Sign Switch Showdown Worksheet
Grade 7 • Rational Numbers CCSS.MATH.7.NS.A.2
Sign Switch Showdown
Multiplying & Dividing Positive & Negative Fractions and Mixed Numbers
Name:
Date:
Score:
/ 24 pts
1. Sign Protocol (Multiplication & Division)
Same Signs: (+)
\((+) \cdot (+) = +\) | \((-) \cdot (-) = +\)
Different Signs: (-)
\((+) \cdot (-) = -\) | \((-) \cdot (+) = -\)
2. Operation Checklist
- • Step 1: Convert any mixed numbers into improper fractions.
- • Step 2: Determine the final sign first (odd number of negatives = negative).
- • Step 3: Cross-simplify common factors, multiply numerators & denominators.
A Sign Detective: Predict the Final Sign
Do not solve completely; circle (+) or (-)
1. \(\left(-\frac{2}{3}\right) \cdot \left(-\frac{9}{10}\right)\)
2. \(\frac{4}{7} \cdot \left(-3\frac{1}{2}\right)\)
3. \(\left(-\frac{1}{2}\right) \cdot \left(-\frac{4}{5}\right) \cdot \left(-\frac{3}{8}\right)\)
4. \(\left(-\frac{5}{12}\right) \div \left(-\frac{2}{3}\right)\)
B Multiplying Signed Fractions & Mixed Numbers
Show all steps & simplify completely
5. Calculate: \(-\frac{3}{4} \cdot \frac{8}{9}\)
Sign & Simplest Form
Answer:
6. Calculate: \(\left(-\frac{5}{6}\right) \cdot \left(-\frac{3}{10}\right)\)
Sign & Simplest Form
Answer:
7. Calculate: \(2\frac{1}{4} \cdot \left(-\frac{2}{3}\right)\)
Convert to improper first
Answer:
8. Calculate: \(\left(-1\frac{7}{8}\right) \cdot \left(-2\frac{2}{5}\right)\)
Convert to improper first
Answer:
9. Calculate: \(\frac{7}{12} \cdot \left(-\frac{4}{21}\right)\)
Cross-simplify factors
Answer:
10. Challenge (3 Factors): \(\left(-\frac{2}{5}\right) \cdot \left(-\frac{15}{16}\right) \cdot \left(-\frac{4}{9}\right)\)
Count negative factors
Answer:
Sign Switch Showdown • Math 7 Page 1 of 2 • Continue on Page 2 →
Part II
Dividing Signed Fractions & Applications
Division Rule: Multiply by the reciprocal! Keep \(\cdot\) Change \(\cdot\) Flip
C Dividing Signed Fractions & Mixed Numbers
Invert divisor, apply sign rules, and reduce
11. Compute: \(-\frac{5}{8} \div \frac{15}{16}\)
Reciprocal: \(\frac{16}{15}\)
Answer:
12. Compute: \(\frac{7}{10} \div \left(-\frac{14}{25}\right)\)
Reciprocal: \(-\frac{25}{14}\)
Answer:
13. Compute: \(\left(-\frac{9}{14}\right) \div \left(-\frac{3}{7}\right)\)
Negative \(\div\) Negative
Answer:
14. Compute: \(-3\frac{1}{2} \div \frac{7}{8}\)
Convert \(-3\frac{1}{2} = -\frac{7}{2}\)
Answer:
15. Compute: \(\left(-4\frac{2}{3}\right) \div \left(-1\frac{1}{6}\right)\)
Both mixed numbers to improper
Answer:
16. Integer Divisor: \(-\frac{8}{9} \div 4\)
Write \(4\) as \(\frac{4}{1}\)
Answer:
D Real-World Scenario & Error Analysis
Apply reasoning & critique student work
17. The Ocean Trench Descent
An oceanographic probe descends into the Mariana Trench at a steady rate of \(-\frac{4}{5}\) meters per second. What is the probe's total change in elevation after descending for \(15\frac{1}{2}\) seconds?
Include correct units
Answer:
18. Error Analysis: Spot Marcus's Mistake
Marcus's Work: \(\left(-2\frac{1}{4}\right) \div \left(-\frac{3}{8}\right) = -\frac{9}{4} \cdot \left(-\frac{8}{3}\right) = -\frac{72}{12} = -6\)
Explain the mistake Marcus made, then write the correct simplified answer.
Correct Value:
Correct:
Confidence Check:
Need Review Getting There Sign Master
Page 2 of 2 • CCSS.MATH.7.NS.A.2
