Integer Navigator Worksheet
Integer Navigator
Multiplying Integers • Visual Number Lines
Name:
Date:
Sign Rules:
Same Signs (+): (+) × (+) = + | (−) × (−) = +
Different Signs (−): (+) × (−) = − | (−) × (+) = −
Step-by-Step Model Problem: 3 × (−2) = −6
1. Check Signs
Different signs → Negative (−)
2. Multiply Values
3 × 2 = 6
3. Combine Sign & Value
Answer = −6
Model: Start at 0, take 3 jumps of −2 to the left Lands on −6
-6 -5 -4 -3 -2 -1 0 1 2
A
Guided Practice: Number Lines & Integer Steps
Draw your jumps on the line, then complete the steps
#1 4 × (−2) =
Draw 4 jumps of −2 to the left:
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
Step 1: Circle Sign
Step 2: 4 × 2 =
Final Product:
#2 2 × (−4) =
Draw 2 jumps of −4 to the left:
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
Step 1: Circle Sign
Step 2: 2 × 4 =
Final Product:
#3 (−3) × (−5) =
Remember: Same Signs = Positive (+)
Step 1: Sign Rule
(−) × (−) becomes ( + )
Step 2: Multiply Values 3 × 5 =
Final Answer:
Tip: Always determine whether your answer will be positive or negative first! Page 1 of 2
Rational Navigator
Multiplying Fractions & Decimals with Signs
Same Sign Rules Apply!
Step-by-Step Fraction Model \( \left(-\frac{1}{2}\right) \times \left(\frac{3}{4}\right) = -\frac{3}{8} \)
1. Check Signs
(−) × (+) → − Negative
2. Multiply Across
Top: \( 1 \times 3 = \mathbf{3} \)
Bottom: \( 2 \times 4 = \mathbf{8} \)
3. Final Fraction
Answer = \( -\frac{3}{8} \)
Visual Model: Half of \( \frac{3}{4} \) shades 3 out of 8 pieces:
3 of 8 parts = \( \frac{3}{8} \)
B
Guided Practice: Fractions & Decimals
Multiply numerators & denominators, or count decimal places
#4 \( \left(-\frac{2}{3}\right) \times \left(-\frac{1}{4}\right) \)
Same signs → Positive (+)
Step 1: Sign
(−) × (−) = +
Step 2: Multiply Across
Top: \( 2 \times 1 = \)
Bottom: \( 3 \times 4 = \)
Final Fraction:
#5 \( \frac{3}{5} \times \left(-\frac{1}{2}\right) \)
Different signs → Negative (−)
Step 1: Sign
(+) × (−) = −
Step 2: Multiply Across
Top: \( 3 \times 1 = \)
Bottom: \( 5 \times 2 = \)
Final Fraction:
#6 Decimals 0.4 × (−0.2) =
(+) × (−) = −
Step 1: Multiply Digits
4 × 2 = 8
Step 2: Decimal Places
1 place + 1 place = 2 decimal places
Final Decimal:
#7 Real World Temperature Change
The temperature drops by 0.5°C each hour for 4 hours.
Calculate the total drop: 4 × (−0.5)
Total Change:
How confident do you feel with these sign rules?
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