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Answer :
Sure! Let's solve the problem step-by-step.
We need to add or subtract the given fractions: [tex]\(-\frac{2}{10} - \frac{3}{5} + \frac{18}{20}\)[/tex].
1. Convert all fractions to have a common denominator:
- The denominators are 10, 5, and 20. The least common multiple (LCM) of these numbers is 20. We will convert all fractions to have a common denominator of 20.
2. Convert each fraction:
- [tex]\(-\frac{2}{10}\)[/tex] can be converted to have a denominator of 20:
[tex]\[
-\frac{2}{10} = -\frac{2 \times 2}{10 \times 2} = -\frac{4}{20}
\][/tex]
- [tex]\(-\frac{3}{5}\)[/tex] can be converted to have a denominator of 20:
[tex]\[
-\frac{3}{5} = -\frac{3 \times 4}{5 \times 4} = -\frac{12}{20}
\][/tex]
- [tex]\(\frac{18}{20}\)[/tex] already has the denominator of 20:
[tex]\[
\frac{18}{20} = \frac{18}{20}
\][/tex]
3. Add or subtract the fractions:
Now we have:
[tex]\[
-\frac{4}{20} - \frac{12}{20} + \frac{18}{20}
\][/tex]
Combine the numerators:
[tex]\[
(-4) + (-12) + 18 = -4 - 12 + 18 = 2
\][/tex]
So the new fraction is:
[tex]\[
\frac{2}{20}
\][/tex]
4. Simplify the fraction if needed:
The fraction [tex]\(\frac{2}{20}\)[/tex] can be simplified. The greatest common factor (GCF) of 2 and 20 is 2, so we divide the numerator and the denominator by their GCF:
[tex]\[
\frac{2 \div 2}{20 \div 2} = \frac{1}{10}
\][/tex]
Therefore, the final simplified answer is [tex]\(\frac{1}{10}\)[/tex].
We need to add or subtract the given fractions: [tex]\(-\frac{2}{10} - \frac{3}{5} + \frac{18}{20}\)[/tex].
1. Convert all fractions to have a common denominator:
- The denominators are 10, 5, and 20. The least common multiple (LCM) of these numbers is 20. We will convert all fractions to have a common denominator of 20.
2. Convert each fraction:
- [tex]\(-\frac{2}{10}\)[/tex] can be converted to have a denominator of 20:
[tex]\[
-\frac{2}{10} = -\frac{2 \times 2}{10 \times 2} = -\frac{4}{20}
\][/tex]
- [tex]\(-\frac{3}{5}\)[/tex] can be converted to have a denominator of 20:
[tex]\[
-\frac{3}{5} = -\frac{3 \times 4}{5 \times 4} = -\frac{12}{20}
\][/tex]
- [tex]\(\frac{18}{20}\)[/tex] already has the denominator of 20:
[tex]\[
\frac{18}{20} = \frac{18}{20}
\][/tex]
3. Add or subtract the fractions:
Now we have:
[tex]\[
-\frac{4}{20} - \frac{12}{20} + \frac{18}{20}
\][/tex]
Combine the numerators:
[tex]\[
(-4) + (-12) + 18 = -4 - 12 + 18 = 2
\][/tex]
So the new fraction is:
[tex]\[
\frac{2}{20}
\][/tex]
4. Simplify the fraction if needed:
The fraction [tex]\(\frac{2}{20}\)[/tex] can be simplified. The greatest common factor (GCF) of 2 and 20 is 2, so we divide the numerator and the denominator by their GCF:
[tex]\[
\frac{2 \div 2}{20 \div 2} = \frac{1}{10}
\][/tex]
Therefore, the final simplified answer is [tex]\(\frac{1}{10}\)[/tex].
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