Rational Numbers Navigator Worksheet
Rational Numbers Navigator
Part 1: Adding & Subtracting Decimals
Name:
Date:
Sign Rules Reference Map
1. Same Signs
Add values • Keep common sign.
\(-2.3 + (-4.1) = -6.4\)
2. Different Signs
Subtract values • Keep sign of larger.
\(-7.5 + 3.2 = -4.3\)
3. Subtracting Negatives
Add opposite (Keep-Change-Change).
\(4.2 - (-1.8) = 4.2 + 1.8\)
Guided Example Model
3 Quick Steps
Step 1: Check Signs
\(-5.4 + 2.1\)
Different signs → Subtract
Step 2: Line Up Decimals
5.4
- 2.1
3.3
Difference is 3.3
Step 3: Keep Larger Sign
5.4 is larger than 2.1, so keep negative.
Answer: \(-3.3\)
Independent Practice: Line Up Decimals & Show Work
4 Points
1 Different Signs
\(6.4 + (-2.9)\)
Line up decimal points:
Final Answer:
2 Same Signs
\(-3.5 + (-4.8)\)
Add values, keep negative:
Final Answer:
3 Subtracting Negative
\(1.7 - (-5.2)\)
Keep → Change → Change:
Final Answer:
4 Subtracting Positive
\(-8.1 - 2.6\)
Rewrite as: \(-8.1 + (-2.6)\)
Final Answer:
Decimal Checkpoint: □ Decimal points lined up □ Calculated correctly □ Sign verified Page 1 of 2
Rational Numbers Navigator
Part 2: Adding & Subtracting Fractions
Name:
4-Step Fraction Strategy
1 Common Denom
Match bottom numbers (LCD).
2 Rewrite
Multiply top and bottom evenly.
3 Add/Sub Tops
Apply signs. Bottom stays same.
4 Simplify
Reduce fraction to lowest terms.
Fraction Example Model
Different Signs & LCD
Problem:
\(-\frac{3}{4} + \frac{1}{2}\)
Denominators: 4 and 2
Make LCD = 4:
\(\frac{1 \times 2}{2 \times 2} = \frac{2}{4}\)
Problem: \(-\frac{3}{4} + \frac{2}{4}\)
Combine Numerators:
\(-3 + 2 = -1\) on top.
Answer: \(-\frac{1}{4}\)
Fraction Practice: Find Common Denominators & Solve
4 Points
5 Same Denominator
\(-\frac{2}{7} + \left(-\frac{3}{7}\right)\)
Keep denominator 7; combine tops:
Final Answer:
6 LCD Needed
\(\frac{5}{6} - \frac{1}{2}\)
Rewrite with common denominator 6:
Final Answer:
7 Different Signs
\(-\frac{1}{3} + \frac{5}{6}\)
Rewrite \(-\frac{1}{3}\) with denominator 6:
Final Answer:
8 Keep • Change • Change
\(\frac{1}{5} - \left(-\frac{2}{5}\right)\)
Change to addition: \(\frac{1}{5} + \frac{2}{5}\)
Final Answer:
Real-World Challenge: Submarine Depth
Bonus Problem
A research submarine starts at \(-12.5\) meters below sea level. It descends another \(8.3\) meters. Find its new depth.
New Depth (with unit):
Fraction Checkpoint: □ Denominators match □ Sign rules applied □ Simplified lowest terms Page 2 of 2
