Problem 52 Estimate each product by first r... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 1: Problem 52

Estimate each product by first rounding to the nearest ten. Show your work. $$ \begin{array}{r} 789 \\ \times 434 \\ \hline \end{array} $$

Short Answer

Expert verified

339700

Step by step solution

Round the numbers to the nearest ten

First, round 789 to the nearest ten. The nearest ten to 789 is 790, because 789 is closer to 790 than to 780. Next, round 434 to the nearest ten. The nearest ten to 434 is 430, because 434 is closer to 430 than to 440.

Estimate the product

Now, multiply the rounded numbers: 790 and 430. To do this, you can break it down: $790 \times 430$ This can be simplified by multiplying 79 and 43, and then adding the two zeros at the end: $79 \times 43 = 3397$, so $790 \times 430 = 339700$.

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.

Estimating Products

Estimating products involves simplifying a multiplication problem to make it easier to solve quickly. This is particularly useful when an exact number isn't necessary, and a rough figure will suffice. For our exercise, the goal is to estimate the product of 789 and 434 by rounding each number to the nearest ten before multiplying. Rounding simplifies the numbers and makes the multiplication process much quicker and easier to handle mentally. Additionally, this technique helps you get comfortable with numbers and understand their approximate values.

Multiplication

Multiplication is a basic arithmetic operation that combines groups of equal sizes. When multiplying two numbers, like in our exercise, here's how you can break it down:
1. Simplify the problem by rounding each number to an easier, nearest value.
2. Multiply these rounded numbers.
For instance, after rounding 789 to 790 and 434 to 430, we can multiply these simpler values. Doing it step by step helps you follow along:

Multiply the two parts: 79 and 43.
Add the zeros at the end.
Combine the results to get the final estimate.

The breakdown makes the multiplication process manageable, especially for big numbers.

Nearest Ten

Rounding to the nearest ten is a technique to simplify numbers to the closest multiple of ten. It's a useful skill when estimating because it makes calculations easier. Let鈥檚 apply this to our exercise:

1. Identify the number you want to round, such as 789.

Locate the digit in the units place (the last digit), which is 9 for 789.
If this digit is 5 or higher (like 9), round the number up, making 789 round up to 790.

2. Apply the same steps for the other number. For 434:

The last digit is 4, which is less than 5.
So, round down, making 434 round to 430.

Remember, rounding simplifies numbers to a nearest multiple, making estimations much faster to compute.

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Estimate each product by first rounding to the nearest ten. Show your work. $$ \begin{array}{r} 789 \\ \times 434 \\ \hline \end{array} $$

Short Answer

Step by step solution

Round the numbers to the nearest ten

Estimate the product

Key Concepts

Estimating Products

Multiplication

Nearest Ten

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Geometry

Calculus

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.