Sure, let's convert each of the given fractions and mixed numbers to their decimal equivalents one by one. Here are the detailed solutions:
1. Convert the given fractions and mixed numbers to decimals:
(a) [tex]\(\frac{5}{10}\)[/tex]:
- Divide the numerator (5) by the denominator (10).
- [tex]\(\frac{5}{10} = 0.5\)[/tex]
(b) [tex]\(3 + \frac{7}{10}\)[/tex]:
- First, convert [tex]\(\frac{7}{10}\)[/tex] to a decimal by dividing 7 by 10.
- [tex]\(\frac{7}{10} = 0.7\)[/tex]
- Add 3 to 0.7.
- [tex]\(3 + 0.7 = 3.7\)[/tex]
(c) [tex]\(200 + 60 + 5 + \frac{1}{10}\)[/tex]:
- Sum the whole numbers first: [tex]\(200 + 60 + 5 = 265\)[/tex].
- Convert [tex]\(\frac{1}{10}\)[/tex] to a decimal by dividing 1 by 10.
- [tex]\(\frac{1}{10} = 0.1\)[/tex]
- Add the decimal to the sum of the whole numbers.
- [tex]\(265 + 0.1 = 265.1\)[/tex]
(d) [tex]\(70 + \frac{8}{10}\)[/tex]:
- Convert [tex]\(\frac{8}{10}\)[/tex] to a decimal by dividing 8 by 10.
- [tex]\(\frac{8}{10} = 0.8\)[/tex]
- Add the decimal to the whole number.
- [tex]\(70 + 0.8 = 70.8\)[/tex]
(e) [tex]\(\frac{88}{10}\)[/tex]:
- Divide the numerator (88) by the denominator (10).
- [tex]\(\frac{88}{10} = 8.8\)[/tex]
(f) [tex]\(4 + \frac{2}{10}\)[/tex]:
- Convert [tex]\(\frac{2}{10}\)[/tex] to a decimal by dividing 2 by 10.
- [tex]\(\frac{2}{10} = 0.2\)[/tex]
- Add the decimal to the whole number.
- [tex]\(4 + 0.2 = 4.2\)[/tex]
(g) [tex]\(\frac{3}{2}\)[/tex]:
- Divide the numerator (3) by the denominator (2).
- [tex]\(\frac{3}{2} = 1.5\)[/tex]
(h) [tex]\(\frac{2}{5}\)[/tex]:
- Divide the numerator (2) by the denominator (5).
- [tex]\(\frac{2}{5} = 0.4\)[/tex]
(i) [tex]\(\frac{12}{5}\)[/tex]:
- Divide the numerator (12) by the denominator (5).
- [tex]\(\frac{12}{5} = 2.4\)[/tex]
(j) [tex]\(3 + \frac{3}{5}\)[/tex]:
- Convert [tex]\(\frac{3}{5}\)[/tex] to a decimal by dividing 3 by 5.
- [tex]\(\frac{3}{5} = 0.6\)[/tex]
- Add this decimal to the whole number.
- [tex]\(3 + 0.6 = 3.6\)[/tex]
Thus, the decimal equivalents for the given fractions and mixed numbers are:
[tex]\[
(0.5, 3.7, 265.1, 70.8, 8.8, 4.2, 1.5, 0.4, 2.4, 3.6)
\][/tex]
