To express the decimal 4.625 as a fraction and then generate additional equivalent fractions with specific constraints on the numerators and denominators, follow these steps:
1. Convert the Decimal to a Fraction:
First, convert 4.625 to a fraction by recognizing it as a mixed number:
[tex]\[
4.625 = 4 \frac{5}{8}
\][/tex]
This mixed number can be converted to an improper fraction by multiplying the whole number part by the denominator and then adding the numerator:
[tex]\[
4 \frac{5}{8} = \frac{4 \times 8 + 5}{8} = \frac{32 + 5}{8} = \frac{37}{8}
\][/tex]
Therefore, 4.625 as a fraction is [tex]\(\frac{37}{8}\)[/tex].
2. Generate Equivalent Fractions:
To create more fractions equivalent to [tex]\(\frac{37}{8}\)[/tex] where the numerator is a three-digit number and the denominator is a two-digit number, multiply the numerator and denominator of [tex]\(\frac{37}{8}\)[/tex] by the same integers.
For instance:
- Multiply by 2:
[tex]\[
\frac{37 \times 2}{8 \times 2} = \frac{74}{16}
\][/tex]
- Multiply by 3:
[tex]\[
\frac{37 \times 3}{8 \times 3} = \frac{111}{24}
\][/tex]
- Multiply by 4:
[tex]\[
\frac{37 \times 4}{8 \times 4} = \frac{148}{32}
\][/tex]
- Multiply by 5:
[tex]\[
\frac{37 \times 5}{8 \times 5} = \frac{185}{40}
\][/tex]
Based on these calculations, the four additional fractions with numerators being three-digit numbers and denominators being two-digit numbers are:
- [tex]\(\frac{74}{16}\)[/tex]
- [tex]\(\frac{111}{24}\)[/tex]
- [tex]\(\frac{148}{32}\)[/tex]
- [tex]\(\frac{185}{40}\)[/tex]
These fractions are all equivalent to the original fraction [tex]\(\frac{37}{8}\)[/tex], and they follow the condition of having a three-digit numerator and a two-digit denominator.
