Answer :
Sure, let's work through these problems step-by-step.
### 1. Adding [tex]\(3 \frac{2}{5}\)[/tex] and [tex]\(5 \frac{3}{8}\)[/tex]
First, convert the mixed numbers to improper fractions:
- [tex]\(3 \frac{2}{5} = \frac{3 \cdot 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}\)[/tex]
- [tex]\(5 \frac{3}{8} = \frac{5 \cdot 8 + 3}{8} = \frac{40 + 3}{8} = \frac{43}{8}\)[/tex]
Next, find the sum of the improper fractions. Use the common denominator:
[tex]\[ \frac{17}{5} + \frac{43}{8} = \frac{17 \cdot 8 + 43 \cdot 5}{5 \cdot 8} = \frac{136 + 215}{40} = \frac{351}{40} \][/tex]
So, [tex]\(3 \frac{2}{5} + 5 \frac{3}{8} = \frac{351}{40} \)[/tex].
### 2. Adding [tex]\(6 \frac{3}{7}\)[/tex] and [tex]\(7 \frac{2}{6}\)[/tex]
First, convert the mixed numbers to improper fractions:
- [tex]\(6 \frac{3}{7} = \frac{6 \cdot 7 + 3}{7} = \frac{42 + 3}{7} = \frac{45}{7}\)[/tex]
- [tex]\(7 \frac{2}{6} = \frac{7 \cdot 6 + 2}{6} = \frac{42 + 2}{6} = \frac{44}{6} = \frac{22}{3}\)[/tex] (note: simplified [tex]\(\frac{44}{6} = \frac{22}{3}\)[/tex])
Next, find the sum of the improper fractions. Use the common denominator:
[tex]\[ \frac{45}{7} + \frac{22}{3} = \frac{45 \cdot 3 + 22 \cdot 7}{7 \cdot 3} = \frac{135 + 154}{21} = \frac{289}{21} \][/tex]
So, [tex]\(6 \frac{3}{7} + 7 \frac{2}{6} = \frac{578}{42} \)[/tex].
### 3. Adding [tex]\(10 \frac{1}{9}\)[/tex] and [tex]\(3 \frac{2}{3}\)[/tex]
First, convert the mixed numbers to improper fractions:
- [tex]\(10 \frac{1}{9} = \frac{10 \cdot 9 + 1}{9} = \frac{90 + 1}{9} = \frac{91}{9}\)[/tex]
- [tex]\(3 \frac{2}{3} = \frac{3 \cdot 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}\)[/tex]
Next, find the sum of the improper fractions. Use the common denominator:
[tex]\[ \frac{91}{9} + \frac{11}{3} = \frac{91 \cdot 3 + 11 \cdot 9}{9 \cdot 3} = \frac{273 + 99}{27} = \frac{372}{27} \][/tex]
So, [tex]\(10 \frac{1}{9} + 3 \frac{2}{3} = \frac{372}{27} \)[/tex].
### 4. Subtracting [tex]\(9 \frac{5}{8}\)[/tex] and [tex]\(2 \frac{3}{7}\)[/tex]
First, convert the mixed numbers to improper fractions:
- [tex]\(9 \frac{5}{8} = \frac{9 \cdot 8 + 5}{8} = \frac{72 + 5}{8} = \frac{77}{8}\)[/tex]
- [tex]\(2 \frac{3}{7} = \frac{2 \cdot 7 + 3}{7} = \frac{14 + 3}{7} = \frac{17}{7}\)[/tex]
Next, find the difference of the improper fractions. Use the common denominator:
[tex]\[ \frac{77}{8} - \frac{17}{7} = \frac{77 \cdot 7 - 17 \cdot 8}{8 \cdot 7} = \frac{539 - 136}{56} = \frac{403}{56} \][/tex]
So, [tex]\(9 \frac{5}{8} - 2 \frac{3}{7} = \frac{403}{56} \)[/tex].
### 5. Subtracting [tex]\(17 \frac{4}{5}\)[/tex] and [tex]\(6 \frac{3}{4}\)[/tex]
First, convert the mixed numbers to improper fractions:
- [tex]\(17 \frac{4}{5} = \frac{17 \cdot 5 + 4}{5} = \frac{85 + 4}{5} = \frac{89}{5}\)[/tex]
- [tex]\(6 \frac{3}{4} = \frac{6 \cdot 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4}\)[/tex]
Next, find the difference of the improper fractions. Use the common denominator:
[tex]\[ \frac{89}{5} - \frac{27}{4} = \frac{89 \cdot 4 - 27 \cdot 5}{5 \cdot 4} = \frac{356 - 135}{20} = \frac{221}{20} \][/tex]
So, [tex]\(17 \frac{4}{5} - 6 \frac{3}{4} = \frac{221}{20} \)[/tex].
### 1. Adding [tex]\(3 \frac{2}{5}\)[/tex] and [tex]\(5 \frac{3}{8}\)[/tex]
First, convert the mixed numbers to improper fractions:
- [tex]\(3 \frac{2}{5} = \frac{3 \cdot 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}\)[/tex]
- [tex]\(5 \frac{3}{8} = \frac{5 \cdot 8 + 3}{8} = \frac{40 + 3}{8} = \frac{43}{8}\)[/tex]
Next, find the sum of the improper fractions. Use the common denominator:
[tex]\[ \frac{17}{5} + \frac{43}{8} = \frac{17 \cdot 8 + 43 \cdot 5}{5 \cdot 8} = \frac{136 + 215}{40} = \frac{351}{40} \][/tex]
So, [tex]\(3 \frac{2}{5} + 5 \frac{3}{8} = \frac{351}{40} \)[/tex].
### 2. Adding [tex]\(6 \frac{3}{7}\)[/tex] and [tex]\(7 \frac{2}{6}\)[/tex]
First, convert the mixed numbers to improper fractions:
- [tex]\(6 \frac{3}{7} = \frac{6 \cdot 7 + 3}{7} = \frac{42 + 3}{7} = \frac{45}{7}\)[/tex]
- [tex]\(7 \frac{2}{6} = \frac{7 \cdot 6 + 2}{6} = \frac{42 + 2}{6} = \frac{44}{6} = \frac{22}{3}\)[/tex] (note: simplified [tex]\(\frac{44}{6} = \frac{22}{3}\)[/tex])
Next, find the sum of the improper fractions. Use the common denominator:
[tex]\[ \frac{45}{7} + \frac{22}{3} = \frac{45 \cdot 3 + 22 \cdot 7}{7 \cdot 3} = \frac{135 + 154}{21} = \frac{289}{21} \][/tex]
So, [tex]\(6 \frac{3}{7} + 7 \frac{2}{6} = \frac{578}{42} \)[/tex].
### 3. Adding [tex]\(10 \frac{1}{9}\)[/tex] and [tex]\(3 \frac{2}{3}\)[/tex]
First, convert the mixed numbers to improper fractions:
- [tex]\(10 \frac{1}{9} = \frac{10 \cdot 9 + 1}{9} = \frac{90 + 1}{9} = \frac{91}{9}\)[/tex]
- [tex]\(3 \frac{2}{3} = \frac{3 \cdot 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}\)[/tex]
Next, find the sum of the improper fractions. Use the common denominator:
[tex]\[ \frac{91}{9} + \frac{11}{3} = \frac{91 \cdot 3 + 11 \cdot 9}{9 \cdot 3} = \frac{273 + 99}{27} = \frac{372}{27} \][/tex]
So, [tex]\(10 \frac{1}{9} + 3 \frac{2}{3} = \frac{372}{27} \)[/tex].
### 4. Subtracting [tex]\(9 \frac{5}{8}\)[/tex] and [tex]\(2 \frac{3}{7}\)[/tex]
First, convert the mixed numbers to improper fractions:
- [tex]\(9 \frac{5}{8} = \frac{9 \cdot 8 + 5}{8} = \frac{72 + 5}{8} = \frac{77}{8}\)[/tex]
- [tex]\(2 \frac{3}{7} = \frac{2 \cdot 7 + 3}{7} = \frac{14 + 3}{7} = \frac{17}{7}\)[/tex]
Next, find the difference of the improper fractions. Use the common denominator:
[tex]\[ \frac{77}{8} - \frac{17}{7} = \frac{77 \cdot 7 - 17 \cdot 8}{8 \cdot 7} = \frac{539 - 136}{56} = \frac{403}{56} \][/tex]
So, [tex]\(9 \frac{5}{8} - 2 \frac{3}{7} = \frac{403}{56} \)[/tex].
### 5. Subtracting [tex]\(17 \frac{4}{5}\)[/tex] and [tex]\(6 \frac{3}{4}\)[/tex]
First, convert the mixed numbers to improper fractions:
- [tex]\(17 \frac{4}{5} = \frac{17 \cdot 5 + 4}{5} = \frac{85 + 4}{5} = \frac{89}{5}\)[/tex]
- [tex]\(6 \frac{3}{4} = \frac{6 \cdot 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4}\)[/tex]
Next, find the difference of the improper fractions. Use the common denominator:
[tex]\[ \frac{89}{5} - \frac{27}{4} = \frac{89 \cdot 4 - 27 \cdot 5}{5 \cdot 4} = \frac{356 - 135}{20} = \frac{221}{20} \][/tex]
So, [tex]\(17 \frac{4}{5} - 6 \frac{3}{4} = \frac{221}{20} \)[/tex].
