Question

Divide \(12,385 \div 152\) A. \(81 \mathrm{R} 73\) B. 81 C. \(81 \mathrm{R} 37\) D. 82

Short answer

The answer is A. 81 R 73.

Step-by-step solution

Set Up the Long Division

Write down the divisor (152) outside the division bracket and the dividend (12,385) inside the bracket. We are going to perform long division to solve this problem.

Divide the First Few Digits

Consider the first three digits of the dividend, which is 123. Determine how many times 152 can divide into 123. Since 152 is greater than 123, it cannot divide into 123, so we consider the first four digits, 1238.

Determine How Many Times the Divisor Fits

Now, determine how many times 152 can fit into 1238. Upon estimation or calculation, 152 can fit into 1238 approximately 8 times since 152 × 8 = 1216 ≤ 1238.

Subtract and Bring Down the Next Digit

Subtract 1216 from 1238, which gives 22. Now bring down the next digit (5 from 12,385), making the number 225.

Divide Again

Determine how many times 152 can fit into 225. It fits 1 time since 152 × 1 = 152 ≤ 225.

Subtract and Bring Down the Remainder

Subtract 152 from 225, which leaves a remainder of 73. Since there are no more digits to bring down and 152 cannot divide into 73, this is the remainder.

Write the Final Answer

Combine the results: the quotient from the division is 81 and the remainder is 73, so the answer to the division is 81 R 73.

Key concepts

Divisors

In division, the number that divides another number is called the divisor. It plays a crucial role as it helps break down the larger number into smaller parts. For example, if you're dividing 12,385 by 152, the number 152 is your divisor. It's the part of the equation that helps determine how many full groups of the divisor can be obtained from the dividend (the number being divided).

• Divisor in this exercise: 152
• Role: Determines how many times it fits into the larger number

Understanding divisors is key in solving division problems. It is the starting point in setting up equations properly.

Quotients

A quotient is the result you get when one number is divided by another. It's a fundamental output of any division problem.

• Quotient in this exercise: 81
• Represents: How many whole times the divisor can fit into the dividend

The quotient shows how many complete groups of the divisor exist within the dividend without exceeding it. In our example division of 12,385 by 152, the quotient is 81. This means that 152 can fully fit into 12,385 exactly 81 times before any remainder occurs.

Remainders

Remainders appear in division when the dividend does not divide perfectly by the divisor. They are the leftovers or the part of the dividend that remains after the largest possible multiples of the divisor have been subtracted.

• Remainder in this exercise: 73
• Purpose: Represents the 'leftover' or balance after division

To identify the remainder, once you calculate how many times the divisor fits into the dividend, subtract the largest possible product from the dividend. Any value left over is the remainder. In this case, after computing the division, 152 fits 81 full times into 12,385, and 73 remains.

Subtraction in Division

Subtraction is at the core of long division. After estimating how many times the divisor fits into the dividend, subtraction helps determine the remainder.

• Process: Subtract the product of the divisor and the current part of the quotient from the dividend
• Importance: Reduces the dividend until only a remainder is left or division is complete

For instance, during the division of 12,385 by 152, subtraction was used at each stage: 1238 minus 1216 left 22, and further on, 225 minus 152 left 73. Subtraction continues until the remainder is less than the divisor. This repetitive subtraction, combined with bringing down the next digits, steadily reduces the dividend.