Which algebraic expression represents each verbal expression?
 
a. 4.2 fewer than the product of 12 and a number 1 of 4.
 
b. 4.2 decreased by the quantity 12 plus a number 2 of 4.
 
c. 4.2 minus the product of 12 and a number 3 of 4.
 
d. 4.2 less than the sum of 12 and a number 4 of 4.

Let's break down and translate each verbal expression into an algebraic expression.

### a. "4.2 fewer than the product of 12 and a number (1 of 4)"
- "The product of 12 and a number" can be written as \( 12x \), where \( x \) is the unknown number.
- "4.2 fewer than" means subtract 4.2 from this product.

Algebraic expression:  
\[
12x - 4.2
\]

---

### b. "4.2 decreased by the quantity 12 plus a number (2 of 4)"
- "The quantity 12 plus a number" can be written as \( 12 + y \), where \( y \) is the unknown number.
- "4.2 decreased by" means subtract this quantity from 4.2.

Algebraic expression:  
\[
4.2 - (12 + y)
\]

---

### c. "4.2 minus the product of 12 and a number (3 of 4)"
- "The product of 12 and a number" can be written as \( 12z \), where \( z \) is the unknown number.
- "4.2 minus" means subtract this product from 4.2.

Algebraic expression:  
\[
4.2 - 12z
\]

---

### d. "4.2 less than the sum of 12 and a number (4 of 4)"
- "The sum of 12 and a number" can be written as \( 12 + w \), where \( w \) is the unknown number.
- "4.2 less than" means subtract 4.2 from this sum.

Algebraic expression:  
\[
(12 + w) - 4.2
\]

---

### Summary:
- **a.** \( 12x - 4.2 \)
- **b.** \( 4.2 - (12 + y) \)
- **c.** \( 4.2 - 12z \)
- **d.** \( (12 + w) - 4.2 \)

Would you like more details on any part of this? Here are some related questions:

1. How do you translate other verbal expressions into algebraic expressions?
2. What is the difference between "fewer than" and "less than" in algebraic translations?
3. How do parentheses affect the structure of algebraic expressions?
4. Can you explain how operations like subtraction affect terms in complex expressions?
5. What are common pitfalls when translating verbal expressions to algebraic forms?

**Tip:** Always pay close attention to the phrasing of expressions like "fewer than" or "less than," as they can change the order of subtraction.

Which algebraic expression represents each verbal expression?

a. 4.2 fewer than the product of 12 and a number 1 of 4.

b. 4.2 decreased by the quantity 12 plus a number 2 of 4.

c. 4.2 minus the product of 12 and a number 3 of 4.

d. 4.2 less than the sum of 12 and a number 4 of 4.

Learn how to translate verbal expressions like '4.2 fewer than the product of 12 and a number' into algebraic expressions. This tutorial breaks down algebraic concepts of subtraction and addition, showing how to form expressions such as 12x - 4.2 and more. Suitable for Grades 6-8.

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