ANTMACK215 × WEALTHWISEGUYS
WealthWiseGuys Practical Mathematics

Chapter 1

Whole Numbers: How to Dissect and Solve Word Problems

Reading, rounding, and operating with whole numbers in real money situations

Every money decision starts with whole numbers: ticket counts, hours worked, items on a receipt. This chapter builds number sense, then gives you a repeatable blueprint for taking any word problem apart.

1.1

Reading, Writing, and Rounding Whole Numbers

Learning objectives

After this section you will be able to:

  1. Identify the place value of any digit in a whole number.
  2. Write whole numbers in words and in numerals.
  3. Round whole numbers to a stated place.

Real-life situation

Sold-out arena

A Philadelphia arena reports that 48,627 fans attended a playoff game. A news anchor says "about 49,000 fans." A ticket app says "over 48,600." Both are rounding the same number to different places.

Ten thousands
4
Thousands
8
Hundreds
6
Tens
2
Ones
7
Figure 1.1 Place-value chart for 48,627

The concept

Our number system is base ten. Each place is worth ten times the place to its right. Digits are grouped in threes, called periods: units, thousands, millions, billions. Commas separate the periods.

To read a number, read each period as a three-digit number and say the period name, except the units period. The word "and" is saved for the decimal point, so we never say it inside a whole number.

To round, find the place you are rounding to and look at the digit immediately to its right. If that digit is 5 or more, add 1 to the rounding digit. If it is 4 or less, leave the rounding digit alone. Every digit to the right becomes zero.

Reading, Writing, and Rounding Whole Numbers: solution map

  1. 1

    Identify the question

    Write 3,206,450 in words.

  2. 2

    Calculation 1

    Split into periods: 3 | 206 | 450.

  3. 3

    Calculation 2

    Millions period: three million.

  4. 4

    Calculation 3

    Thousands period: two hundred six thousand.

  5. 5

    Calculation 4

    Units period: four hundred fifty.

  6. 6

    Interpret and check

    Three million, two hundred six thousand, four hundred fifty

Figure 1.1.V Reading, Writing, and Rounding Whole Numbers: solution map. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • business

    An organization that makes or sells goods or services to earn money.

  • revenue

    The total money a business brings in from sales, before any costs are paid.

  • cost

    The amount paid to make or buy an item before it is sold.

Key terms

Whole numbers
The numbers 0, 1, 2, 3, and so on, with no fractions or decimals.
Place value
The value a digit has because of its position in the number.
Period
A group of three places (units, thousands, millions, ...) separated by commas.
Rounding
Replacing a number with a nearby, simpler number to a chosen place.

Formulas & rules

  • Rounding rule

    Digit to the right ≥ 5 → round up; ≤ 4 → keep

    All digits to the right of the rounding place become 0.

    In plain words

    1. Find the place you are rounding to.
    2. Look at the digit just to its right.
    3. 5 or more: bump up by 1. 4 or less: leave it.
    4. Turn every digit after it into 0.

    Try it with real numbers: 48,627 to the nearest thousand → look at 6 → 8 becomes 9 → 49,000

Worked examples

Example 1Writing a number in words

Write 3,206,450 in words.

Solution

  1. 1Split into periods: 3 | 206 | 450.
  2. 2Millions period: three million.
  3. 3Thousands period: two hundred six thousand.
  4. 4Units period: four hundred fifty.

Answer: Three million, two hundred six thousand, four hundred fifty

Example 2Rounding attendance

Round 48,627 to the nearest thousand and to the nearest hundred.

Solution

  1. 1Nearest thousand: the thousands digit is 8. The digit to its right is 6, which is 5 or more, so 8 becomes 9: 49,000.
  2. 2Nearest hundred: the hundreds digit is 6. The digit to its right is 2, which is 4 or less, so 6 stays: 48,600.

Answer: 49,000 (thousand); 48,600 (hundred)

Practice exercises 1.1

  1. Write 7,045 in words.
  2. Round 6,349 to the nearest hundred.
  3. Round 82,501 to the nearest thousand.
  4. What is the place value of the 5 in 352,108?
  5. Write "two hundred thousand, nine" as a numeral.

Recap quiz 1.1

1. Round 1,950 to the nearest hundred.
2. Which digit is in the thousands place of 64,812?
3. "Ninety thousand, ninety" as a numeral is:

Section 1.1 recap

  • A digit's value depends on its place — each move left is 10 times greater.
  • Rounding looks at the digit to the right: 5 or more rounds up, 4 or less stays.
Answer key with explanations: Section 1.1

Practice exercises

  1. Seven thousand, forty-five
  2. 6,300
  3. 83,000
  4. Ten thousands (the 5 is worth 50,000)
  5. 200,009

Recap quiz

  1. 2,000: The digit right of the hundreds place is 5, so 9 hundreds rounds up to 10 hundreds: 2,000.
  2. 4: Reading right to left: units 2, tens 1, hundreds 8, thousands 4.
  3. 90,090: 90 in the thousands period and 090 in the units period: 90,090.
1.2

Adding and Subtracting Whole Numbers

Learning objectives

After this section you will be able to:

  1. Add whole numbers and check the sum.
  2. Subtract whole numbers, including borrowing, and check the difference.
  3. Estimate sums by rounding first.

Real-life situation

Lunch at the corner market

Dev buys lunch for himself and two friends and pays with a $20 bill. Before he walks away he wants to know: what was the total, and is his change right?

Broad St. Corner Market

10/14 · Thank you!

1 × Turkey hoagie @ $8.00$8.00
2 × Soda @ $2.00$4.00
3 × Chips @ $1.00$3.00
TOTAL$15.00
CASH$20.00
CHANGE$5.00
Figure 1.2 Corner market receipt (whole-dollar prices)

The concept

To add, line up the digits by place value and add right to left. When a column adds to 10 or more, write the ones digit and carry the tens digit to the next column.

To subtract, line up the larger number (minuend) on top. When a top digit is smaller than the one below it, borrow 1 from the next place to the left, which adds 10 to the current place.

Always check. Addition checks by adding the column in the opposite direction. Subtraction checks by adding the difference back to the subtrahend; you should get the minuend.

Adding and Subtracting Whole Numbers: solution map

  1. 1

    Identify the question

    Find Dev's total and his change from $20.

  2. 2

    Calculation 1

    Line totals: hoagie 1 × $8 = $8; sodas 2 × $2 = $4; chips 3 × $1 = $3.

  3. 3

    Calculation 2

    Total: $8 + $4 + $3 = $15.

  4. 4

    Calculation 3

    Change: $20 − $15 = $5.

  5. 5

    Calculation 4

    Check: $5 + $15 = $20. ✓

  6. 6

    Interpret and check

    Total $15; change $5

Figure 1.2.V Adding and Subtracting Whole Numbers: solution map. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • expense

    Money a business spends to run, such as rent, supplies, or wages.

  • profit

    What is left when expenses are subtracted from revenue.

  • budget

    A plan that shows expected income and how it will be spent.

Key terms

Addends
The numbers being added.
Sum
The result of addition.
Minuend
The number you subtract from (the starting amount).
Subtrahend
The number being subtracted.
Difference
The result of subtraction.

Formulas & rules

  • Addition

    Addend + Addend = Sum

    The letters are just stand-ins for numbers

    • Addend = each amount you are putting together
    • Sum = the total of everything

    In plain words

    1. Line up the amounts by place value.
    2. Add them together.
    3. The answer is the total (sum).

    Try it with real numbers: $8 hoagie + $4 sodas + $3 chips = $15 total

  • Subtraction

    Minuend − Subtrahend = Difference

    The letters are just stand-ins for numbers

    • Minuend = what you started with
    • Subtrahend = what you spent or took away
    • Difference = what is left

    In plain words

    1. Start with what you had.
    2. Take away what you spent.
    3. What remains is the difference.

    Try it with real numbers: $20 paid − $15 lunch = $5 change

  • Subtraction check

    Difference + Subtrahend = Minuend

    The letters are just stand-ins for numbers

    • Difference = what was left
    • Subtrahend = what you spent
    • Minuend = what you started with

    In plain words

    1. Add what is left to what you spent.
    2. You should land back on what you started with.
    3. If not, redo the subtraction.

    Try it with real numbers: $5 change + $15 lunch = $20 ✓

Worked examples

Example 1Checking the receipt

Find Dev's total and his change from $20.

Solution

  1. 1Line totals: hoagie 1 × $8 = $8; sodas 2 × $2 = $4; chips 3 × $1 = $3.
  2. 2Total: $8 + $4 + $3 = $15.
  3. 3Change: $20 − $15 = $5.
  4. 4Check: $5 + $15 = $20. ✓

Answer: Total $15; change $5

Example 2Subtracting with borrowing

Jada saved $1,245 over the summer and spent $389 on sneakers. How much is left?

Solution

  1. 1Ones: 5 − 9 cannot be done; borrow from the tens. 15 − 9 = 6.
  2. 2Tens: 3 (after lending) − 8 cannot be done; borrow from the hundreds. 13 − 8 = 5.
  3. 3Hundreds: 1 (after lending) − 3 cannot be done; borrow from the thousands. 11 − 3 = 8.
  4. 4Thousands: 0. Result 856.
  5. 5Check: 856 + 389 = 1,245. ✓

Answer: $856

Practice exercises 1.2

  1. 4,508 + 2,976
  2. 10,000 − 3,587
  3. A basketball team scored 87, 94, and 79 points in three games. What is the total?
  4. An account had $2,350. You withdrew $875. What is the new balance?
  5. Estimate 612 + 389 by rounding each to the nearest hundred, then find the exact sum.

Recap quiz 1.2

1. 503 − 278 =
2. How do you check a subtraction answer?
3. In 1,999 + 1 = 2,000, the number 2,000 is the:

Section 1.2 recap

  • Line up digits by place value before adding or subtracting.
  • Check subtraction by adding the difference back to the smaller number.
Answer key with explanations: Section 1.2

Practice exercises

  1. 7,484
  2. 6,413
  3. 260 points
  4. $1,475
  5. Estimate 600 + 400 = 1,000; exact 1,001

Recap quiz

  1. 225: Check: 225 + 278 = 503.
  2. Add the difference to the subtrahend: Difference + subtrahend must equal the minuend.
  3. Sum: The result of addition is the sum.
1.3

Multiplying, Dividing, and the Word-Problem Blueprint

Learning objectives

After this section you will be able to:

  1. Multiply and divide whole numbers, including remainders.
  2. Decide what a remainder means in a real situation.
  3. Use the four-part blueprint to dissect a word problem.

Real-life situation

The candy-bar fundraiser

The youth league orders 24 cases of candy bars. Each case holds 36 bars, and each bar sells for $2. The coach needs to know how many bars there are, how much money a sellout brings in, and how many bags of 25 bars she can pack for sellers.

Bars in one case: 36

Figure 1.3 One case: 36 bars (6 rows of 6)

The concept

Multiplication is repeated addition. 24 cases of 36 bars means 36 added 24 times, which is 24 × 36.

Division splits a total into equal groups. When the total does not split evenly, the leftover is the remainder. In real life, decide whether the remainder is dropped (only full bags count), rounded up (you need another bus), or reported (14 bars left over).

The Blueprint. Before you calculate, write four things: (1) Facts given, (2) What you are solving for, (3) Steps to take, (4) Key points to watch. This keeps you from using the wrong numbers or answering the wrong question.

Multiplying, Dividing, and the Word-Problem Blueprint: solution map

  1. 1

    Identify the question

    How many bars are in 24 cases, and how much does a sellout raise?

  2. 2

    Calculation 1

    Facts: 24 cases, 36 bars per case, $2 per bar.

  3. 3

    Calculation 2

    Solving for: total bars, total dollars.

  4. 4

    Calculation 3

    24 × 36 = 864 bars.

  5. 5

    Calculation 4

    864 × $2 = $1,728.

  6. 6

    Interpret and check

    864 bars; $1,728

Figure 1.3.V Multiplying, Dividing, and the Word-Problem Blueprint: solution map. Hypothetical teaching data.

Money Words

Plain-language words you will use in this lesson — learn them before we reach the formulas.

  • gross profit

    Revenue minus the direct cost of the items sold, before other expenses.

  • net profit

    The final profit after every cost is paid — sometimes called the bottom line.

  • balance

    The amount of money in an account at a given moment.

Key terms

Factors
Numbers being multiplied.
Product
The result of multiplication.
Dividend
The number being divided.
Divisor
The number you divide by.
Quotient
The result of division.
Remainder
What is left when a dividend does not divide evenly.

Formulas & rules

  • Multiplication

    Factor × Factor = Product

    The letters are just stand-ins for numbers

    • Factor = the numbers being multiplied, like how many groups and how many in each
    • Product = the total

    In plain words

    1. Count how many groups you have.
    2. Count how many are in each group.
    3. Multiply them to get the total.

    Try it with real numbers: 24 cases × 36 bars per case = 864 bars

  • Division check

    Divisor × Quotient + Remainder = Dividend

    The letters are just stand-ins for numbers

    • Divisor = the size of each group or bag
    • Quotient = how many full groups you made
    • Remainder = the loose leftovers
    • Dividend = the total you started with

    In plain words

    1. Multiply full groups by the group size.
    2. Add the leftovers.
    3. You should get the starting total back.

    Try it with real numbers: 25 bars per bag × 34 bags + 14 left over = 864 bars ✓

Worked examples

Example 1Total bars and sales

How many bars are in 24 cases, and how much does a sellout raise?

Solution

  1. 1Facts: 24 cases, 36 bars per case, $2 per bar.
  2. 2Solving for: total bars, total dollars.
  3. 324 × 36 = 864 bars.
  4. 4864 × $2 = $1,728.

Answer: 864 bars; $1,728

Example 2Packing bags

Bars are packed in bags of 25 for each seller. How many full bags, and how many bars are left?

Solution

  1. 1864 ÷ 25: 25 × 34 = 850, and 864 − 850 = 14.
  2. 2Quotient 34, remainder 14.
  3. 3Check: 25 × 34 + 14 = 864. ✓
  4. 4Only full bags go to sellers, so the remainder is reported as leftover.

Answer: 34 full bags, 14 bars left over

Example 3Blueprint: paycheck after rent

Marcus earns $15 per hour and works 32 hours per week. His share of rent is $1,100 per month. Using 4 weeks per month, how much is left after rent?

Solution

  1. 1Facts: $15/hour, 32 hours/week, 4 weeks, rent $1,100.
  2. 2Solving for: money left after rent for the month.
  3. 3Steps: weekly pay = 15 × 32 = $480. Monthly = 480 × 4 = $1,920. Left = 1,920 − 1,100 = $820.
  4. 4Key point: this ignores taxes, so real take-home will be lower.

Answer: $820 (before taxes)

Practice exercises 1.3

  1. 125 × 48
  2. 7,236 ÷ 6
  3. 400 students ride buses that each hold 52. How many buses are needed?
  4. Three concert tickets cost $45 each, plus one $20 parking pass. What is the total?
  5. Write the blueprint (facts, solving for, steps, key points) and solve: $1,000 shared equally by 8 people.

Recap quiz 1.3

1. 56 × 10 =
2. 95 ÷ 4 =
3. The first step of the blueprint is:

Section 1.3 recap

  • Estimate first, then compute, then compare — the estimate catches wild errors.
  • The word-problem blueprint: find what is known, what is asked, and the operation that connects them.
Answer key with explanations: Section 1.3

Practice exercises

  1. 6,000
  2. 1,206
  3. 400 ÷ 52 = 7 R36, so 8 buses (the remainder means one more bus)
  4. 3 × 45 + 20 = $155
  5. Facts: $1,000, 8 people. Solving for: each share. Steps: 1,000 ÷ 8. Key point: equal shares. Answer $125 each

Recap quiz

  1. 560: Multiplying by 10 attaches one zero.
  2. 23 R3: 4 × 23 = 92, and 95 − 92 = 3.
  3. Identify the facts given: Know your facts before choosing operations.

Chapter 1 Organizer and Review

Chapter Organizer

Every section at a glance: key formulas, key terms, and the main idea.

  • 1.1 Reading, Writing, and Rounding Whole Numbers

    Key formulas

    • Rounding rule: Digit to the right ≥ 5 → round up; ≤ 4 → keep

    Key terms

    Whole numbers, Place value, Period, Rounding

    Remember

    A digit's value depends on its place — each move left is 10 times greater.

  • 1.2 Adding and Subtracting Whole Numbers

    Key formulas

    • Addition: Addend + Addend = Sum
    • Subtraction: Minuend − Subtrahend = Difference
    • Subtraction check: Difference + Subtrahend = Minuend

    Key terms

    Addends, Sum, Minuend, Subtrahend, Difference

    Remember

    Line up digits by place value before adding or subtracting.

  • 1.3 Multiplying, Dividing, and the Word-Problem Blueprint

    Key formulas

    • Multiplication: Factor × Factor = Product
    • Division check: Divisor × Quotient + Remainder = Dividend

    Key terms

    Factors, Product, Dividend, Divisor, Quotient, Remainder

    Remember

    Estimate first, then compute, then compare — the estimate catches wild errors.

Cumulative Review

Mixed practice from this chapter and the two chapters before it.

  1. Section 1.1

    Write "two hundred thousand, nine" as a numeral.

    Show answer

    200,009

  2. Section 1.2

    Estimate 612 + 389 by rounding each to the nearest hundred, then find the exact sum.

    Show answer

    Estimate 600 + 400 = 1,000; exact 1,001

  3. Section 1.3

    Write the blueprint (facts, solving for, steps, key points) and solve: $1,000 shared equally by 8 people.

    Show answer

    Facts: $1,000, 8 people. Solving for: each share. Steps: 1,000 ÷ 8. Key point: equal shares. Answer $125 each

All prices, stores, people, and accounts in this chapter are hypothetical and for teaching only. Product references are generic categories; no brand endorses or is endorsed by this textbook.

Chapter 2