/*! 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 12 Multiply. \(7 \cdot 7,000\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 12

Multiply. \(7 \cdot 7,000\)

Short Answer

Expert verified
The product of 7 and 7,000 is 49,000.

Step by step solution

01

Understand the Problem

We need to multiply 7 by 7,000. This is asking for the product of these two numbers.
02

Simplify Multiplication with Zeroes

Notice that 7,000 is 7 times 1,000. This simplifies our problem to multiplying 7 by (7 times 1,000), which can be written as \[ 7 imes (7 imes 1,000) \]
03

Multiply the Numbers

First, multiply 7 by 7, which gives us 49. Now, we multiply this result by 1,000.\[ 49 imes 1,000 = 49,000 \]
04

Conclusion

We've multiplied 7 by 7,000 by breaking it down into simpler steps. The product is 49,000.

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.

Simplifying Multiplication
Simplifying multiplication can make complex problems a lot easier to handle. Suppose you need to multiply numbers like 7 and 7,000. Instead of struggling with large figures, look for simpler ways. Break down the numbers into components that are easier to multiply. In the example of 7 multiplied by 7,000, notice that 7,000 is essentially 7 times 1,000.
This helps you transform the problem into an easier one: multiplying 7 by 7, and then by 1,000. Let's break that down:
  • First, observe that 7 times 1,000 is essentially 7 followed by three zeroes.
  • Then, solve the smaller multiplication: 7 times 7 is 49.
  • Finally, add the three zeroes to 49, giving 49,000 as the answer.
This approach of simplifying multiplication doesn't just make calculations quicker. It also aids in confirming that your answers are correct, and helps to build confidence in dealing with larger numbers.
Mathematics Problem Solving
Tackling a mathematics problem involves understanding what is being asked. Before you jump into calculations, analyze the problem. With the multiplication task of 7 and 7,000, the objective is to find their product.
Here's a structured path to solving it:
  • Grasp the question: Recognize that 7 is being multiplied by 7,000, which is an extended multiplication due to zeroes.
  • Simplify the problem: Reduce the larger number into a more manageable form like breaking down 7,000 into 7 times 1,000.
  • Follow a step-by-step computation: First multiply the simpler numbers (7 times 7), then handle the powers of ten (times 1,000).
  • Verify your result: Confirm the final calculation was done accurately.
This clear and methodical approach aids in resolving mathematical challenges with precision. Taking these steps not only helps in getting to the right answer, but also strengthens your problem-solving skills.
Basic Arithmetic Operations
Understanding basic arithmetic operations is pivotal in solving math problems efficiently. Multiplication, a fundamental operation, is a step beyond simple addition. It signifies repeated addition and is vital in everyday calculations.
Take the numbers 7 and 7,000. When you multiply these, you're essentially adding 7 to itself 7,000 times, a daunting task if done manually.
However, basic multiplication principles simplify this task. Here's how arithmetic principles assist:
  • Identify the multiplication rule: Know that any number times 1 remains unchanged. Likewise, multiplying by multiples of 10, like 1,000, effectively shifts decimal places.
  • Use commutativity: In multiplication, the order doesn't change the result. So 7 times 7,000 is the same as 7,000 times 7.
  • Apply associativity: Rearrange numbers for easier computation, like calculating 7 times 7 first, then multiplying the result by 1,000.
Grasping these principles ensures arithmetic operations become second nature. It's an effective way to handle numbers quickly and without errors, building a strong foundation in basic mathematics.

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

Rewrite each of the following using the associative property of addition. $$(2+1)+6$$

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{r} 36 \\ 46 \\ \hline \end{array}$$

The application problems that follow may involve more than merely division. Some may require addition, subtraction, or multiplication, whereas others may use a combination of two or more operations. Fitness Walking The guidelines for fitness now indicate that a person who walks \(10,000\) steps daily is physically fit. According to The Walking Site on the Internet, it takes just over \(2,000\) steps to walk one mile. If that is the case, how many miles do you need to walk in order to take \(10,000\) steps? (image cannot copy)

The application problems that follow may involve more than merely division. Some may require addition, subtraction, or multiplication, whereas others may use a combination of two or more operations. Milligrams of Calcium Suppose one egg contains 25 milligrams of calcium, a piece of toast contains 40 milligrams of calcium, and a glass of milk contains 215 milligrams of calcium. How many milligrams of calcium are contained in a breakfast that consists of three eggs, two glasses of milk, and four pieces of toast?

Work Problems 35 through 38 mentally, without using a calculator. The quotient \(24,471 \div 523\) is closest to which of the following numbers? a. 5 b. 50 c. 500 d. \(5,000\)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Geometry

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.