Chapter 1 Review and Practice Test

Learning objectives

Learning objectives

• Review the key ideas of this chapter.

• Apply the chapter's methods to review exercises.

• Check your understanding with a practice test.

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Worked example

coordinate

A number paired with a point on a number line is called the coordinate of the point.

counting numbers

The counting numbers are the numbers 1, 2, 3, ….

difference

The difference is the result of subtracting two or more numbers.

dividend

When dividing two numbers, the dividend is the number being divided.

divisor

When dividing two numbers, the divisor is the number dividing the dividend.

number line

A number line is used to visualize numbers. The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left.

origin

The origin is the point labeled 0 on a number line.

place value system

Our number system is called a place value system because the value of a digit depends on its position, or place, in a number.

product

The product is the result of multiplying two or more numbers.

quotient

The quotient is the result of dividing two numbers.

rounding

The process of approximating a number is called rounding.

sum

The sum is the result of adding two or more numbers.

whole numbers

The whole numbers are the numbers 0, 1, 2, 3, ….

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Key Concepts

Key Terms

coordinate

A number paired with a point on a number line is called the coordinate of the point.

counting numbers

The counting numbers are the numbers 1, 2, 3, ….

difference

The difference is the result of subtracting two or more numbers.

dividend

When dividing two numbers, the dividend is the number being divided.

divisor

When dividing two numbers, the divisor is the number dividing the dividend.

number line

A number line is used to visualize numbers. The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left.

origin

The origin is the point labeled 0 on a number line.

place value system

Our number system is called a place value system because the value of a digit depends on its position, or place, in a number.

product

The product is the result of multiplying two or more numbers.

quotient

The quotient is the result of dividing two numbers.

rounding

The process of approximating a number is called rounding.

sum

The sum is the result of adding two or more numbers.

whole numbers

The whole numbers are the numbers 0, 1, 2, 3, ….

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Key Concepts

1.1 Introduction to Whole Numbers

• Name a whole number in words. Step 1. Starting at the digit on the left, name the number in each period, followed by the period name. Do not include the period name for the ones. Step 2. Use commas in the number to separate the periods.

• Use place value to write a whole number. Step 1. Identify the words that indicate periods. (Remember the ones period is never named.) Step 2. Draw three blanks to indicate the number of places needed in each period. Step 3. Name the number in each period and place the digits in the correct place value position.

• Round a whole number to a specific place value. Step 1. Locate the given place value. All digits to the left of that place value do not change unless the given place value is a 9, in which case it may. (See Step 3.). Step 2. Underline the digit to the right of the given place value. Step 3. Determine if this digit is greater than or equal to 5. If yes—add 1 to the digit in the given place value. If that digit is 9, replace it with 0 and add 1 to the digit immediately to its left. If that digit is also a 9, repeat. If no—do not change the digit in the given place value. Step 4. Replace all digits to the right of the given place value with zeros.

1.2 Add Whole Numbers

• Addition Notation To describe addition, we can use symbols and words. Operation Notation Expression Read as ResultAddition $+$$3+4$ three plus four the sum of $3$ and $4$

• Identity Property of Addition The sum of any number $a$ and $0$ is the number. $a+0=a$$0+a=a$

• Commutative Property of Addition Changing the order of the addends $a$ and $b$ does not change their sum. $a+b=b+a$.

• Add whole numbers. Step 1. Write the numbers so each place value lines up vertically. Step 2. Add the digits in each place value. Work from right to left starting with the ones place. If a sum in a place value is more than 9, carry to the next place value. Step 3. Continue adding each place value from right to left, adding each place value and carrying if needed.

• Subtract whole numbers. Step 1. Write the numbers so each place value lines up vertically. Step 2. Subtract the digits in each place value. Work from right to left starting with the ones place. If the digit on top is less than the digit below, borrow as needed. Step 3. Continue subtracting each place value from right to left, borrowing if needed. Step 4. Check by adding.

• Multiplication Property of Zero The product of any number and 0 is 0. $a\cdot{}0=0$$0\cdot{}a=0$

• Identity Property of Multiplication The product of any number and 1 is the number. $1\cdot{}a=a$$a\cdot{}1=a$

• Commutative Property of Multiplication Changing the order of the factors does not change their product. $a\cdot{}b=b\cdot{}a$

• Multiply two whole numbers to find the product. Step 1. Write the numbers so each place value lines up vertically. Step 2. Multiply the digits in each place value. Step 3. Work from right to left, starting with the ones place in the bottom number. Step 4. Multiply the bottom number by the ones digit in the top number, then by the tens digit, and so on. Step 5. If a product in a place value is more than 9, carry to the next place value. Step 6. Write the partial products, lining up the digits in the place values with the numbers above. Repeat for the tens place in the bottom number, the hundreds place, and so on. Step 7. Insert a zero as a placeholder with each additional partial product. Step 8. Add the partial products.

• Division Properties of One Any number (except 0) divided by itself is one. $a\mathrm{÷}a=1$ Any number divided by one is the same number. $a\mathrm{÷}1=a$

• Division Properties of Zero Zero divided by any number is 0. $0\mathrm{÷}a=0$ Dividing a number by zero is undefined. $a\mathrm{÷}0$ undefined

• Divide whole numbers. Step 1. Divide the first digit of the dividend by the divisor. If the divisor is larger than the first digit of the dividend, divide the first two digits of the dividend by the divisor, and so on. Step 2. Write the quotient above the dividend. Step 3. Multiply the quotient by the divisor and write the product under the dividend. Step 4. Subtract that product from the dividend. Step 5. Bring down the next digit of the dividend. Step 6. Repeat from Step 1 until there are no more digits in the dividend to bring down. Step 7. Check by multiplying the quotient times the divisor.

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Review Exercises

Identify Counting Numbers and Whole Numbers

In the following exercises, determine which of the following are (a) counting numbers (b) whole numbers.

Model Whole Numbers

In the following exercises, model each number using $\mathrm{base-10}$ blocks and then show its value using place value notation.

Identify the Place Value of a Digit

In the following exercises, find the place value of the given digits.

Use Place Value to Name Whole Numbers

In the following exercises, name each number in words.

Use Place Value to Write Whole Numbers

In the following exercises, write as a whole number using digits.

Round Whole Numbers

In the following exercises, round to the nearest ten.

In the following exercises, round to the nearest hundred.

Use Addition Notation

In the following exercises, translate the following from math notation to words.

Model Addition of Whole Numbers

In the following exercises, model the addition.

Add Whole Numbers

In the following exercises, fill in the missing values in each chart.

In the following exercises, add.

Translate Word Phrases to Math Notation

In the following exercises, translate each phrase into math notation and then simplify.

Add Whole Numbers in Applications

In the following exercises, solve.

In the following exercises, find the perimeter of each figure.

Use Subtraction Notation

In the following exercises, translate the following from math notation to words.

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

Subtract Whole Numbers

In the following exercises, subtract and then check by adding.

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.

Subtract Whole Numbers in Applications

In the following exercises, solve.

Use Multiplication Notation

In the following exercises, translate from math notation to words.

Model Multiplication of Whole Numbers

In the following exercises, model the multiplication.

Multiply Whole Numbers

In the following exercises, fill in the missing values in each chart.

In the following exercises, multiply.

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.

Multiply Whole Numbers in Applications

In the following exercises, solve.

Use Division Notation

Translate from math notation to words.

Model Division of Whole Numbers

In the following exercises, model.

Divide Whole Numbers

In the following exercises, divide. Then check by multiplying.

Translate Word Phrases to Math Notation

In the following exercises, translate and simplify.

Divide Whole Numbers in Applications

In the following exercises, solve.

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Simplify.

Translate each phrase to math notation and then simplify.

In the following exercises, solve.

1. $0,2,99$

2. $0,4,90$

3. $472,981$

1. ⓐ $8$

2. ⓑ $4$

3. ⓒ $1$

4. ⓓ $7$

5. ⓔ $2$

4. $5,280$

1. $5,012,582$

2. fifteen thousand, two hundred fifty-three

3. three hundred forty million, nine hundred twelve thousand, sixty-one

4. $3,556$

1. $38,975$

2. $81,486$

3. $75,992$

4. $4+3$

1. $571+629$

2. ⓐ $0+19$ ⓑ $19+0$

3. ⓐ $7+6$ ⓑ $6+7$

4. $7,281+12,546$

1. the sum of $30$ and $12$

2. $25$ more than $39$

3. Shopping for an interview Nathan bought a new shirt, tie, and slacks to wear to a job interview. The shirt cost $\text{\textdollar 24,}$ the tie cost $\text{\textdollar 14,}$ and the slacks cost $\text{\textdollar 38.}$ What was Nathan’s total cost?

4. $14-5$

1. $351-249$

2. $10,000-15$

3. the difference of nineteen and thirteen

4. seventy-four decreased by eight

1. Temperature The high temperature in Peoria one day was $86$ degrees Fahrenheit and the low temperature was $28$ degrees Fahrenheit. What was the difference between the high and low temperatures?

2. $8\,\times\,5$

3. $(10)(95)$

4. ⓐ $7\cdot{}4$ ⓑ $4\cdot{}7$

1. $9,261\,\times\,3$

2. $162\,\times\,493$

3. $3,624\,\times\,517$

4. the product of $15$ and $28$

1. twice $575$

2. Gardening Geniece bought $8$ packs of marigolds to plant in her yard. Each pack has $6$ flowers. How many marigolds did Geniece buy?

3. Multiplex There are twelve theaters at the multiplex and each theater has $150$ seats. What is the total number of seats at the multiplex?

4. $54\mathrm{÷}9$

1. $\frac{72}{8}$

2. $100\mathrm{÷}0$

3. $\frac{7505}{25}$

4. the quotient of $64$ and $16$

1. Ribbon One spool of ribbon is $27$ feet. Lizbeth uses $3$ feet of ribbon for each gift basket that she wraps. How many gift baskets can Lizbeth wrap from one spool of ribbon?

2. Determine which of the following numbers are

1. ⓐ counting numbers

2. ⓑ whole numbers.

$0,4,87$

3. Write each number as a whole number using digits.

1. ⓐ six hundred thirteen

2. ⓑ fifty-five thousand two hundred eight

4. $7\cdot{}475$

1. The sum of $16$ and $58$

2. The difference of $32$ and $18$

3. Twice $524$

4. $50$ less than $300$

1. Last month, Stan’s take-home pay was $\text{\textdollar 3,816}$ and his expenses were $\text{\textdollar 3,472.}$ How much of his take-home pay did Stan have left after he paid his expenses?

2. Clayton walked $12$ blocks to his mother’s house, $6$ blocks to the gym, and $9$ blocks to the grocery store before walking the last $3$ blocks home. What was the total number of blocks that Clayton walked?