Problem 70 - Intermediate Algebra

Question

Use each word below in a sentence that indicates a mathematical operation. If you are unsure of the meaning of a word, look it up in a dictionary. $$\begin{array}{llll}\text { quadrupled } & \text { deleted } & \text { bisected } & \text { garnished } \\ \text { confiscated } & \text { annexed } & \text { docked } & \text { quintupled }\end{array}$$

Step-by-Step Solution

Answer

Each word indicates a mathematical operation: quadrupled (x4), deleted (-), bisected (divided by 2), garnished (+), confiscated (-), annexed (+), docked (-), quintupled (x5).

Step 1: Quadrupled

The term 'quadrupled' means to multiply by four. Example sentence: The length of the wall was quadrupled to make the room larger.

Step 2: Deleted

'Deleted' is typically used to indicate removal or subtraction in a mathematical context. Example sentence: After noticing the error, the engineer deleted 5 from the total sum.

Step 3: Bisected

'Bisected' refers to dividing something into two equal parts. Example sentence: The path through the park is bisected by the new highway, splitting it into two equal sections.

Step 4: Garnished

'Garnished' does not typically relate to mathematical operations, but it can imply an addition or enhancement. Example sentence: The salad was garnished with extra toppings, adding to its visual appeal.

Step 5: Confiscated

'Confiscated' means to take away or remove, indicating subtraction. Example sentence: The teacher confiscated two cell phones from the students, reducing distractions in class.

Step 6: Annexed

'Annexed' means to add or join, typically used to describe adding something to a territory. Example sentence: The smaller territory was annexed to the empire, increasing its total land area.

Step 7: Docked

'Docked' refers to a deduction or subtraction from a total amount. Example sentence: The sailor's pay was docked by $50 as a penalty for being late.

Step 8: Quintupled

The term 'quintupled' means to multiply by five. Example sentence: Her collection of stamps was quintupled after receiving a large donation.

Key Concepts

Multiplication

Multiplication is one of the four fundamental mathematical operations. It is essentially repeated addition, and it's used to find the total number of items in groups of the same size. For example, if you have 3 groups of 4 apples, you can use multiplication to find out how many apples you have in total, which is \( 3 \times 4 = 12 \).
Multiplication can be represented by the symbol \(\times\) or sometimes by a dot \(\cdot\). It's a quick way to add the same number multiple times, saving a lot of time over traditional addition.

• "Quadrupled" means multiplying by four.
• "Quintupled" means multiplying by five.

This operation is applied in various real-life situations like scaling recipes, calculating area, and much more. Understanding multiplication can help in simplifying complex problems by breaking them down into smaller, manageable parts.

Subtraction

Subtraction is the operation of finding the difference between numbers or removing quantities. If we have 10 apples and eat 3, we subtract 3 from 10 to find out how many apples are left, which is \( 10 - 3 = 7 \).
This operation is symbolized by the minus sign "\(-\)" and is the opposite of addition. Subtraction can describe scenarios where something is removed or lost.

• "Deleted" and "confiscated" imply subtraction, as they refer to removing something.
• "Docked" also means to subtract, like reducing a salary.

Subtraction is useful for calculating changes in quantities, finding how much is left, or for determining differences between measurements. It's essential for understanding how to manage resources, balance budgets, or in troubleshooting disputes.

Division

Division is the mathematical process of splitting a number into equal parts. Imagine you have 12 candies and you want to share them equally among 4 friends. You would divide \( 12 \div 4 = 3 \), meaning each friend gets 3 candies.
Division can also be considered the inverse of multiplication. It involves "bisecting" or splitting quantities.

• "Bisected" means dividing something into two equal parts.

This operation is crucial in many real-world applications, such as distributing resources, dividing tasks among team members, and converting units. Division helps to understand ratio and proportion, and it lays the groundwork for advanced mathematical concepts like fractions and percentages.

Addition

Addition is the process of finding the total or sum by combining two or more numbers or quantities. If you have 5 apples and then get 3 more, the total number of apples becomes \( 5 + 3 = 8 \).
Represented by the plus sign "\(+\)", addition is often the first operation people learn.

• "Annexed" suggests an addition, indicating something being joined or included.
• "Garnished" can imply addition in a more decorative or supplemental sense.

Addition is used extensively in everyday life; from simple tasks like grocery shopping to more complex data analysis. Understanding addition helps build a strong foundation for other mathematical operations, enabling one to easily transition into multiplication, which is essentially repeated addition.