Rational Numbers Workout Worksheet
Unit 1 • Lesson 2 Practice
Rational Numbers & Ratios
Name:
Date:
Period:
1 Ratios in Three Simplified Forms
Write in word form, colon form, and fraction form (always simplify)
Model: 4 circles to 6 squares → Words: 2 to 3 | Colon: 2 : 3 | Fraction: \(\frac{2}{3}\)
Simplified
Wildlife Count
🦌
🦌
🦌
🦌
🦌
🦌
🐻
🐻
🐻
🐻
Deer: 6 Bears: 4 Total: 10
1. Deer to Bears
Word:
Colon:
Fraction:
2. Bears to Deer
Word:
Colon:
Fraction:
3. Bears to Total Animals
Word:
Colon:
Fraction:
4. Deer to Total Animals
Word:
Colon:
Fraction:
2 Greatest Common Factor (GCF)
List factors or use prime factorization to find the GCF
5. 8 and 20
F(8):
F(20):
GCF =
6. 12 and 30
F(12):
F(30):
GCF =
7. 18 and 24
F(18):
F(24):
GCF =
8. 16 and 40
F(16):
F(40):
GCF =
3 Evaluating Absolute Value
Distance from zero on the number line: \(|x| \ge 0\)
Core Concept: Absolute value measures distance from 0. Distance is never negative! \(|-7| = 7\), \(|4| = 4\)
9. \(|8| =\)
10. \(|-2| =\)
11. \(|-10| =\)
12. \(|10| =\)
13. \(|0| =\)
14. \(\left|\frac{1}{3}\right| =\)
15. \(\left|\frac{7}{8}\right| =\)
16. \(\left|-\frac{5}{9}\right| =\)
Turn page for Comparisons, Real-World Data & Ordering Rational Numbers → Page 1 of 2
Unit 1 • Lesson 2 Practice (Continued)
Name:
4 Comparing Values Using <, >, or =
Write the evaluated value in each blank under the numbers first!
2
\(|-5|\)
Val: 2
Val:
\(|-1|\)
\(|-8|\)
Val:
Val:
\(|5|\)
\(|-5|\)
Val:
Val:
\(|-2|\)
0
Val:
Val: 0
\(-6\)
\(|-6|\)
Val: -6
Val:
\(\left|-\frac{3}{4}\right|\)
\(\frac{1}{2}\)
Val:
Val: 0.5
5 Modeling Real Life: Freezing Temperatures
Apply absolute value and integer comparison to temperature
Liquid Freezing Points
| Liquid | Freezing Pt (°C) |
|---|
| Butter | \(35\) |
| Airplane fuel | \(-53\) |
| Honey | \(-3\) |
| Mercury | \(-39\) |
| Candle wax | \(53\) |
a. Which liquid in the table has the lowest freezing point?
Answer:
b. Is mercury (\(-39^\circ\text{C}\)) or butter (\(35^\circ\text{C}\)) closer to the freezing point of water (\(0^\circ\text{C}\))?
Dist. of butter: \(|35| =\)
Dist. of mercury: \(|-39| =\)
Closer liquid:
c. How many degrees colder is airplane fuel (\(-53^\circ\text{C}\)) than honey (\(-3^\circ\text{C}\))?
Difference:
6 Ordering Rational Numbers
Evaluate absolute values first, then order original values from least to greatest
23. Order the set: \(8, \quad |3|, \quad -5, \quad |-2|, \quad -2\) Least → Greatest
Step 1 (Values): 8, |3| = , -5, |-2| = , -2
Step 2 (Originals):
<
<
<
<
24. Order the set: \(-4, \quad |-7|, \quad 0, \quad |1|, \quad -1.5\) Least → Greatest
Step 1 (Values): -4, |-7| = , 0, |1| = , -1.5
Step 2 (Originals):
<
<
<
<
Rational Numbers & Absolute Value • Practice & Modeling Page 2 of 2
Rational Rules Review Slides
Unit 1 • Core Reference
Rules of the Core Topics
Essential guide for GEMDAS & Exponents, Ratios, GCF, and Absolute Value.
01
GEMDAS & Exponents
02
3 Ratio Forms
03
Finding GCF
04
Absolute Value
Topic 1 • Order of Operations Priority of Operations
GEMDAS & Exponents Review
The GEMDAS Order
G: Grouping • \(()\), \([]\), and \(|x|\) bars!
E: Exponents • Evaluate powers next
M/D: Multiply & Divide • Left to right
A/S: Add & Subtract • Left to right
Exponents Anatomy
In \(4^3\), 4 is the base and 3 is the exponent.
\(4^3 = 4 \times 4 \times 4 = 64\)
Repeated multiplication, not \(4 \times 3\)!
Absolute Value Connection: Absolute value bars count as Grouping (G). Simplify inside the bars first!
Topic 2 • Relationships Rule: Order Matters
Three Ways to Write a Ratio
Form 1
Word Form
Uses the word “to”
6 to 4 → 3 to 2
Form 2
Colon Form
Uses a colon symbol
6 : 4 → 3 : 2
Form 3
Fraction Form
Top over bottom
\(\frac{6}{4} \rightarrow \frac{3}{2}\)
Golden Rule: Always simplify ratios by dividing by the GCF! Divide by 2
Topic 3 • Divisibility Highest Shared Divisor
Greatest Common Factor (GCF)
List Method (12 and 30)
12: 1, 2, 3, 4, 6, 12
30: 1, 2, 3, 5, 6, 10, 15, 30
Common factors: 1, 2, 3, 6
The Greatest Factor
\(\text{GCF} = 6\)
Use GCF to reduce fractions and ratios in one single step.
Rule: The GCF must divide into both numbers with no remainder.
Topic 4 • Distance Distance From Zero
Absolute Value & Ordering Rules
Distance is Never Negative
\(|x|\) is the steps from 0 on the number line.
\(|-10| = 10\) and \(|10| = 10\)
Comparing & Ordering Steps
Step 1: Simplify bars first (\(|-5| = 5\))
