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Chapter 4: Problem 77

For Exercises 77鈥�84, divide. Write the quotient as a mixed number. $$309 \div 7$$

Short Answer

Expert verified
44 1/7

Step by step solution

01

Set Up the Division

Start by setting up the long division for 309 divided by 7. Place 309 inside the division bracket and 7 outside.
02

Divide the First Digit

Look at the first digit of 309, which is 3. Since 3 is less than 7, include the next digit to make 30.
03

Divide 30 by 7

Determine how many times 7 goes into 30. It goes in 4 times since 7 times 4 is 28. Write down 4 above the line.
04

Multiply and Subtract

Multiply 4 by 7 to get 28. Subtract 28 from 30 to get a remainder of 2.
05

Bring Down the Next Digit

Bring down the next digit, which is 9, to make the number 29.
06

Divide 29 by 7

Determine how many times 7 goes into 29. It goes in 4 times since 7 times 4 is 28. Write down 4 above the line next to the previous 4.
07

Multiply and Subtract Again

Multiply 4 by 7 to get 28. Subtract 28 from 29 to get a remainder of 1.
08

Write the Quotient as a Mixed Number

The quotient is 44 with a remainder of 1. Write the quotient as a mixed number: 44 1/7.

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Key Concepts

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

Understanding Mixed Numbers
A mixed number combines a whole number and a fraction. It is useful when the division doesn't result in an exact whole number. For example, in the exercise \(309 \div 7\), the quotient is \(44 \and \frac{1}{7}\). Here, '44' is the whole number and '1/7' is the fraction part. Mixed numbers make it easier to understand and visualize non-integer results.
What is a Remainder?
When dividing numbers, the remainder is the part left over after the division. In our example, \(309 \div 7\), the remainder is what remains after dividing \(309\) by \(7\) completely. After completing the division, multiplying, and subtracting, we get a remainder of \(1\). This remainder forms the fraction part of our mixed number, \(\frac{1}{7}\). Understanding remainders is crucial for converting division results into mixed numbers accurately.
Dividing Multi-Digit Numbers
Dividing multi-digit numbers can look tough, but breaking it down makes it easier. For \(309 \div 7\), we begin by looking at

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