/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 49 Divide and then check by multipl... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 49

Divide and then check by multiplying. $$6578 \div 13$$

Short Answer

Expert verified
The quotient is 506.

Step by step solution

01

Set up the division

To divide 6578 by 13, set it up as a long division problem with 6578 as the dividend inside the division bracket and 13 as the divisor outside the bracket.
02

Perform the division

Start dividing from the left. 13 goes into 65 five times (since 13 x 5 = 65). Write 5 above the line. Subtract and bring down the next digit to get 7. Now 13 goes into 7 zero times. Bring down the 8 to make it 78. 13 goes into 78 six times (since 13 x 6 = 78).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Divisor
In long division, the divisor is the number you are dividing by. It is placed outside the division bracket. In our example, the number 13 is the divisor.
  • The divisor determines how many groups you are trying to make out of the dividend.
  • Your goal is to see how many times the divisor can go into each part of the dividend.
Remember that if the divisor is larger than the section of the dividend you're looking at, you should bring down another digit from the dividend.
Dividend
The dividend is the number you want to divide up. It's placed inside the division bracket. Here, 6578 is the dividend.
  • Think of the dividend as the 'big number' being divided into the divisor's smaller parts.
  • Line up digits of the dividend with corresponding parts of the quotient as you work through the division.
Understanding the relationship between the divisor and dividend is crucial. Each step in long division gives you a piece of the final answer.
Quotient
The quotient is the result of the division. It's written above the line over the dividend. In our division, when you divide 6578 by 13, the quotient is 506.
  • The quotient tells you how many full groups of the divisor fit into the dividend.
  • Keep aligning the numbers well to avoid mistakes; digits should be directly over the previous column they came from.
The beauty of the quotient is that it provides the answer to the division problem, but completing the problem doesn't end there.
Multiplication Check
To ensure your division is correct, use the multiplication check. Multiply the quotient by the divisor. If it equals the dividend, the division was performed accurately. For our exercise:
  • Compute: 506 (quotient) multiplied by 13 (divisor).
  • The result should exactly match the original dividend, 6578.
This step helps confirm the accuracy of your division and is a great way to double-check your work.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write each phrase as a variable expression. Use \(x\) to represent "a number." Twelve subtracted from a number

The local college library is having a Million Pages of Reading promotion. The freshmen have read a total of 289,462 pages; the sophomores have read a total of 369,477 pages; the juniors have read a total of 218,287 pages; and the seniors have read a total of 121,685 pages. Have they reached the goal of one million pages? If not, how many more pages need to be read?

Find and correct the error when evaluating each expression for \(x=3\) and \(y=5 .\) \(\begin{aligned} 7 x+y^{2} &=7(3)+5^{2} \\ &=21+10 \\ &=31 \end{aligned}\)

Use a calculator to evaluate each expression for \(x=23\) and \(y=72\). \(2(x+y)^{2}\)

Perform each indicated operation. Watch the operation symbol. $$304 \div 31$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.