ .

Now, we can rewrite the original expression using the improper fraction instead of the mixed number.
$\frac{7}{4} \div \frac{7}{4}$

The division of two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
So, we rewrite the expression as $\frac{}{4} \times \frac{4}{}$

Now, we can multiply the fractions. When multiplying fractions, we multiply the numerators together and the denominators together.
$\frac{7 \times4}{4 \times7}$

Calculate the multiplication.
$\frac{7 \times4}{4 \times7} = \frac{28}{28}$

implify the fraction.
$\frac{28}{28} =$ So, the simplified form of $\frac{7}{4} \div \frac{3}{4}$ is $$.