To determine if 0.3 is the multiplicative inverse of the mixed fraction [tex]\(3 \frac{1}{3}\)[/tex], we need to follow these steps:
1. Convert the mixed fraction to an improper fraction:
- The mixed fraction [tex]\(3 \frac{1}{3}\)[/tex] can be converted into an improper fraction. Here's how:
- Multiply the whole number part (3) by the denominator of the fractional part (3): [tex]\(3 \times 3 = 9\)[/tex].
- Add the numerator of the fractional part (1): [tex]\(9 + 1 = 10\)[/tex].
- This gives the improper fraction [tex]\( \frac{10}{3} \)[/tex].
2. Find the multiplicative inverse of [tex]\( \frac{10}{3} \)[/tex]:
- The multiplicative inverse of a fraction [tex]\( \frac{a}{b} \)[/tex] is [tex]\( \frac{b}{a} \)[/tex].
- Therefore, the multiplicative inverse of [tex]\( \frac{10}{3} \)[/tex] is [tex]\( \frac{3}{10} \)[/tex].
3. Convert the multiplicative inverse to a decimal:
- Convert [tex]\( \frac{3}{10} \)[/tex] to a decimal:
- [tex]\( \frac{3}{10} = 0.3 \)[/tex].
4. Compare the result with 0.3:
- Upon comparison, we see that [tex]\( 0.3 = 0.3 \)[/tex].
Hence, 0.3 is indeed the multiplicative inverse of [tex]\( 3 \frac{1}{3} \)[/tex]. This is because when you multiply [tex]\( 3 \frac{1}{3} \)[/tex] (or [tex]\( \frac{10}{3} \)[/tex]) by 0.3, the result is 1, confirming that 0.3 and [tex]\( 3 \frac{1}{3} \)[/tex] are multiplicative inverses.
