/*! 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 30 Divide and then check by multipl... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 30

Divide and then check by multiplying. $$56 \div 8$$

Short Answer

Expert verified
56 divided by 8 equals 7; verified as 7 times 8 is 56.

Step by step solution

01

Divide

Start by dividing 56 by 8. To do this, see how many times 8 can fit into 56 without exceeding it. You can find that 8 fits exactly 7 times into 56 because \( 8 \times 7 = 56 \). Therefore, \( 56 \div 8 = 7 \).
02

Multiply to Check

Now, multiply the result (which is 7) by the divisor (which is 8) to verify if we get back the original number. Compute \( 7 \times 8 \). This calculation gives \( 56 \), which matches the original dividend. Thus, the division is verified to be correct.

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.

Multiplication
Multiplication is one of the basic operations of arithmetic that deals with finding the total number of objects in groups of the same size. For example, when you multiply two numbers, let's say 8 and 7, you are essentially adding 8 to itself 7 times. The formula for this is:\[8 \times 7 = 56\]Multiplication is handy for various calculations and especially useful in verifying division problems, as it allows you to confirm the correctness of a division result by reversing the operation.
Verification of Division
Verifying division can help ensure that your division calculations are correct. When you divide a number, in this case, 56 by 8, and find the quotient, you can check your work by multiplying the quotient by the divisor. Reversing the operation like this should result in the original number (dividend). The process follows the equation:\[\text{Dividend} = \text{Quotient} \times \text{Divisor}\]In the given example:
  • Divided 56 by 8 to get a quotient of 7
  • Then multiplied 7 by 8, obtaining the original number, 56
If the multiplication gives you the original dividend, your division is verified as correct. This method adds accuracy to your calculations and gives you confidence in your answer.
Basic Arithmetic
Basic arithmetic involves the basic operations such as addition, subtraction, multiplication, and division. These operations form the foundation of mathematics that are used in various aspects of everyday life.
In basic arithmetic, division is usually explained as the process of splitting a number into equal parts. When you divide 56 by 8, you are asking how many equal parts of size 8 fit into 56.
It's also important to understand each operation not as an isolated function but how they interrelate:
  • Add: Combine numbers to find the total.
  • Subtract: Find the difference between numbers.
  • Multiply: Add a number to itself repeatedly.
  • Divide: Split a number into equal parts.
This holistic understanding boosts your ability to tackle more complex mathematical problems effectively.

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." A number divided by 11

Celestial Seasonings of Boulder, Colorado, is a tea company that specializes in herbal teas. Their plant in Boulder has bagging machines capable of bagging over 1000 bags of tea per minute. If the plant runs 24 hours day, how many tea bags are produced in one day? (Source: Celestial Seasonings)

Write each whole number in expanded form. $$209$$

Write each phrase as a variable expression. Use \(x\) to represent "a number." The sum of seventeen and a number added to the product of five and the number

Write each phrase as a variable expression. Use \(x\) to represent "a number." The difference of twice a number, and four
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

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.