Solved on Feb 10, 2024

Perform long division on the expression $\frac{113}{9}$ .

STEP 1

Assumptions
1. We are performing long division of the fraction $\frac{113}{9}$ .
2. The dividend is 113 and the divisor is 9.

STEP 2

Set up the long division by writing 113 as the dividend inside the division bracket and 9 as the divisor outside.
$\begin{array}{r} \phantom{0} \\ 9 \overline{\smash{\big)}113} \\ \end{array}$

STEP 3

Determine how many times 9 can go into the first digit of the dividend (1) without exceeding it. Since 9 is greater than 1, we cannot divide 1 by 9. We then consider the first two digits of the dividend (11).
$\begin{array}{r} \phantom{0} \\ 9 \overline{\smash{\big)}11\phantom{3}} \\ \end{array}$

STEP 4

Determine how many times 9 can go into 11 without exceeding it. 9 goes into 11 once (1 times 9 is 9).
$\begin{array}{r} \phantom{0}1 \\ 9 \overline{\smash{\big)}113} \\ \phantom{0}9\phantom{3} \\ \end{array}$

STEP 5

Subtract the product of the divisor and the quotient from the first part of the dividend. Write the result below the first part of the dividend.
$\begin{array}{r} \phantom{0}1 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}2\phantom{3} \\ \end{array}$

STEP 6

Bring down the next digit of the dividend (which is 3) to the right of the remainder from the previous step.
$\begin{array}{r} \phantom{0}1 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}23 \\ \end{array}$

STEP 7

Determine how many times 9 can go into 23 without exceeding it. 9 goes into 23 two times (2 times 9 is 18).
$\begin{array}{r} \phantom{0}12 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}23 \\ -(18) \\ \end{array}$

STEP 8

Subtract the product of the divisor and the new quotient from the number you got after bringing down the last digit. Write the result below.
$\begin{array}{r} \phantom{0}12 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}23 \\ -(18) \\ \phantom{00}5 \\ \end{array}$

STEP 9

Since there are no more digits to bring down, the number at the bottom (5) is the remainder of the division.

STEP 10

Write the final answer, which includes the quotient and the remainder. The quotient is 12 and the remainder is 5.
$\frac{113}{9} = 12 \text{ remainder } 5$
Alternatively, we can express the remainder as a fraction by placing it over the original divisor:
$\frac{113}{9} = 12 \frac{5}{9}$

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Perform long division on the expression $\frac{113}{9}$ .

STEP 1

Assumptions
1. We are performing long division of the fraction $\frac{113}{9}$ .
2. The dividend is 113 and the divisor is 9.

STEP 2

Set up the long division by writing 113 as the dividend inside the division bracket and 9 as the divisor outside.
$\begin{array}{r} \phantom{0} \\ 9 \overline{\smash{\big)}113} \\ \end{array}$

STEP 3

Determine how many times 9 can go into the first digit of the dividend (1) without exceeding it. Since 9 is greater than 1, we cannot divide 1 by 9. We then consider the first two digits of the dividend (11).
$\begin{array}{r} \phantom{0} \\ 9 \overline{\smash{\big)}11\phantom{3}} \\ \end{array}$

STEP 4

Determine how many times 9 can go into 11 without exceeding it. 9 goes into 11 once (1 times 9 is 9).
$\begin{array}{r} \phantom{0}1 \\ 9 \overline{\smash{\big)}113} \\ \phantom{0}9\phantom{3} \\ \end{array}$

STEP 5

Subtract the product of the divisor and the quotient from the first part of the dividend. Write the result below the first part of the dividend.
$\begin{array}{r} \phantom{0}1 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}2\phantom{3} \\ \end{array}$

STEP 6

Bring down the next digit of the dividend (which is 3) to the right of the remainder from the previous step.
$\begin{array}{r} \phantom{0}1 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}23 \\ \end{array}$

STEP 7

Determine how many times 9 can go into 23 without exceeding it. 9 goes into 23 two times (2 times 9 is 18).
$\begin{array}{r} \phantom{0}12 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}23 \\ -(18) \\ \end{array}$

STEP 8

Subtract the product of the divisor and the new quotient from the number you got after bringing down the last digit. Write the result below.
$\begin{array}{r} \phantom{0}12 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}23 \\ -(18) \\ \phantom{00}5 \\ \end{array}$

STEP 9

Since there are no more digits to bring down, the number at the bottom (5) is the remainder of the division.

STEP 10

Write the final answer, which includes the quotient and the remainder. The quotient is 12 and the remainder is 5.
$\frac{113}{9} = 12 \text{ remainder } 5$
Alternatively, we can express the remainder as a fraction by placing it over the original divisor:
$\frac{113}{9} = 12 \frac{5}{9}$

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Perform long division on the expression 1139\frac{113}{9}9113​.

STEP 1

Assumptions1. We are performing long division of the fraction 1139\frac{113}{9}9113​.2. The dividend is 113 and the divisor is 9.

STEP 2

Set up the long division by writing 113 as the dividend inside the division bracket and 9 as the divisor outside.09)113‾ \begin{array}{r} \phantom{0} \\ 9 \overline{\smash{\big)}113} \\ \end{array} 09)113​

STEP 3

STEP 4

Determine how many times 9 can go into 11 without exceeding it. 9 goes into 11 once (1 times 9 is 9).019)113‾093 \begin{array}{r} \phantom{0}1 \\ 9 \overline{\smash{\big)}113} \\ \phantom{0}9\phantom{3} \\ \end{array} 019)113093​

STEP 5

STEP 6

Bring down the next digit of the dividend (which is 3) to the right of the remainder from the previous step.019)113‾−(93)023 \begin{array}{r} \phantom{0}1 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}23 \\ \end{array} 019)113−(93)023​

STEP 7

Determine how many times 9 can go into 23 without exceeding it. 9 goes into 23 two times (2 times 9 is 18).0129)113‾−(93)023−(18) \begin{array}{r} \phantom{0}12 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}23 \\ -(18) \\ \end{array} 0129)113−(93)023−(18)​

STEP 8

STEP 9

Since there are no more digits to bring down, the number at the bottom (5) is the remainder of the division.

STEP 10

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Perform long division on the expression $\frac{113}{9}$ .

Assumptions
1. We are performing long division of the fraction $\frac{113}{9}$ .
2. The dividend is 113 and the divisor is 9.

Set up the long division by writing 113 as the dividend inside the division bracket and 9 as the divisor outside.
$\begin{array}{r} \phantom{0} \\ 9 \overline{\smash{\big)}113} \\ \end{array}$

Determine how many times 9 can go into 11 without exceeding it. 9 goes into 11 once (1 times 9 is 9).
$\begin{array}{r} \phantom{0}1 \\ 9 \overline{\smash{\big)}113} \\ \phantom{0}9\phantom{3} \\ \end{array}$

Bring down the next digit of the dividend (which is 3) to the right of the remainder from the previous step.
$\begin{array}{r} \phantom{0}1 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}23 \\ \end{array}$

Determine how many times 9 can go into 23 without exceeding it. 9 goes into 23 two times (2 times 9 is 18).
$\begin{array}{r} \phantom{0}12 \\ 9 \overline{\smash{\big)}113} \\ -(9\phantom{3}) \\ \phantom{0}23 \\ -(18) \\ \end{array}$