Math

Question Divide 49244924 by 77 and express the result.

Studdy Solution

STEP 1

Assumptions
1. We are performing a division operation.
2. The dividend is 4924.
3. The divisor is 7.

STEP 2

To perform the division, we will use long division. We start by determining how many times the divisor (7) can fit into the first digit of the dividend (4).
747 \nmid 4

STEP 3

Since 7 cannot fit into 4, we consider the first two digits of the dividend (49).
7497 \mid 49

STEP 4

Now we divide 49 by 7 to find how many times 7 fits into 49.
497=7\frac{49}{7} = 7

STEP 5

We write down 7 above the line in the quotient place corresponding to the tens place, since we divided 49 (which is in the tens and units place of the dividend).
\begin{array}{r} 7 \, \enclose{longdiv}{4924} \\ \cline{2-5} \phantom{0}7 & & & & \\ \end{array}

STEP 6

Next, we multiply the divisor (7) by the quotient (7) we just found and write the result (49) under the 49 of the dividend, and subtract it from 49.
49(7×7)=4949=049 - (7 \times 7) = 49 - 49 = 0

STEP 7

After subtracting, we bring down the next digit of the dividend (2) next to the 0.
\begin{array}{r} 7 \, \enclose{longdiv}{4924} \\ \cline{2-5} \phantom{0}7 & & & & \\ \phantom{0} & -49 & & & \\ \cline{2-3} \phantom{00}0 & 2 & & & \\ \end{array}

STEP 8

Now we determine how many times the divisor (7) fits into the new number (2). Since 7 cannot fit into 2, we write 0 in the quotient place corresponding to the hundreds place.
\begin{array}{r} 7 \, \enclose{longdiv}{4924} \\ \cline{2-5} \phantom{0}7 & 0 & & & \\ \phantom{0} & -49 & & & \\ \cline{2-3} \phantom{00}0 & 2 & & & \\ \end{array}

STEP 9

We bring down the next digit of the dividend (4) next to the 2.
\begin{array}{r} 7 \, \enclose{longdiv}{4924} \\ \cline{2-5} \phantom{0}7 & 0 & & & \\ \phantom{0} & -49 & & & \\ \cline{2-3} \phantom{00}0 & 24 & & & \\ \end{array}

STEP 10

Now we determine how many times the divisor (7) fits into 24.
247=3 with a remainder of 3\frac{24}{7} = 3 \text{ with a remainder of } 3

STEP 11

We write down 3 above the line in the quotient place corresponding to the units place.
\begin{array}{r} 7 \, \enclose{longdiv}{4924} \\ \cline{2-5} \phantom{0}7 & 0 & 3 & & \\ \phantom{0} & -49 & & & \\ \cline{2-3} \phantom{00}0 & 24 & & & \\ \end{array}

STEP 12

Multiply the divisor (7) by the quotient (3) we just found and write the result (21) under the 24, and subtract it from 24.
24(7×3)=2421=324 - (7 \times 3) = 24 - 21 = 3

STEP 13

Write down the remainder (3) under the subtraction we just performed.
\begin{array}{r} 7 \, \enclose{longdiv}{4924} \\ \cline{2-5} \phantom{0}7 & 0 & 3 & & \\ \phantom{0} & -49 & & & \\ \cline{2-3} \phantom{00}0 & 24 & & & \\ \phantom{00} & -21 & & & \\ \cline{3-4} \phantom{00} & \phantom{0}3 & & & \\ \end{array}

STEP 14

Since there are no more digits to bring down from the dividend, we have completed the division. The quotient is 703 and the remainder is 3.
The solution to the division problem is 703 with a remainder of 3.
\begin{array}{r} 7 \, \enclose{longdiv}{4924} \\ \cline{2-5} 703 & & & & \\ \phantom{0} & -49 & & & \\ \cline{2-3} \phantom{00}0 & 24 & & & \\ \phantom{00} & -21 & & & \\ \cline{3-4} \phantom{00} & \phantom{0}3 & & & \\ \end{array}

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