Problem 75 - Prealgebra

Question

Perform each of the following divisions. $$2 0 \longdiv { 5 , 9 6 0 }$$

Step-by-Step Solution

Answer

5,960 divided by 20 is 298.

Step 1: Set up the division

We are tasked with dividing 5,960 by 20. Let's set this up using the long division method, where 5,960 is placed under the division bracket, and 20 is the divisor.

Step 2: Divide the first part

Look at the first digit of the dividend, which is 5. Since 20 is greater than 5, we need to consider the first two digits. Next, consider 59 (from 5,960). Divide 59 by 20 to get 2, as 20 times 2 is 40 (and 3 times 20 would be 60, which is too much). Place the 2 above the division line.

Step 3: Multiply and subtract

Multiply 2 by 20 to get 40. Subtract 40 from 59 to get 19. Now, bring down the next digit from the dividend, which is 6, making it 196.

Step 4: Continue the division

Divide 196 by 20. The result is 9, as 20 times 9 is 180. Place the 9 in the quotient after 2. Now, multiply 9 by 20 to get 180 and subtract it from 196, leaving 16.

Step 5: Bring down final digit and complete division

Bring down the final digit of the dividend (0) to get 160. Divide 160 by 20 to get 8. Multiply 8 by 20 to get 160. Subtract 160 from 160 to get 0.

Key Concepts

Dividing Multi-Digit Numbers

Dividing multi-digit numbers may seem challenging at first, but with practice, it becomes an essential skill in math. The primary goal is to determine how many times the divisor can fit into the dividend. Here's a simple breakdown to help you understand:

• Identify the divisor and dividend. In the division problem, the divisor is the number you're dividing by, and the dividend is the number being divided. In this case, 20 is the divisor, and 5,960 is the dividend.
• Set up the long division. Place the dividend inside the division bracket and the divisor outside.
• Work from left to right. Start by comparing the largest group of digits in the dividend that can be divided by the divisor without exceeding it. If necessary, move to smaller groups of numbers.

Using these steps, long division becomes manageable. By breaking the dividend into smaller, more workable groups, you simplify each step until the entire number is divided.

Arithmetic Operations

Arithmetic operations are the foundation of math, and long division primarily uses them to solve problems. Understanding these operations can make dividing multi-digit numbers more intuitive:

• Addition: Involves bringing down the next number from the dividend.
• Subtraction: Used after multiplying the divisor and the current quotient, you subtract the product from the part of the dividend you're dealing with.
• Multiplication: This operation checks how many times the divisor fits into the selected portion of the dividend.

Long division combines these operations systematically to break the problem into smaller steps. Each operation builds on the one before, helping you towards the solution systematically and efficiently. Practice allows you to get better at visualizing these steps and solving problems without feeling overwhelmed.

Step-by-Step Math Solutions

Learning math becomes easier when you break down complex problems into smaller, logical steps. Step-by-step solutions provide a pathway toward understanding such problems, particularly in long division. Here's why they are helpful:

• Clarity: Each step focuses on a specific part of the problem, minimizing confusion.
• Progress Tracking: By knowing each stage, you can see how the solution develops and identify mistakes more easily.
• Repetition: Practicing each individual step reinforces learning and aids in memory retention.

Following a methodical approach ensures that nothing is overlooked and builds confidence in solving similar problems. Over time, these steps engrain themselves in your mind, making it easier to tackle other arithmetic challenges.