Rational Numbers Test
Grade 7 Mathematics • Unit Assessment
The Number System Mastery Test
Standards: 7.NS.2, 7.NS.3, 7.NS.4, 7.NS.5, 7.NS.6 • Total: 40 Points
Name: __________________
Date: _________
Period: _____
Score: _____ / 40
Directions: Show all steps clearly. Express rational answers as simplified fractions, mixed numbers, or exact decimals. Calculators Permitted
PART 1
Distance & Absolute Value on the Number Line
(Standard 7.NS.2)
6 Points
1. Points \(A = -3.5\) and \(B = 2\frac{1}{4}\) 3 pts
Write an absolute value expression \(|A - B|\) and evaluate exact distance:
Distance = ________
2. Elevation Distance 3 pts
Submersible at \(-92.4\text{ m}\) and sensor at \(48\frac{3}{5}\text{ m}\). Find vertical distance:
Distance = ________ m
PART 2
Adding & Subtracting Mixed Rational Numbers
(Fractions, Mixed Numbers & Decimals)
8 Points
3. Mixed Operations: Evaluate each sum or difference. Simplify all fractional answers. 8 pts
a) Mixed Numbers [2.5 pts]:
\(\left(-4\frac{1}{2}\right) - \left(-2\frac{3}{4}\right)\)
Answer = ________
b) Decimal & Mixed [2.5 pts]:
\(-6.4 + \left(-2\frac{3}{5}\right)\)
Answer = ________
c) Mixed Subtraction [3 pts]:
\(5.25 - \left(-3\frac{1}{2}\right)\)
Answer = ________
PART 3
Multiplying Signed Fractions & Decimals
(Standard 7.NS.3)
8 Points
4. Fraction & Decimal Products: Evaluate each expression completely. Show all steps. 8 pts
a) Three-Factor Product [2.5 pts]:
\(\left(-\frac{5}{6}\right) \cdot \left(-\frac{9}{10}\right) \cdot \left(-\frac{2}{3}\right)\)
Answer = ________
b) Mixed & Decimal [2.5 pts]:
\(\left(-2\frac{1}{2}\right) \cdot (-3.4)\)
Answer = ________
c) Distributive Property [3 pts]:
\(-4 \cdot \left[3.25 + \left(-1\frac{1}{2}\right)\right]\)
Answer = ________
Grade 7 Mathematics • The Number System Page 1 of 2 Turn to Page 2 →
The Number System Mastery Test | Student Name: ____________________________________
Page 2 of 2
PART 4
Signed Division & Equivalent Rational Forms
(Standard 7.NS.4)
8 Points
5. Equivalent Rational Quotients 4 pts
a) Circle ALL expressions equivalent to \(-\frac{15}{4}\):
\(\frac{-15}{4}\)
\(\frac{15}{-4}\)
\(\frac{-15}{-4}\)
\(-3.75\)
\(-3\frac{3}{4}\)
\(+3.75\)
b) Write \(\frac{-21}{6}\) as a simplified mixed number AND as a decimal:
Mixed: ________ | Decimal: ________
6. Mixed Signed Division & Error Analysis 4 pts
a) Evaluate mixed fraction divided by decimal [2 pts]:
\(\left(-4\frac{1}{2}\right) \div 0.75\)
Quotient = ________
b) Error Analysis [2 pts]: Elena writes: “\((-5.4) \div (-0.6) = -9\)”. Explain her sign error and write the correct quotient:
Correct Value = ________
PART 5
Prime Factorization, Exponents & Square Roots
(Standards 7.NS.5 & 7.NS.6)
10 Points
7. Prime Factorization with Exponents: Find the prime factorization of each number. Show a factor tree or repeated division ladder, then write your final answer using exponents. 4 pts
a) Prime factorization of \(180\):
\(180\) = ____________________
b) Prime factorization of \(504\):
\(504\) = ____________________
8. Perfect Square Roots: Find each principal square root: 2 pts
\(\sqrt{64} =\) _____
\(\sqrt{121} =\) _____
\(\sqrt{169} =\) _____
\(\sqrt{225} =\) _____
9. Geometric Area Context: A square research station floor has an area of \(196\text{ m}^2\). 4 pts
a) Write an equation using \(A = s^2\) and solve for side length \(s\):
Side Length \(s\) = ________ m
b) Compute the total perimeter of the floor (\(P = 4s\)):
Perimeter = ________ m
Grade 7 Mathematics • The Number System Page 2 of 2 • End of Assessment Total Available Points: 40
Rational Numbers Answer Key
Teacher Resource Grading Key & Rubric
The Number System Test • Answer Key
Standards: 7.NS.2, 7.NS.3, 7.NS.4, 7.NS.5, 7.NS.6 • Total Available: 40 Points
Passing Benchmark: 28/40 (70%)
Mastery Benchmark: 35/40 (88%)
Grading Guidelines: Award partial credit as indicated. Accept exact decimals or equivalent simplified fractions. Page 1 Points: 22 pts
PART 1 KEY
Distance & Absolute Value (7.NS.2)
6 Points Total
Q1: Number Line Distance [3 pts]:
\(|-3.5 - 2.25| = |-5.75| = \mathbf{5.75}\) (or \(\mathbf{5\frac{3}{4}}\))
1.5 pts expression; 1.5 pts evaluated distance.
Q2: Elevation Distance [3 pts]:
\(|48.6 - (-92.4)| = |141.0| = \mathbf{141\text{ meters}}\)
1.5 pts expression; 1.5 pts distance with units.
PART 2 KEY
Adding & Subtracting Mixed Rational Numbers
8 Points Total
3a) Mixed Numbers [2.5 pts]:
\(-4\frac{2}{4} + 2\frac{3}{4} = -\frac{18}{4} + \frac{11}{4}\)
\(= -\frac{7}{4} = \mathbf{-1\frac{3}{4}}\) (or \(\mathbf{-1.75}\))
Answer = \(-1\frac{3}{4}\)
3b) Decimal & Mixed [2.5 pts]:
\(-6.4 + (-2.6) = \mathbf{-9.0}\)
Or: \(-6\frac{2}{5} + \left(-2\frac{3}{5}\right) = -8\frac{5}{5} = \mathbf{-9}\)
Answer = \(-9\)
3c) Mixed Subtraction [3 pts]:
\(5.25 - (-3.5) = 5.25 + 3.5\)
\(= \mathbf{8.75}\) (or \(\mathbf{8\frac{3}{4}}\))
Answer = \(8.75\)
PART 3 KEY
Multiplying Signed Fractions & Decimals (7.NS.3)
8 Points Total
4a) 3-Factor Product [2.5 pts]:
\(\left(+\frac{45}{60}\right) \cdot \left(-\frac{2}{3}\right) = \frac{3}{4} \cdot \left(-\frac{2}{3}\right)\)
\(= -\frac{6}{12} = \mathbf{-\frac{1}{2}}\) (or \(\mathbf{-0.5}\))
Answer = \(-\frac{1}{2}\)
4b) Mixed & Decimal [2.5 pts]:
\((-2.5) \cdot (-3.4) = \mathbf{+8.5}\)
Or: \(\left(-\frac{5}{2}\right) \cdot \left(-\frac{17}{5}\right) = +\frac{17}{2} = \mathbf{8\frac{1}{2}}\)
Answer = \(8.5\)
4c) Distributive Property [3 pts]:
\(-4 \cdot 3.25 + (-4) \cdot (-1.5)\)
\(= -13 + 6 = \mathbf{-7}\)
Answer = \(-7\)
• Mixed Operations Common Error Note:
In subtraction such as \(5.25 - (-3\frac{1}{2})\), remind students to rewrite as addition of the opposite (\(5.25 + 3.5 = 8.75\)). For \(-\frac{7}{4}\), confirm students simplify to \(-1\frac{3}{4}\).
