Subtract Rational Numbers Lesson Plans & Worksheets - Free Printable

It looks like you've uploaded a math worksheet titled "Adding and Subtracting Rational Numbers", which includes problems involving fractions, decimals, and negative numbers. Since I can't view images directly, I’ll guide you through solving the types of problems typically found on such worksheets.

Let me walk you through how to solve these kinds of problems step by step, using common examples from this type of worksheet. If you can provide specific problems or clarify which ones you'd like help with, I can give more targeted solutions.

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🔹 General Rules for Adding and Subtracting Rational Numbers:

1. Same Signs: Add absolute values, keep the sign.
2. Different Signs: Subtract smaller absolute value from larger, take the sign of the larger.
3. Fractions: Find a common denominator before adding/subtracting.
4. Decimals: Line up decimal points and add/subtract as usual.
5. Negative Numbers: Follow rules of signs (e.g., $-a + (-b) = -(a+b)$).

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🔹 Example Problems & Solutions

Let’s assume some typical problems from your worksheet:

#### Problem 1:
Find each sum or difference:
a. $-\frac{3}{4} + \left(-\frac{1}{2}\right)$

✔ Solution:
Both are negative → add absolute values:
$\frac{3}{4} + \frac{1}{2} = \frac{3}{4} + \frac{2}{4} = \frac{5}{4}$
So, $-\frac{5}{4}$ or $-1\frac{1}{4}$

✔️ Answer: $-\frac{5}{4}$

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#### Problem 2:
b. $-\frac{1}{3} - \frac{2}{3}$

✔ Solution:
Subtracting is same as adding the opposite:
$-\frac{1}{3} + (-\frac{2}{3}) = -\frac{3}{3} = -1$

✔️ Answer: $-1$

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#### Problem 3:
c. $-0.8 + 1.5$

✔ Solution:
Different signs → subtract: $1.5 - 0.8 = 0.7$, take sign of larger: positive
Answer: $0.7$

✔️ Answer: $0.7$

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#### Problem 4:
d. $\frac{2}{5} + (-\frac{1}{4})$

✔ Solution:
Common denominator: 20
$\frac{2}{5} = \frac{8}{20},\quad -\frac{1}{4} = -\frac{5}{20}$
$\frac{8}{20} - \frac{5}{20} = \frac{3}{20}$

✔️ Answer: $\frac{3}{20}$

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#### Problem 5:
Evaluate: $-3.2 + (-1.6)$

✔ Solution:
Same signs → add: $3.2 + 1.6 = 4.8$, both negative → $-4.8$

✔️ Answer: $-4.8$

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🔹 Tips for Solving These:

- Convert all numbers to the same form (fractions or decimals) if needed.
- Use number lines or visual models if helpful.
- Always check signs carefully.

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If you can tell me specific problems from the image (e.g., “Problem #12” or “the one with $-2.7 + 1.9$”), I can solve them exactly.

Alternatively, copy-paste the actual problems here, and I’ll solve them step-by-step!