Book cover for Prealgebra

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

ISBN #9781938168994

1st Edition

5,729 Questions

Group icon
210,912 Students Helped

Homework Questions

Right arrow
Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section provided an introduction to whole numbers, emphasizing the importance of counting numbers and the inclusion of zero in whole numbers. Key topics included modeling numbers using base-10 blocks, understanding place value, writing and naming numbers, and rounding whole numbers to various place values. Additionally, the basic addition notation was introduced, setting the foundation for further operations in algebra. Understanding these fundamental concepts fosters numerical literacy and prepares learners for more complex mathematical reasoning.

Learning Objectives

1

Distinguish between counting numbers and whole numbers, including the role of zero.

2

Model whole numbers using place value concepts, such as base-10 blocks and place value charts.

3

Identify the place value of digits in multi-digit numbers and use this to write and name whole numbers.

4

Apply rounding rules to whole numbers to achieve approximations needed in real-life contexts.

5

Translate arithmetic expressions and apply basic addition notation in practical problem solving.

Key Concepts

CONCEPT

DEFINITION

Counting Numbers

The sequence of numbers used for counting objects (1, 2, 3, …). Also known as natural numbers.

Whole Numbers

The set of counting numbers including zero (0, 1, 2, 3, …).

Place Value

A method where the value of a digit is determined by its position in a number, with each place representing a power of ten.

Base-10 Blocks

Manipulative tools (ones, tens, hundreds) used to visually model the place value system.

Rounding

A mathematical process of approximating a number to a specific place value based on the digit immediately to its right.

Addition Notation

A symbolic method to represent the addition of numbers, using the plus symbol (+) to denote combining addends.

Example Problems

Example 1

In the following exercises, determine which of the following numbers are a counting numbers b whole numbers. $$0, \frac{2}{3}, 5,8.1,125$$

Example 2

In the following exercises, determine which of the following numbers are a counting numbers b whole numbers. $$0, \frac{7}{10}, 3,20.5,300$$

Example 3

In the following exercises, determine which of the following numbers are a counting numbers b whole numbers. $$0, \frac{4}{9}, 3.9,50,221$$

Example 4

In the following exercises, determine which of the following numbers are a counting numbers b whole numbers. $$0, \frac{3}{5}, 10,303,422.6$$

Example 5

In the following exercises, use place value notation to find the value of the number modeled by the base-10 blocks.
Scroll left
Scroll right

Step-by-Step Explanations

QUESTION

In the number 63,407,218, what are the place values of the digits 7, 0, 1, 6, and 3?

STEP-BY-STEP ANSWER:

Step 1: Write the number in a place value chart, aligning the digits from right (ones) to left with increasing powers of ten.
Step 2: Identify that the digit 7 is located in the thousands period.
Step 3: Recognize that the digit 0 falls in the ten thousands place.
Step 4: Note that the digit 1 is in the tens place (since counting from the right, ones, tens, hundreds, etc.).
Step 5: Determine that the digit 6 is in the ten millions place.
Step 6: Identify the digit 3 in the millions place.
Final Answer: 7 is in the thousands place, 0 is in the ten thousands place, 1 is in the tens place, 6 is in the ten millions place, and 3 is in the millions place.

Determining Place Value in a Number

QUESTION

Round the number 76 to the nearest ten.

STEP-BY-STEP ANSWER:

Step 1: Identify the tens place digit which is 7 in the number 76.
Step 2: Look at the ones place digit (6) to determine how to round.
Step 3: Since 6 is greater than or equal to 5, increase the tens digit by 1.
Step 4: Replace the ones digit with zero.
Final Answer: 76 rounded to the nearest ten is 80.

Rounding a Whole Number

QUESTION

Translate and solve the expression 3 + 4.

STEP-BY-STEP ANSWER:

Step 1: Identify the two addends, which are 3 and 4.
Step 2: Write the expression as 3 + 4 using the plus symbol.
Step 3: Add the two numbers together.
Final Answer: The sum of 3 and 4 is 7.

Addition Notation

Scroll left
Scroll right

Common Mistakes

  • Confusing counting numbers with whole numbers by mistakenly including zero as a counting number.
  • Misidentifying the place value of digits, leading to errors in writing or reading numbers.
  • Neglecting the importance of placeholders (zeros) in maintaining correct place value especially when writing numbers in standard form.
  • Applying rounding rules incorrectly, such as rounding down when the digit is exactly 5 instead of rounding up consistently.