To solve the question, let's break it down step by step.
### Adding [tex]\( 4 + \frac{2}{3} \)[/tex]
1. Identify Components: We have two terms to add: an integer [tex]\( 4 \)[/tex] and a fraction [tex]\( \frac{2}{3} \)[/tex].
2. Convert the Integer to Fractional Form: The integer 4 can also be viewed as [tex]\( \frac{4}{1} \)[/tex]. This helps in understanding its fractional representation.
3. Add the Two Values: When adding an integer and a fraction, consider:
[tex]\[
4 + \frac{2}{3}
\][/tex]
To add these, think of 4 as a fraction:
[tex]\[
4 = \frac{4}{1}
\][/tex]
4. Find a Common Denominator: The denominators here are 1 and 3. The common denominator will be 3.
5. Adjust Fractions to Have the Common Denominator:
[tex]\[
4 = \frac{4}{1} = \frac{4 \cdot 3}{1 \cdot 3} = \frac{12}{3}
\][/tex]
The second fraction remains:
[tex]\[
\frac{2}{3}
\][/tex]
6. Add the Numerators:
[tex]\[
\frac{12}{3} + \frac{2}{3} = \frac{12 + 2}{3} = \frac{14}{3}
\][/tex]
Hence, the sum of [tex]\( 4 + \frac{2}{3} \)[/tex] is [tex]\( \frac{14}{3} \)[/tex]. This fraction is equivalent to approximately [tex]\( 4.666666666666667 \)[/tex] in decimal form.
### Fraction Representation of Integer 4
Here we are asked to identify a fraction that represents the integer 4. The correct representation is:
[tex]\[
\frac{4}{1}
\][/tex]
This is because:
[tex]\[
\frac{4}{1} = 4
\][/tex]
So, the choices given are:
- A [tex]\( \frac{4}{1} \)[/tex]
- B 4.0
- C [tex]\( \frac{1}{4} \)[/tex]
Clearly, the correct fraction representing the integer 4 is:
[tex]\[
A. \frac{4}{1}
\][/tex]
### Conclusion
1. The addition [tex]\( 4 + \frac{2}{3} \)[/tex] gives us approximately [tex]\( 4.666666666666667 \)[/tex].
2. The integer 4 can be represented as the fraction [tex]\( \frac{4}{1} \)[/tex].
The correct answers are:
- For adding [tex]\( 4 + \frac{2}{3} \)[/tex]: [tex]\( 4.666666666666667 \)[/tex]
- The fraction that represents the integer 4 is: Choice A [tex]\( \frac{4}{1} \)[/tex].
