Answer :
We need to simplify each subtraction of fractions and then reduce the result to its lowest terms. Let’s work through each one step by step.
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1. Simplify
[tex]\[
\frac{16}{18} - \frac{10}{24}.
\][/tex]
Step 1. Simplify each fraction if possible.
[tex]\[
\frac{16}{18} = \frac{8}{9} \quad \text{(dividing numerator and denominator by 2)}
\][/tex]
[tex]\[
\frac{10}{24} = \frac{5}{12} \quad \text{(dividing numerator and denominator by 2)}
\][/tex]
Step 2. To subtract, find a common denominator. The denominators are 9 and 12. The least common multiple (LCM) of 9 and 12 is 36.
Convert each fraction:
[tex]\[
\frac{8}{9} = \frac{8 \times 4}{9 \times 4} = \frac{32}{36},
\][/tex]
[tex]\[
\frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36}.
\][/tex]
Step 3. Subtract:
[tex]\[
\frac{32}{36} - \frac{15}{36} = \frac{32 - 15}{36} = \frac{17}{36}.
\][/tex]
──────────────────────────────
2. Simplify
[tex]\[
\frac{5}{6} - \frac{4}{5}.
\][/tex]
Step 1. The denominators 6 and 5 have LCM 30. Convert each fraction:
[tex]\[
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30},
\][/tex]
[tex]\[
\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}.
\][/tex]
Step 2. Subtract:
[tex]\[
\frac{25}{30} - \frac{24}{30} = \frac{1}{30}.
\][/tex]
──────────────────────────────
3. Simplify
[tex]\[
\frac{3}{10} - \frac{1}{10}.
\][/tex]
Because the denominators are the same, subtract the numerators directly:
[tex]\[
\frac{3 - 1}{10} = \frac{2}{10}.
\][/tex]
Simplify by dividing numerator and denominator by 2:
[tex]\[
\frac{2}{10} = \frac{1}{5}.
\][/tex]
──────────────────────────────
4. Simplify
[tex]\[
\frac{17}{21} - \frac{1}{7}.
\][/tex]
Step 1. Write both fractions with a common denominator. Note that [tex]$7$[/tex] divides [tex]$21$[/tex], so we can write:
[tex]\[
\frac{1}{7} = \frac{3}{21}.
\][/tex]
Step 2. Subtract:
[tex]\[
\frac{17}{21} - \frac{3}{21} = \frac{14}{21}.
\][/tex]
Step 3. Simplify by dividing numerator and denominator by 7:
[tex]\[
\frac{14}{21} = \frac{2}{3}.
\][/tex]
──────────────────────────────
5. Simplify
[tex]\[
\frac{3}{5} - \frac{7}{12}.
\][/tex]
Step 1. Find the LCM of the denominators 5 and 12, which is 60. Convert each fraction:
[tex]\[
\frac{3}{5} = \frac{3 \times 12}{5 \times 12} = \frac{36}{60},
\][/tex]
[tex]\[
\frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60}.
\][/tex]
Step 2. Subtract:
[tex]\[
\frac{36}{60} - \frac{35}{60} = \frac{1}{60}.
\][/tex]
──────────────────────────────
6. Simplify
[tex]\[
\frac{27}{30} - \frac{2}{6}.
\][/tex]
Step 1. Simplify each fraction if possible.
[tex]\[
\frac{27}{30} = \frac{9}{10} \quad \text{(dividing numerator and denominator by 3)},
\][/tex]
[tex]\[
\frac{2}{6} = \frac{1}{3} \quad \text{(dividing numerator and denominator by 2)}.
\][/tex]
Step 2. Find a common denominator for [tex]$\frac{9}{10}$[/tex] and [tex]$\frac{1}{3}$[/tex]. The LCM of 10 and 3 is 30. Convert:
[tex]\[
\frac{9}{10} = \frac{9 \times 3}{10 \times 3} = \frac{27}{30},
\][/tex]
[tex]\[
\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}.
\][/tex]
Step 3. Subtract:
[tex]\[
\frac{27}{30} - \frac{10}{30} = \frac{17}{30}.
\][/tex]
──────────────────────────────
Summary of answers:
1. [tex]$\displaystyle \frac{16}{18}-\frac{10}{24}=\frac{17}{36}$[/tex]
2. [tex]$\displaystyle \frac{5}{6}-\frac{4}{5}=\frac{1}{30}$[/tex]
3. [tex]$\displaystyle \frac{3}{10}-\frac{1}{10}=\frac{1}{5}$[/tex]
4. [tex]$\displaystyle \frac{17}{21}-\frac{1}{7}=\frac{2}{3}$[/tex]
5. [tex]$\displaystyle \frac{3}{5}-\frac{7}{12}=\frac{1}{60}$[/tex]
6. [tex]$\displaystyle \frac{27}{30}-\frac{2}{6}=\frac{17}{30}$[/tex]
──────────────────────────────
1. Simplify
[tex]\[
\frac{16}{18} - \frac{10}{24}.
\][/tex]
Step 1. Simplify each fraction if possible.
[tex]\[
\frac{16}{18} = \frac{8}{9} \quad \text{(dividing numerator and denominator by 2)}
\][/tex]
[tex]\[
\frac{10}{24} = \frac{5}{12} \quad \text{(dividing numerator and denominator by 2)}
\][/tex]
Step 2. To subtract, find a common denominator. The denominators are 9 and 12. The least common multiple (LCM) of 9 and 12 is 36.
Convert each fraction:
[tex]\[
\frac{8}{9} = \frac{8 \times 4}{9 \times 4} = \frac{32}{36},
\][/tex]
[tex]\[
\frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36}.
\][/tex]
Step 3. Subtract:
[tex]\[
\frac{32}{36} - \frac{15}{36} = \frac{32 - 15}{36} = \frac{17}{36}.
\][/tex]
──────────────────────────────
2. Simplify
[tex]\[
\frac{5}{6} - \frac{4}{5}.
\][/tex]
Step 1. The denominators 6 and 5 have LCM 30. Convert each fraction:
[tex]\[
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30},
\][/tex]
[tex]\[
\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}.
\][/tex]
Step 2. Subtract:
[tex]\[
\frac{25}{30} - \frac{24}{30} = \frac{1}{30}.
\][/tex]
──────────────────────────────
3. Simplify
[tex]\[
\frac{3}{10} - \frac{1}{10}.
\][/tex]
Because the denominators are the same, subtract the numerators directly:
[tex]\[
\frac{3 - 1}{10} = \frac{2}{10}.
\][/tex]
Simplify by dividing numerator and denominator by 2:
[tex]\[
\frac{2}{10} = \frac{1}{5}.
\][/tex]
──────────────────────────────
4. Simplify
[tex]\[
\frac{17}{21} - \frac{1}{7}.
\][/tex]
Step 1. Write both fractions with a common denominator. Note that [tex]$7$[/tex] divides [tex]$21$[/tex], so we can write:
[tex]\[
\frac{1}{7} = \frac{3}{21}.
\][/tex]
Step 2. Subtract:
[tex]\[
\frac{17}{21} - \frac{3}{21} = \frac{14}{21}.
\][/tex]
Step 3. Simplify by dividing numerator and denominator by 7:
[tex]\[
\frac{14}{21} = \frac{2}{3}.
\][/tex]
──────────────────────────────
5. Simplify
[tex]\[
\frac{3}{5} - \frac{7}{12}.
\][/tex]
Step 1. Find the LCM of the denominators 5 and 12, which is 60. Convert each fraction:
[tex]\[
\frac{3}{5} = \frac{3 \times 12}{5 \times 12} = \frac{36}{60},
\][/tex]
[tex]\[
\frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60}.
\][/tex]
Step 2. Subtract:
[tex]\[
\frac{36}{60} - \frac{35}{60} = \frac{1}{60}.
\][/tex]
──────────────────────────────
6. Simplify
[tex]\[
\frac{27}{30} - \frac{2}{6}.
\][/tex]
Step 1. Simplify each fraction if possible.
[tex]\[
\frac{27}{30} = \frac{9}{10} \quad \text{(dividing numerator and denominator by 3)},
\][/tex]
[tex]\[
\frac{2}{6} = \frac{1}{3} \quad \text{(dividing numerator and denominator by 2)}.
\][/tex]
Step 2. Find a common denominator for [tex]$\frac{9}{10}$[/tex] and [tex]$\frac{1}{3}$[/tex]. The LCM of 10 and 3 is 30. Convert:
[tex]\[
\frac{9}{10} = \frac{9 \times 3}{10 \times 3} = \frac{27}{30},
\][/tex]
[tex]\[
\frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}.
\][/tex]
Step 3. Subtract:
[tex]\[
\frac{27}{30} - \frac{10}{30} = \frac{17}{30}.
\][/tex]
──────────────────────────────
Summary of answers:
1. [tex]$\displaystyle \frac{16}{18}-\frac{10}{24}=\frac{17}{36}$[/tex]
2. [tex]$\displaystyle \frac{5}{6}-\frac{4}{5}=\frac{1}{30}$[/tex]
3. [tex]$\displaystyle \frac{3}{10}-\frac{1}{10}=\frac{1}{5}$[/tex]
4. [tex]$\displaystyle \frac{17}{21}-\frac{1}{7}=\frac{2}{3}$[/tex]
5. [tex]$\displaystyle \frac{3}{5}-\frac{7}{12}=\frac{1}{60}$[/tex]
6. [tex]$\displaystyle \frac{27}{30}-\frac{2}{6}=\frac{17}{30}$[/tex]
