Test Questions on Rational Numbers and the Number Line

📚 Quick Study Guide

• 📍 Rational Numbers: Numbers that can be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. This includes fractions, integers, terminating decimals, and repeating decimals.
• ➕ Addition/Subtraction: To add or subtract rational numbers, find a common denominator. If $q$ is the common denominator, then $\frac{a}{q} + \frac{b}{q} = \frac{a+b}{q}$ and $\frac{a}{q} - \frac{b}{q} = \frac{a-b}{q}$.
• ✖️ Multiplication/Division: To multiply rational numbers, multiply the numerators and the denominators: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$. To divide, multiply by the reciprocal: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$.
• 📈 Number Line Representation: Rational numbers can be plotted on a number line. Positive numbers are to the right of zero, and negative numbers are to the left. The distance from zero represents the absolute value of the number.
• ↔️ Ordering Rational Numbers: To compare rational numbers, convert them to a common denominator or decimal form. Then, compare the numerators or the decimal values.

📝 Practice Quiz

1. Which of the following is a rational number?
   1. $\sqrt{2}$
   2. $\pi$
   3. 0.333...
   4. $i$
2. Which point on the number line best represents -2/3?
   1. A point slightly to the left of -1
   2. A point slightly to the right of -1
   3. A point slightly to the left of 0
   4. A point slightly to the right of 0
3. What is the sum of 1/4 and 2/5?
   1. 3/9
   2. 3/20
   3. 13/20
   4. 1/2
4. What is the result of multiplying -3/4 by 2/5?
   1. -6/20
   2. 6/20
   3. -5/9
   4. 5/9
5. Which of the following rational numbers is the largest?
   1. 1/2
   2. 2/5
   3. 3/8
   4. 5/12
6. What is the value of -5/6 divided by 2/3?
   1. -5/9
   2. 5/9
   3. -5/4
   4. 5/4
7. Which of these numbers is between 0.2 and 0.3?
   1. 1/6
   2. 1/3
   3. 1/5
   4. 1/4