Math

QuestionExplain how to represent division with 2-digit divisors in math problems.

Studdy Solution

STEP 1

Assumptions1. We are dealing with division involving-digit divisors. . We are using the standard long division method.
3. The dividend (the number being divided) and divisor (the number we are dividing by) are both positive integers.

STEP 2

Let's take an example where we divide1254 by12. The first step in long division is to write the problem in long division format.
121254\begin{array}{r|l} 12 &1254\end{array}

STEP 3

Next, we look at the first digit of the dividend (1 in this case) and compare it with the divisor (12). If the first digit is less than the divisor, we then consider the first two digits of the dividend.

STEP 4

In our example,1 is less than12, so we consider the first two digits of the dividend, which is12. We then divide12 by12, which equals1. We write this1 above the line, in line with the second digit of the dividend.
\begin{array}{r|l} 12 &1254 \\ \cline{2-2} &1\end{array}

STEP 5

Next, we multiply the divisor (12) by the quotient we just found (1) and write the result (12) under the first two digits of the dividend.
\begin{array}{r|l} 12 &1254 \\ \cline{2-2} &1 \\ &12\end{array}

STEP 6

We then subtract the result from the first two digits of the dividend and write the difference below.
\begin{array}{r|l} 12 &1254 \\ \cline{2-2} &1 \\ &12 \\ \cline{2-2} &0\end{array}

STEP 7

Next, we bring down the next digit of the dividend (5 in this case) and append it to the difference we just found (0), making it05.
\begin{array}{r|l} 12 &1254 \\ \cline{2-2} &1 \\ &12 \\ \cline{2-2} &05\end{array}

STEP 8

We then repeat the process divide05 by12. Since05 is less than12, the result is0. We write this0 above the line, in line with the third digit of the dividend.
\begin{array}{r|l} 12 &1254 \\ \cline{2-2} &10 \\ &12 \\ \cline{2-2} &05\end{array}

STEP 9

We repeat the process of multiplying the divisor by the new quotient, subtracting the result from the current dividend, and bringing down the next digit.

STEP 10

In this case, since the quotient was0, there is no change in the dividend. We bring down the next digit (4) to get054.
\begin{array}{r|l} 12 &1254 \\ \cline{2-2} &10 \\ &12 \\ \cline{2-2} &054\end{array}

STEP 11

We then divide054 by, which equals4. We write this4 above the line, in line with the fourth digit of the dividend.
\begin{array}{r|l} &1254 \\ \cline{-} &104 \\ & \\ \cline{-} &054\end{array}

STEP 12

We then multiply the divisor (12) by the new quotient (4) and write the result (48) under the current dividend (054).
\begin{array}{r|l} 12 &1254 \\ \cline{2-2} &104 \\ &12 \\ \cline{2-2} &054 \\ &48\end{array}

STEP 13

We subtract the result from the current dividend and write the difference below. This difference is the remainder.
\begin{array}{r|l} 12 &125 \\ \cline{2-2} &104 \\ &12 \\ \cline{2-2} &054 \\ &48 \\ \cline{2-2} &6\end{array}So,125 divided by12 equals104 with a remainder of6.

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