Certainly! To address this incomplete expression, let's consider the given mathematical component, [tex]\( 2 \frac{1}{3} \)[/tex].
Step-by-step, here's what this mixed number represents and how you would approach potential operations involving it:
1. Understanding the Mixed Number:
A mixed number consists of a whole number and a fractional part. Here, we have [tex]\( 2 \frac{1}{3} \)[/tex], which consists of the whole number 2 and the fraction [tex]\( \frac{1}{3} \)[/tex].
2. Converting to an Improper Fraction:
To convert the mixed number into an improper fraction:
- Multiply the whole number (2) by the denominator (3) of the fractional part: [tex]\( 2 \times 3 = 6 \)[/tex].
- Add the numerator (1) of the fractional part to this product: [tex]\( 6 + 1 = 7 \)[/tex].
- The result is [tex]\( \frac{7}{3} \)[/tex].
3. Converting to a Decimal:
We can convert [tex]\( \frac{7}{3} \)[/tex] to its decimal form:
- Perform the division [tex]\( 7 \div 3 \)[/tex].
- The result is approximately [tex]\( 2.3333333333333335 \)[/tex], which continues indefinitely.
4. Using the Decimal in Further Calculations:
If you're asked to multiply [tex]\( 2 \frac{1}{3} \)[/tex] by a certain value, you can use the decimal form for simplicity. For example, if you're multiplying by a variable [tex]\( h \)[/tex]:
[tex]\[
2 \frac{1}{3} h = 2.3333333333333335 \times h
\][/tex]
Thus, the mixed number [tex]\( 2 \frac{1}{3} \)[/tex] in decimal form is approximately [tex]\( 2.3333333333333335 \)[/tex]. This value can now be used in any further calculations you might encounter.
