Halloween Hidden Picture: Classify Real Numbers | Worksheet ... - Free Printable

To solve the problem of classifying real numbers into the given categories (orange, brown, green, purple), we need to carefully analyze each number and determine its classification based on the definitions provided in the table. Let's break it down step by step.

Definitions Recap:

1. Orange: Integers
2. Brown: Rational numbers that are not integers
3. Green: Whole numbers that are not natural numbers
4. Purple: Irrational numbers

Step-by-Step Analysis:

#### 1. First Row:
- \( \sqrt{5} \): This is an irrational number because \( \sqrt{5} \) cannot be expressed as a fraction of two integers.
- Classification: Purple

- \( -1 + \sqrt{7} \): This is also an irrational number because \( \sqrt{7} \) is irrational, and adding or subtracting an integer from an irrational number results in an irrational number.
- Classification: Purple

- \( 28 \): This is an integer.
- Classification: Orange

- \( -6 \): This is an integer.
- Classification: Orange

- \( 1 + (-\sqrt{7}) \): Simplifies to \( 1 - \sqrt{7} \), which is irrational.
- Classification: Purple

- \( 41 + 0.9 \): Simplifies to \( 41.9 \), which is a rational number but not an integer.
- Classification: Brown

- \( 9 - \sqrt{4} \): Simplifies to \( 9 - 2 = 7 \), which is an integer.
- Classification: Orange

- \( 13 + 0.7 \): Simplifies to \( 13.7 \), which is a rational number but not an integer.
- Classification: Brown

#### 2. Second Row:
- \( \frac{3}{5} \): This is a rational number but not an integer.
- Classification: Brown

- \( 9 + 2 \): Simplifies to \( 11 \), which is an integer.
- Classification: Orange

- \( 7.4 \): This is a rational number but not an integer.
- Classification: Brown

- \( 9 + 0.\overline{7} \): The repeating decimal \( 0.\overline{7} \) can be expressed as a fraction (\( \frac{7}{9} \)), so this is a rational number but not an integer.
- Classification: Brown

- \( 0.3 - 2 \): Simplifies to \( -1.7 \), which is a rational number but not an integer.
- Classification: Brown

- \( -2.6 \): This is a rational number but not an integer.
- Classification: Brown

- \( 0.1 + \sqrt{7} \): Since \( \sqrt{7} \) is irrational, adding a rational number to it results in an irrational number.
- Classification: Purple

- \( \frac{1}{2} - \frac{1}{3} \): Simplifies to \( \frac{3}{6} - \frac{2}{6} = \frac{1}{6} \), which is a rational number but not an integer.
- Classification: Brown

#### 3. Third Row:
- \( 6 \div 2 \): Simplifies to \( 3 \), which is an integer.
- Classification: Orange

- \( 6 - 6 \): Simplifies to \( 0 \), which is a whole number but not a natural number.
- Classification: Green

- \( 33 \): This is an integer.
- Classification: Orange

- \( -5 - 8 \): Simplifies to \( -13 \), which is an integer.
- Classification: Orange

- \( 1 - (-0.5) \): Simplifies to \( 1 + 0.5 = 1.5 \), which is a rational number but not an integer.
- Classification: Brown

- \( 13 + 0.7 \): Simplifies to \( 13.7 \), which is a rational number but not an integer.
- Classification: Brown

#### 4. Fourth Row:
- \( \frac{1}{2} \): This is a rational number but not an integer.
- Classification: Brown

- \( 1887.5 \): This is a rational number but not an integer.
- Classification: Brown

- \( 3.14 \): This is a rational number but not an integer.
- Classification: Brown

- \( 10 \): This is an integer.
- Classification: Orange

- \( 3.2 - 1 \): Simplifies to \( 2.2 \), which is a rational number but not an integer.
- Classification: Brown

- \( -1.2 \): This is a rational number but not an integer.
- Classification: Brown

- \( 2.5 \times 2.5 \): Simplifies to \( 6.25 \), which is a rational number but not an integer.
- Classification: Brown

- \( -0.2 - 0.6 \): Simplifies to \( -0.8 \), which is a rational number but not an integer.
- Classification: Brown

- \( 1.65 \): This is a rational number but not an integer.
- Classification: Brown

#### 5. Fifth Row:
- \( 0.75 \): This is a rational number but not an integer.
- Classification: Brown

- \( 2^2 \): Simplifies to \( 4 \), which is an integer.
- Classification: Orange

- \( 6 + \sqrt{3} \): Since \( \sqrt{3} \) is irrational, adding a rational number to it results in an irrational number.
- Classification: Purple

- \( -\frac{3}{2} \): This is a rational number but not an integer.
- Classification: Brown

- \( 0 - 0.5 \): Simplifies to \( -0.5 \), which is a rational number but not an integer.
- Classification: Brown

- \( -\sqrt{2} \): This is an irrational number.
- Classification: Purple

- \( m \div n \): Without specific values for \( m \) and \( n \), we cannot definitively classify this. However, if \( m \) and \( n \) are integers and \( n \neq 0 \), this could be rational or irrational depending on the values. For the sake of this problem, let's assume it is rational but not an integer.
- Classification: Brown

- \( m - 1 \): Without specific values for \( m \), we cannot definitively classify this. However, if \( m \) is an integer, then \( m - 1 \) is also an integer.
- Classification: Orange

- \( \frac{4}{9} \): This is a rational number but not an integer.
- Classification: Brown

#### 6. Sixth Row:
- \( -10.02 \): This is a rational number but not an integer.
- Classification: Brown

- \( 0.5 \): This is a rational number but not an integer.
- Classification: Brown

- \( 0.9 - 0.7 \): Simplifies to \( 0.2 \), which is a rational number but not an integer.
- Classification: Brown

- \( \sqrt{5} + 5 \): Since \( \sqrt{5} \) is irrational, adding a rational number to it results in an irrational number.
- Classification: Purple

- \( 43.8 \): This is a rational number but not an integer.
- Classification: Brown

- \( 6 + 2\pi \): Since \( \pi \) is irrational, adding a rational number to it results in an irrational number.
- Classification: Purple

- \( -\frac{5}{2} \): This is a rational number but not an integer.
- Classification: Brown

- \( 5 + 0.8 \): Simplifies to \( 5.8 \), which is a rational number but not an integer.
- Classification: Brown

- \( -7.5 \): This is a rational number but not an integer.
- Classification: Brown

#### 7. Seventh Row:
- \( 3 - 0.3 \): Simplifies to \( 2.7 \), which is a rational number but not an integer.
- Classification: Brown

- \( -\frac{3}{7} \): This is a rational number but not an integer.
- Classification: Brown

- \( -\frac{7}{2} \): This is a rational number but not an integer.
- Classification: Brown

- \( -\frac{2}{9} \): This is a rational number but not an integer.
- Classification: Brown

- \( -9.5 \): This is a rational number but not an integer.
- Classification: Brown

- \( 1.0 \): This is a rational number but not an integer.
- Classification: Brown

#### 8. Eighth Row:
- \( 4 - 1.3 \): Simplifies to \( 2.7 \), which is a rational number but not an integer.
- Classification: Brown

- \( 0.\overline{2} \): This is a rational number but not an integer.
- Classification: Brown

- \( 77.\overline{58} \): This is a rational number but not an integer.
- Classification: Brown

- \( 0.2 + 2 \): Simplifies to \( 2.2 \), which is a rational number but not an integer.
- Classification: Brown

- \( 0.5 \): This is a rational number but not an integer.
- Classification: Brown

- \( 0.1 + 4 \): Simplifies to \( 4.1 \), which is a rational number but not an integer.
- Classification: Brown

- \( -\frac{1}{3} \): This is a rational number but not an integer.
- Classification: Brown

- \( -0.6 \): This is a rational number but not an integer.
- Classification: Brown

#### 9. Ninth Row:
- \( \frac{1}{3} \): This is a rational number but not an integer.
- Classification: Brown

- \( -\sqrt{2} \): This is an irrational number.
- Classification: Purple

- \( 0.6 - 2 \): Simplifies to \( -1.4 \), which is a rational number but not an integer.
- Classification: Brown

- \( 2 \): This is an integer.
- Classification: Orange

- \( m - 0.03 \): Without specific values for \( m \), we cannot definitively classify this. However, if \( m \) is an integer, then \( m - 0.03 \) is a rational number but not an integer.
- Classification: Brown

- \( m \div \sqrt{2} \): Since \( \sqrt{2} \) is irrational, dividing a rational number by it results in an irrational number.
- Classification: Purple

- \( m + 7 \): Without specific values for \( m \), we cannot definitively classify this. However, if \( m \) is an integer, then \( m + 7 \) is also an integer.
- Classification: Orange

- \( -\frac{1}{10} \): This is a rational number but not an integer.
- Classification: Brown

#### 10. Tenth Row:
- \( -9 \): This is an integer.
- Classification: Orange

- \( \frac{1}{2} \): This is a rational number but not an integer.
- Classification: Brown

- \( 2n \): Without specific values for \( n \), we cannot definitively classify this. However, if \( n \) is an integer, then \( 2n \) is also an integer.
- Classification: Orange

- \( \sqrt{4} - \sqrt{9} \): Simplifies to \( 2 - 3 = -1 \), which is an integer.
- Classification: Orange

- \( 5 - 5 \): Simplifies to \( 0 \), which is a whole number but not a natural number.
- Classification: Green

- \( 5 - 5 \): Simplifies to \( 0 \), which is a whole number but not a natural number.
- Classification: Green

- \( 1.0 \): This is a rational number but not an integer.
- Classification: Brown

- \( 7 - 0.2 \): Simplifies to \( 6.8 \), which is a rational number but not an integer.
- Classification: Brown

#### 11. Eleventh Row:
- \( 4.7 - 0.7 \): Simplifies to \( 4 \), which is an integer.
- Classification: Orange

- \( 0.7 \): This is a rational number but not an integer.
- Classification: Brown

- \( 8 - 1.8 \): Simplifies to \( 6.2 \), which is a rational number but not an integer.
- Classification: Brown

- \( -\frac{1}{2} \): This is a rational number but not an integer.
- Classification: Brown

- \( \sqrt{4} - 2 \): Simplifies to \( 2 - 2 = 0 \), which is a whole number but not a natural number.
- Classification: Green

- \( -5.3 \): This is a rational number but not an integer.
- Classification: Brown

- \( 9 + n \): Without specific values for \( n \), we cannot definitively classify this. However, if \( n \) is an integer, then \( 9 + n \) is also an integer.
- Classification: Orange

- \( \frac{3}{4} \): This is a rational number but not an integer.
- Classification: Brown

- \( \sqrt{1000} \): Simplifies to \( 10 \), which is an integer.
- Classification: Orange

#### 12. Twelfth Row:
- \( U_6 \): Without specific context for \( U_6 \), we cannot definitively classify this. However, if \( U_6 \) is an integer, then it is classified as such.
- Assumption: Integer
- Classification: Orange

- \( 3 - \frac{1}{2} \): Simplifies to \( 2.5 \), which is a rational number but not an integer.
- Classification: Brown

- \( \frac{2}{3} + \frac{1}{3} \): Simplifies to \( 1 \), which is an integer.
- Classification: Orange

- \( \frac{3}{4} \): This is a rational number but not an integer.
- Classification: Brown

- \( 19.4 \): This is a rational number but not an integer.
- Classification: Brown

- \( \frac{5}{2} \): This is a rational number but not an integer.
- Classification: Brown

- \( 0.9 - 0.8 \): Simplifies to \( 0.1 \), which is a rational number but not an integer.
- Classification: Brown

- \( 4.6 - 1 \): Simplifies to \( 3.6 \), which is a rational number but not an integer.
- Classification: Brown

- \( \frac{9}{2} \): This is a rational number but not an integer.
- Classification: Brown

- \( -4 - (-8) \): Simplifies to \( -4 + 8 = 4 \), which is an integer.
- Classification: Orange

Final Answer:

The classifications for each number are as follows:

\[
\boxed{
\begin{array}{c|c|c|c|c}
& \text{Orange} & \text{Brown} & \text{Green} & \text{Purple} \\
\hline
\sqrt{5} & & & & \checkmark \\
-1 + \sqrt{7} & & & & \checkmark \\
28 & \checkmark & & & \\
-6 & \checkmark & & & \\
1 + (-\sqrt{7}) & & & & \checkmark \\
41 + 0.9 & & \checkmark & & \\
9 - \sqrt{4} & \checkmark & & & \\
13 + 0.7 & & \checkmark & & \\
\vdots & \vdots & \vdots & \vdots & \vdots \\
\end{array}
}
\]

Each number has been classified based on the definitions provided. The complete grid can be filled similarly following the same logic.