Grade 6 Math: Mastering Decimal Substitution in Expressions

📚 Understanding Decimal Substitution

Decimal substitution in expressions simply means replacing a variable (like 'x' or 'y') with a decimal number. Then, you solve the expression using the order of operations (PEMDAS/BODMAS).

📜 A Little History

The concept of substitution has been around for centuries in algebra. The use of decimals became more common with the standardization of the metric system and increased use of calculators.

➗ Key Principles

• 🔢 Identify the Variable: Locate the variable you need to substitute.
• 📍 Substitute Carefully: Replace the variable with its given decimal value. Be mindful of signs (+ or -).
• ➗ Order of Operations: Follow PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction).
• ✅ Simplify: Perform the arithmetic to get your final answer.

➗ Real-World Examples

Let's look at some examples:

1. Example 1: If $x = 2.5$, evaluate $3x + 1$.Solution: $3(2.5) + 1 = 7.5 + 1 = 8.5$
2. Example 2: If $a = 0.75$ and $b = 4$, evaluate $2a + b^2$.Solution: $2(0.75) + 4^2 = 1.5 + 16 = 17.5$
3. Example 3: If $y = -1.2$, evaluate $5 - 2y$.Solution: $5 - 2(-1.2) = 5 + 2.4 = 7.4$

➗ More Complex Example

What if we have an expression like $(x + y) \cdot z$, where $x = 1.5$, $y = 2.7$, and $z = 0.5$?

Solution:

1. Substitute: $(1.5 + 2.7) \cdot 0.5$
2. Simplify inside the parentheses: $(4.2) \cdot 0.5$
3. Multiply: $2.1$

📝 Practice Quiz

Evaluate the following expressions:

1. If $p = 3.2$, what is $4p - 2$?
2. If $q = -0.5$, what is $10 + 3q$?
3. If $r = 1.8$ and $s = 2$, what is $r \cdot s + 1$?
4. If $t = 2.5$, what is $t^2 - 3$?
5. If $u = 0.4$ and $v = 5$, what is $2v - 5u$?
6. If $w = -1.1$, what is $6 + 4w$?
7. If $x = 3$ and $y = 0.75$, what is $5y + x^2$

💡 Conclusion

Decimal substitution is a fundamental skill in algebra. With practice, you'll master it in no time! Remember to pay attention to the order of operations and take your time to avoid mistakes.