/*! 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 35 Multiply. Simplify, if possible.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 35

Multiply. Simplify, if possible. $$ 25 \times 462 $$

Short Answer

Expert verified
11550

Step by step solution

01

Write the problem as it is

Start with the multiplication problem: \resizebox{!}{40px}\text{\resizebox{!}{40px}{\(25 \times 462\)}}
02

Break down the multiplication

Separate the numbers into more manageable parts. Use the distributive property: \resizebox{!}{40px}\text{\resizebox{!}{40px}{\(25 \times (400 + 60 + 2)\)}}
03

Apply the distributive property

Multiply 25 by each part separately and then sum the results: \resizebox{!}{40px}\text{\resizebox{!}{40px}{\(25 \times 400 + 25 \times 60 + 25 \times 2\)}}
04

Perform each multiplication

Calculate each multiplication:\resizebox{!}{40px}\text{\resizebox{!}{40px}{\(25 \times 400 = 10000\)}}\resizebox{!}{40px}\text{\resizebox{!}{40px}{\(25 \times 60 = 1500\)}}\resizebox{!}{40px}\text{\resizebox{!}{40px}{\(25 \times 2 = 50\)}}
05

Add the results together

Sum the individual products to get the final result:\resizebox{!}{40px}\text{\resizebox{!}{40px}{\(10000 + 1500 + 50 = 11550\)}}

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.

distributive property
The distributive property is a handy tool in mathematics. It allows you to simplify complex multiplication by breaking it down into smaller, easier pieces. The property states that multiplying a number by a sum is the same as doing each multiplication separately. For example, in our problem, we transform \(25 \times 462\) into \(25 \times (400 + 60 + 2)\). This works because you are distributing the 25 across each part within the parentheses.
breaking down numbers
Breaking down numbers, also known as decomposition, is an essential technique to simplify calculations. Here, we break 462 into 400, 60, and 2. This simplification makes the multiplication more manageable. By dealing with smaller numbers, it's easier to perform quick mental calculations or ensure accuracy when using pen and paper. It's like cutting a big task into smaller, digestible pieces, making the overall task less daunting.
step-by-step calculation
Step-by-step calculation involves solving a problem in clear, sequential stages. This approach ensures that you understand and correctly perform each part of the process. We start with the initial problem: \(25 \times 462\). First, we express it as \(25 \times (400 + 60 + 2)\) using the distributive property. Next, we perform the multiplication individually: \(25 \times 400\), \(25 \times 60\), and \(25 \times 2\). Finally, we sum up the results: \(10000 + 1500 + 50 = 11550\). Breaking the problem into these small steps helps avoid mistakes and makes complex problems easier to handle.

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

After Raena poured a 4-lb bag of birdseed into her new bird feeder, the feeder was \(\frac{2}{3}\) full. How much seed does the feeder hold when it is full? \([2.7 \mathrm{~d}]\)

Simplify. $$ 2600 \div 13-5^{3} \quad[1.9 \mathrm{c}] $$

Estimating a Whale Population. To determine the number of humpback whales in a population, a marine biologist, using tail markings, identifies 27 individual whales. Several weeks later, 40 whales from the population are sighted at random. Of the 40 sighted, 12 are among the 27 originally identified. Estimate the number of whales in the population.

Find the ratio of the first number to the second and simplify. $$ 128 \text { to } 256 $$

Find the ratio of the first number to the second and simplify. $$ 28 \text { to } 36 $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

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.