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Sagot :
Sure, let's work through the addition of these fractions and mixed numbers step-by-step, and ensure we express the answers in their lowest terms.
1) [tex]\(\frac{1}{7} + \frac{1}{4}\)[/tex]
To add these fractions, we need to find a common denominator. The least common denominator (LCD) of 7 and 4 is 28. We rewrite the fractions with this common denominator:
[tex]\[ \frac{1}{7} = \frac{4}{28}, \quad \frac{1}{4} = \frac{7}{28} \][/tex]
Now we add them:
[tex]\[ \frac{4}{28} + \frac{7}{28} = \frac{4 + 7}{28} = \frac{11}{28} \][/tex]
So, [tex]\(\frac{1}{7} + \frac{1}{4} = \frac{11}{28}\)[/tex]
2) [tex]\(\frac{2}{6} + \frac{1}{2}\)[/tex]
First, we simplify [tex]\(\frac{2}{6}\)[/tex]:
[tex]\[ \frac{2}{6} = \frac{1}{3} \][/tex]
Next, we find a common denominator for [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]. The least common denominator of 3 and 2 is 6. We rewrite the fractions with this common denominator:
[tex]\[ \frac{1}{3} = \frac{2}{6}, \quad \frac{1}{2} = \frac{3}{6} \][/tex]
Now we add them:
[tex]\[ \frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6} \][/tex]
So, [tex]\(\frac{2}{6} + \frac{1}{2} = \frac{5}{6}\)[/tex]
3) [tex]\(\frac{1}{2} + \frac{3}{5}\)[/tex]
To add these fractions, we need to find a common denominator. The least common denominator of 2 and 5 is 10. We rewrite the fractions with this common denominator:
[tex]\[ \frac{1}{2} = \frac{5}{10}, \quad \frac{3}{5} = \frac{6}{10} \][/tex]
Now we add them:
[tex]\[ \frac{5}{10} + \frac{6}{10} = \frac{5 + 6}{10} = \frac{11}{10} \][/tex]
So, [tex]\(\frac{1}{2} + \frac{3}{5} = \frac{11}{10}\)[/tex]
4) [tex]\(\frac{5}{6} + \frac{1}{2}\)[/tex]
To add these fractions, we need to find a common denominator. The least common denominator of 6 and 2 is 6. We rewrite the fractions with this common denominator:
[tex]\[ \frac{1}{2} = \frac{3}{6} \][/tex]
Now we add them:
[tex]\[ \frac{5}{6} + \frac{3}{6} = \frac{5 + 3}{6} = \frac{8}{6} \][/tex]
Simplify the result:
[tex]\[ \frac{8}{6} = \frac{4}{3} \][/tex]
So, [tex]\(\frac{5}{6} + \frac{1}{2} = \frac{4}{3}\)[/tex]
5) [tex]\(4 \frac{6}{10} + \frac{1}{2}\)[/tex]
First, we convert the mixed number to an improper fraction:
[tex]\[ 4 \frac{6}{10} = 4 + \frac{6}{10} = 4 + \frac{3}{5} \][/tex]
Now let's add [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]. The least common denominator of 5 and 2 is 10. We rewrite the fractions with this common denominator:
[tex]\[ \frac{3}{5} = \frac{6}{10}, \quad \frac{1}{2} = \frac{5}{10} \][/tex]
Now we add them:
[tex]\[ \frac{6}{10} + \frac{5}{10} = \frac{6 + 5}{10} = \frac{11}{10} \][/tex]
Now we add this result to 4:
[tex]\[ 4 + \frac{11}{10} = \frac{40}{10} + \frac{11}{10} = \frac{40 + 11}{10} = \frac{51}{10} \][/tex]
So, [tex]\(4 \frac{6}{10} + \frac{1}{2} = \frac{51}{10}\)[/tex]
1) [tex]\(\frac{1}{7} + \frac{1}{4}\)[/tex]
To add these fractions, we need to find a common denominator. The least common denominator (LCD) of 7 and 4 is 28. We rewrite the fractions with this common denominator:
[tex]\[ \frac{1}{7} = \frac{4}{28}, \quad \frac{1}{4} = \frac{7}{28} \][/tex]
Now we add them:
[tex]\[ \frac{4}{28} + \frac{7}{28} = \frac{4 + 7}{28} = \frac{11}{28} \][/tex]
So, [tex]\(\frac{1}{7} + \frac{1}{4} = \frac{11}{28}\)[/tex]
2) [tex]\(\frac{2}{6} + \frac{1}{2}\)[/tex]
First, we simplify [tex]\(\frac{2}{6}\)[/tex]:
[tex]\[ \frac{2}{6} = \frac{1}{3} \][/tex]
Next, we find a common denominator for [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]. The least common denominator of 3 and 2 is 6. We rewrite the fractions with this common denominator:
[tex]\[ \frac{1}{3} = \frac{2}{6}, \quad \frac{1}{2} = \frac{3}{6} \][/tex]
Now we add them:
[tex]\[ \frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6} \][/tex]
So, [tex]\(\frac{2}{6} + \frac{1}{2} = \frac{5}{6}\)[/tex]
3) [tex]\(\frac{1}{2} + \frac{3}{5}\)[/tex]
To add these fractions, we need to find a common denominator. The least common denominator of 2 and 5 is 10. We rewrite the fractions with this common denominator:
[tex]\[ \frac{1}{2} = \frac{5}{10}, \quad \frac{3}{5} = \frac{6}{10} \][/tex]
Now we add them:
[tex]\[ \frac{5}{10} + \frac{6}{10} = \frac{5 + 6}{10} = \frac{11}{10} \][/tex]
So, [tex]\(\frac{1}{2} + \frac{3}{5} = \frac{11}{10}\)[/tex]
4) [tex]\(\frac{5}{6} + \frac{1}{2}\)[/tex]
To add these fractions, we need to find a common denominator. The least common denominator of 6 and 2 is 6. We rewrite the fractions with this common denominator:
[tex]\[ \frac{1}{2} = \frac{3}{6} \][/tex]
Now we add them:
[tex]\[ \frac{5}{6} + \frac{3}{6} = \frac{5 + 3}{6} = \frac{8}{6} \][/tex]
Simplify the result:
[tex]\[ \frac{8}{6} = \frac{4}{3} \][/tex]
So, [tex]\(\frac{5}{6} + \frac{1}{2} = \frac{4}{3}\)[/tex]
5) [tex]\(4 \frac{6}{10} + \frac{1}{2}\)[/tex]
First, we convert the mixed number to an improper fraction:
[tex]\[ 4 \frac{6}{10} = 4 + \frac{6}{10} = 4 + \frac{3}{5} \][/tex]
Now let's add [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]. The least common denominator of 5 and 2 is 10. We rewrite the fractions with this common denominator:
[tex]\[ \frac{3}{5} = \frac{6}{10}, \quad \frac{1}{2} = \frac{5}{10} \][/tex]
Now we add them:
[tex]\[ \frac{6}{10} + \frac{5}{10} = \frac{6 + 5}{10} = \frac{11}{10} \][/tex]
Now we add this result to 4:
[tex]\[ 4 + \frac{11}{10} = \frac{40}{10} + \frac{11}{10} = \frac{40 + 11}{10} = \frac{51}{10} \][/tex]
So, [tex]\(4 \frac{6}{10} + \frac{1}{2} = \frac{51}{10}\)[/tex]
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