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Chapter 1: Problem 370

Divide. Then check by multiplying. $$42 \div 7$$

Short Answer

Expert verified
42 divided by 7 equals 6. Verification: 6 times 7 equals 42.

Step by step solution

01

Divide the Numbers

Divide 42 by 7. \[ 42 \div 7 = 6 \]
02

Multiply the Quotient

Multiply the quotient (6) by the divisor (7) to check the division. \[ 6 \times 7 = 42 \]
03

Verify the Result

Since the multiplication result 42 matches the original dividend, the division is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

division
Division is one of the basic arithmetic operations used to find out how many times one number is contained within another. In the provided exercise, we are asked to divide 42 by 7. This is written as: \[ 42 \div 7 = 6 \] '42' here is known as the dividend, '7' is the divisor, and '6' is the quotient, which is the result of our division. Division can be thought of as the process of splitting into equal parts or groups. In a practical sense, if you have 42 apples and you want to distribute them equally into 7 baskets, each basket will have 6 apples. This simple visualization helps in understanding the concept of division better.
multiplication as a check
Multiplication is a useful method to verify the result of a division problem. This involves multiplying the quotient we obtained from the division by the divisor. In our example, the quotient is '6', and the divisor is '7'. We perform the following check: \[ 6 \times 7 = 42 \] Here, '6' (quotient) times '7' (divisor) gives us '42', exactly matching our original number (dividend). If this result doesn鈥檛 match the original dividend, it indicates that there might have been an error in the division process. By using multiplication in this way, you can confidently verify that the division has been done correctly, ensuring a crucial accuracy check in arithmetic operations.
basic arithmetic operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations form the foundation of most math problems you will encounter. Here鈥檚 a brief overview:
  • Addition: This operation combines two or more numbers to get a total sum. For example, \[ 5 + 3 = 8 \]
  • Subtraction: This operation finds the difference between two numbers by taking one away from the other. For example, \[ 9 - 4 = 5 \]
  • Multiplication: This operation results in the product by combining equal groups. For example, \[ 7 \times 6 = 42 \]
  • Division: This operation splits a number into equal parts. For example, \[ 42 \div 7 = 6 \]
Understanding these basic operations is crucial because they are often intertwined. For instance, division and multiplication are inverse operations. This means that knowing one helps in understanding and checking the other. Understanding how to use these operations effectively helps in solving more complex mathematical problems accurately.

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