Let's break down how to solve each of these problems step by step:
1. [tex]\(1.2 + 1 \frac{2}{3} + 1 \frac{2}{9}\)[/tex]
First, let's convert the mixed fractions to improper fractions:
[tex]\[ 1 \frac{2}{3} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \][/tex]
[tex]\[ 1 \frac{2}{9} = 1 + \frac{2}{9} = \frac{9}{9} + \frac{2}{9} = \frac{11}{9} \][/tex]
Now let's express these in decimal form for easier addition:
[tex]\[ \frac{5}{3} \approx 1.66667 \][/tex]
[tex]\[ \frac{11}{9} \approx 1.22222 \][/tex]
Now, summing these values with 1.2:
[tex]\[ 1.2 + 1.66667 + 1.22222 \approx 4.088888888888889 \][/tex]
So, the first result is approximately:
[tex]\[ 4.088888888888889 \][/tex]
2. [tex]\( 2 \cdot \frac{1}{2} - \frac{1}{6} \)[/tex]
First, multiply:
[tex]\[ 2 \cdot \frac{1}{2} = 1 \][/tex]
Then, subtract:
[tex]\[ 1 - \frac{1}{6} \][/tex]
Convert 1 to a fraction with the same denominator:
[tex]\[ 1 = \frac{6}{6} \][/tex]
So, the operation becomes:
[tex]\[ \frac{6}{6} - \frac{1}{6} = \frac{5}{6} \][/tex]
In decimal form:
[tex]\[ \frac{5}{6} \approx 0.8333333333333334 \][/tex]
So, the second result is:
[tex]\[ 0.8333333333333334 \][/tex]
3. [tex]\( 1 \frac{7}{8} - \frac{1}{4} \)[/tex]
First, convert the mixed fraction to an improper fraction:
[tex]\[ 1 \frac{7}{8} = 1 + \frac{7}{8} = \frac{8}{8} + \frac{7}{8} = \frac{15}{8} \][/tex]
Convert [tex]\(\frac{1}{4}\)[/tex] to have a common denominator:
[tex]\[ \frac{1}{4} = \frac{2}{8} \][/tex]
Now, subtract:
[tex]\[ \frac{15}{8} - \frac{2}{8} = \frac{13}{8} \][/tex]
In decimal form:
[tex]\[ \frac{13}{8} = 1.625 \][/tex]
So, the third result is:
[tex]\[ 1.625 \][/tex]
4. [tex]\( \frac{2}{5} + \frac{3}{10} \)[/tex]
Convert to a common denominator (10 in this case):
[tex]\[ \frac{2}{5} = \frac{4}{10} \][/tex]
Now, add:
[tex]\[ \frac{4}{10} + \frac{3}{10} = \frac{7}{10} \][/tex]
So, the fourth result is:
[tex]\[ 0.7 \][/tex]
Therefore, the final results are:
1. [tex]\( \approx 4.088888888888889 \)[/tex]
2. [tex]\( \approx 0.8333333333333334 \)[/tex]
3. [tex]\( 1.625 \)[/tex]
4. [tex]\( 0.7 \)[/tex]
