Problem 377 - Prealgebra

Question

Divide. Then check by multiplying. $$19 \div 1$$

Step-by-Step Solution

Answer

19 \div \ 1 = 19.Checked: 19 \times \ 1 = 19.

Step 1: Understand the Division Problem

The problem given is to divide 19 by 1. Division is the process of determining how many times one number is contained within another.

Step 2: Perform the Division

Divide the number 19 by 1. Any number divided by 1 is the number itself, so: \( 19 \div \ 1 = 19 \)

Step 3: Check the Result by Multiplying

To check if the division is correct, multiply the quotient by the divisor. This means multiplying 19 by 1. If the result equals the original number (19), the division is correct: \( 19 \times \ 1 = 19 \)

Key Concepts

Division Problems

Division problems ask us to find out how many times one number can fit into another number. For example, in the problem given, we are asked to divide 19 by 1. This means we want to know how many times 1 can fit into 19.
Division can be thought of as repeated subtraction. In this case, we subtract 1 from 19 repeatedly until we reach 0. Here, we would subtract 1 exactly 19 times.
This gives us the answer: \[ 19 \, \div \, 1 \, = \, 19 \]where 19 is the quotient (result of division) and 1 is the divisor (the number we are dividing by).
Understanding these key terms can help you solve and check division problems efficiently.

Checking Division with Multiplication

Once we have our division result, it’s important to verify our answer. This is where multiplication comes in handy.
The way to check division is simple: we take the quotient and multiply it by the divisor. The product should equal the original number (dividend). In this exercise, our quotient is 19 and our divisor is 1.
Thus, we perform the multiplication: \[ 19 \, \times \, 1 \, = \, 19 \]If the product equals the original number we started with, then our division was correct. In this case, 19 equals the original number, so our division answer is confirmed as correct.
Checking with multiplication helps you catch errors and ensures your understanding of the problem.

Basic Arithmetic Operations

Division is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication.
Understanding basic division starts with recognizing that dividing by 1 always gives the original number. Why? Because anything divided by 1 is itself.
Arithmetic operations are interconnected:

• Addition lets us combine numbers.
• Subtraction allows us to take away from numbers.
• Multiplication is repeated addition.
• Division is essentially repeated subtraction or the inverse of multiplication.

When you master these elementary operations, solving complex problems becomes easier. Each operation has its own set of rules and properties, but they all link together to provide different methods of handling numbers. Being familiar with these connections will help you solve textbook exercises more confidently.