Prealgebra Chapter 5: Decimal Multiplication and Applications

Vocabulary and concept flashcards covering decimal multiplication, front-end rounding, decimal placement rules, area formulas, and word problem applications from Prealgebra Chapter 5.

Multiplying Two Decimals

A two-step procedure where you first multiply as you would integers, and then place the decimal point in the product so that the number of decimal places equals the combined number of decimal places of both factors.

Front-End Rounding

A rounding technique where each factor is rounded to its left-most nonzero digit, primarily used to estimate products and verify the correct placement of decimal points.

Decimal Place Placement Diagram

A step-by-step visual demonstration adding 3 decimal places from $11.914$ and 1 decimal place from $0.8$ to place 4 decimal places in the product $9.5312$.

Front-End Rounding Estimation Example

An estimation process rounding $29.3$ to $30$ and $2.8$ to $3$ to obtain an estimated product of $90$, confirming that the actual product $82.04$ has its decimal point correctly placed in the tens place.

Product of $11.914 \times 0.8$

$$9.5312$$

Product of $(19.7)(4.1)$

$$80.77$$

Product of $(29.3)(2.8)$

$$82.04$$

Product and Estimation of $(1.9)(29.1)$

The exact product is $55.29$, which is close to the front-end estimation of $2 \times 30 = 60$.

Jane Marie's Tennis Cans Calculation

An application problem calculating total bill: 8 cans of tennis balls at $\$3.79$ each equal $\$30.32$, plus $\$1.97$ sales tax, yielding a total of $\$32.29$.

Book Club Order Total Bill

An application problem calculating total bill: 12 books at $\$8.99$ each equal $\$107.88$, plus $\$4.95$ shipping, yielding a total of $\$112.83$.

Area of a Rectangle

The formula $A = l \cdot w$, where $A$ represents area, $l$ represents length, and $w$ represents width.

Area of the Mona Lisa Painting

The total surface area of Leonardo da Vinci's painting with dimensions $30\,\text{in.}$ by $20.875\,\text{in.}$, which equals $626.25\,\text{in.}^2$.

Area of the Museum IMAX Screen

The total area of the Museum of Science and Discovery IMAX movie screen with dimensions $18\,\text{m}$ by $24.4\,\text{m}$, which equals $439.2\,\text{m}^2$.

Community College Athletic Department Bill

A multi-item word problem combining 20 pizzas at $\$12.95$ each ($\$259.00$), 10 Greek salads at $\$5.95$ each ($\$59.50$), and 60 soft drinks at $\$1.29$ each ($\$77.40$) with $\$27.71$ sales tax to reach a total bill of $\$423.61$.

Tire Store Savings Calculation

The total savings of $\$111.61$ achieved by buying a set of four tires for $\$769.99$ instead of four single tires at $\$220.40$ each ($\$881.60$ total).