1.9 As A Fraction In Simplest Form - Free Printable

To simplify improper fractions to mixed numbers in lowest terms, we follow these steps:

1. Divide the numerator by the denominator to find the whole number part.
2. Find the remainder of the division, which becomes the new numerator.
3. Keep the same denominator.
4. Simplify the resulting fraction if possible.

Let's solve each fraction step by step.

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First Row:

1. $\frac{304}{64}$:
- Divide: $304 \div 64 = 4$ with a remainder of $304 - (64 \times 4) = 304 - 256 = 48$.
- Mixed number: $4 \frac{48}{64}$.
- Simplify $\frac{48}{64}$: Both 48 and 64 are divisible by 16.
$$ \frac{48}{64} = \frac{48 \div 16}{64 \div 16} = \frac{3}{4} $$
- Final answer: $4 \frac{3}{4}$.

2. $\frac{189}{63}$:
- Divide: $189 \div 63 = 3$ with a remainder of $189 - (63 \times 3) = 189 - 189 = 0$.
- Mixed number: $3$ (no fractional part).
- Final answer: $3$.

3. $\frac{130}{35}$:
- Divide: $130 \div 35 = 3$ with a remainder of $130 - (35 \times 3) = 130 - 105 = 25$.
- Mixed number: $3 \frac{25}{35}$.
- Simplify $\frac{25}{35}$: Both 25 and 35 are divisible by 5.
$$ \frac{25}{35} = \frac{25 \div 5}{35 \div 5} = \frac{5}{7} $$
- Final answer: $3 \frac{5}{7}$.

4. $\frac{78}{72}$:
- Divide: $78 \div 72 = 1$ with a remainder of $78 - (72 \times 1) = 78 - 72 = 6$.
- Mixed number: $1 \frac{6}{72}$.
- Simplify $\frac{6}{72}$: Both 6 and 72 are divisible by 6.
$$ \frac{6}{72} = \frac{6 \div 6}{72 \div 6} = \frac{1}{12} $$
- Final answer: $1 \frac{1}{12}$.

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Second Row:

5. $\frac{168}{32}$:
- Divide: $168 \div 32 = 5$ with a remainder of $168 - (32 \times 5) = 168 - 160 = 8$.
- Mixed number: $5 \frac{8}{32}$.
- Simplify $\frac{8}{32}$: Both 8 and 32 are divisible by 8.
$$ \frac{8}{32} = \frac{8 \div 8}{32 \div 8} = \frac{1}{4} $$
- Final answer: $5 \frac{1}{4}$.

6. $\frac{30}{24}$:
- Divide: $30 \div 24 = 1$ with a remainder of $30 - (24 \times 1) = 30 - 24 = 6$.
- Mixed number: $1 \frac{6}{24}$.
- Simplify $\frac{6}{24}$: Both 6 and 24 are divisible by 6.
$$ \frac{6}{24} = \frac{6 \div 6}{24 \div 6} = \frac{1}{4} $$
- Final answer: $1 \frac{1}{4}$.

7. $\frac{70}{56}$:
- Divide: $70 \div 56 = 1$ with a remainder of $70 - (56 \times 1) = 70 - 56 = 14$.
- Mixed number: $1 \frac{14}{56}$.
- Simplify $\frac{14}{56}$: Both 14 and 56 are divisible by 14.
$$ \frac{14}{56} = \frac{14 \div 14}{56 \div 14} = \frac{1}{4} $$
- Final answer: $1 \frac{1}{4}$.

8. $\frac{128}{24}$:
- Divide: $128 \div 24 = 5$ with a remainder of $128 - (24 \times 5) = 128 - 120 = 8$.
- Mixed number: $5 \frac{8}{24}$.
- Simplify $\frac{8}{24}$: Both 8 and 24 are divisible by 8.
$$ \frac{8}{24} = \frac{8 \div 8}{24 \div 8} = \frac{1}{3} $$
- Final answer: $5 \frac{1}{3}$.

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Third Row:

9. $\frac{50}{24}$:
- Divide: $50 \div 24 = 2$ with a remainder of $50 - (24 \times 2) = 50 - 48 = 2$.
- Mixed number: $2 \frac{2}{24}$.
- Simplify $\frac{2}{24}$: Both 2 and 24 are divisible by 2.
$$ \frac{2}{24} = \frac{2 \div 2}{24 \div 2} = \frac{1}{12} $$
- Final answer: $2 \frac{1}{12}$.

10. $\frac{81}{81}$:
- Divide: $81 \div 81 = 1$ with a remainder of $81 - (81 \times 1) = 81 - 81 = 0$.
- Mixed number: $1$ (no fractional part).
- Final answer: $1$.

11. $\frac{119}{63}$:
- Divide: $119 \div 63 = 1$ with a remainder of $119 - (63 \times 1) = 119 - 63 = 56$.
- Mixed number: $1 \frac{56}{63}$.
- Simplify $\frac{56}{63}$: Both 56 and 63 are divisible by 7.
$$ \frac{56}{63} = \frac{56 \div 7}{63 \div 7} = \frac{8}{9} $$
- Final answer: $1 \frac{8}{9}$.

12. $\frac{160}{48}$:
- Divide: $160 \div 48 = 3$ with a remainder of $160 - (48 \times 3) = 160 - 144 = 16$.
- Mixed number: $3 \frac{16}{48}$.
- Simplify $\frac{16}{48}$: Both 16 and 48 are divisible by 16.
$$ \frac{16}{48} = \frac{16 \div 16}{48 \div 16} = \frac{1}{3} $$
- Final answer: $3 \frac{1}{3}$.

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Fourth Row:

13. $\frac{102}{60}$:
- Divide: $102 \div 60 = 1$ with a remainder of $102 - (60 \times 1) = 102 - 60 = 42$.
- Mixed number: $1 \frac{42}{60}$.
- Simplify $\frac{42}{60}$: Both 42 and 60 are divisible by 6.
$$ \frac{42}{60} = \frac{42 \div 6}{60 \div 6} = \frac{7}{10} $$
- Final answer: $1 \frac{7}{10}$.

14. $\frac{116}{20}$:
- Divide: $116 \div 20 = 5$ with a remainder of $116 - (20 \times 5) = 116 - 100 = 16$.
- Mixed number: $5 \frac{16}{20}$.
- Simplify $\frac{16}{20}$: Both 16 and 20 are divisible by 4.
$$ \frac{16}{20} = \frac{16 \div 4}{20 \div 4} = \frac{4}{5} $$
- Final answer: $5 \frac{4}{5}$.

15. $\frac{240}{45}$:
- Divide: $240 \div 45 = 5$ with a remainder of $240 - (45 \times 5) = 240 - 225 = 15$.
- Mixed number: $5 \frac{15}{45}$.
- Simplify $\frac{15}{45}$: Both 15 and 45 are divisible by 15.
$$ \frac{15}{45} = \frac{15 \div 15}{45 \div 15} = \frac{1}{3} $$
- Final answer: $5 \frac{1}{3}$.

16. $\frac{75}{20}$:
- Divide: $75 \div 20 = 3$ with a remainder of $75 - (20 \times 3) = 75 - 60 = 15$.
- Mixed number: $3 \frac{15}{20}$.
- Simplify $\frac{15}{20}$: Both 15 and 20 are divisible by 5.
$$ \frac{15}{20} = \frac{15 \div 5}{20 \div 5} = \frac{3}{4} $$
- Final answer: $3 \frac{3}{4}$.

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Fifth Row:

17. $\frac{123}{24}$:
- Divide: $123 \div 24 = 5$ with a remainder of $123 - (24 \times 5) = 123 - 120 = 3$.
- Mixed number: $5 \frac{3}{24}$.
- Simplify $\frac{3}{24}$: Both 3 and 24 are divisible by 3.
$$ \frac{3}{24} = \frac{3 \div 3}{24 \div 3} = \frac{1}{8} $$
- Final answer: $5 \frac{1}{8}$.

18. $\frac{203}{84}$:
- Divide: $203 \div 84 = 2$ with a remainder of $203 - (84 \times 2) = 203 - 168 = 35$.
- Mixed number: $2 \frac{35}{84}$.
- Simplify $\frac{35}{84}$: Both 35 and 84 are divisible by 7.
$$ \frac{35}{84} = \frac{35 \div 7}{84 \div 7} = \frac{5}{12} $$
- Final answer: $2 \frac{5}{12}$.

19. $\frac{371}{70}$:
- Divide: $371 \div 70 = 5$ with a remainder of $371 - (70 \times 5) = 371 - 350 = 21$.
- Mixed number: $5 \frac{21}{70}$.
- Simplify $\frac{21}{70}$: Both 21 and 70 are divisible by 7.
$$ \frac{21}{70} = \frac{21 \div 7}{70 \div 7} = \frac{3}{10} $$
- Final answer: $5 \frac{3}{10}$.

20. $\frac{95}{20}$:
- Divide: $95 \div 20 = 4$ with a remainder of $95 - (20 \times 4) = 95 - 80 = 15$.
- Mixed number: $4 \frac{15}{20}$.
- Simplify $\frac{15}{20}$: Both 15 and 20 are divisible by 5.
$$ \frac{15}{20} = \frac{15 \div 5}{20 \div 5} = \frac{3}{4} $$
- Final answer: $4 \frac{3}{4}$.

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Sixth Row:

21. $\frac{66}{22}$:
- Divide: $66 \div 22 = 3$ with a remainder of $66 - (22 \times 3) = 66 - 66 = 0$.
- Mixed number: $3$ (no fractional part).
- Final answer: $3$.

22. $\frac{70}{60}$:
- Divide: $70 \div 60 = 1$ with a remainder of $70 - (60 \times 1) = 70 - 60 = 10$.
- Mixed number: $1 \frac{10}{60}$.
- Simplify $\frac{10}{60}$: Both 10 and 60 are divisible by 10.
$$ \frac{10}{60} = \frac{10 \div 10}{60 \div 10} = \frac{1}{6} $$
- Final answer: $1 \frac{1}{6}$.

23. $\frac{18}{6}$:
- Divide: $18 \div 6 = 3$ with a remainder of $18 - (6 \times 3) = 18 - 18 = 0$.
- Mixed number: $3$ (no fractional part).
- Final answer: $3$.

24. $\frac{378}{84}$:
- Divide: $378 \div 84 = 4$ with a remainder of $378 - (84 \times 4) = 378 - 336 = 42$.
- Mixed number: $4 \frac{42}{84}$.
- Simplify $\frac{42}{84}$: Both 42 and 84 are divisible by 42.
$$ \frac{42}{84} = \frac{42 \div 42}{84 \div 42} = \frac{1}{2} $$
- Final answer: $4 \frac{1}{2}$.

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Seventh Row:

25. $\frac{430}{120}$:
- Divide: $430 \div 120 = 3$ with a remainder of $430 - (120 \times 3) = 430 - 360 = 70$.
- Mixed number: $3 \frac{70}{120}$.
- Simplify $\frac{70}{120}$: Both 70 and 120 are divisible by 10.
$$ \frac{70}{120} = \frac{70 \div 10}{120 \div 10} = \frac{7}{12} $$
- Final answer: $3 \frac{7}{12}$.

26. $\frac{165}{60}$:
- Divide: $165 \div 60 = 2$ with a remainder of $165 - (60 \times 2) = 165 - 120 = 45$.
- Mixed number: $2 \frac{45}{60}$.
- Simplify $\frac{45}{60}$: Both 45 and 60 are divisible by 15.
$$ \frac{45}{60} = \frac{45 \div 15}{60 \div 15} = \frac{3}{4} $$
- Final answer: $2 \frac{3}{4}$.

27. $\frac{20}{15}$:
- Divide: $20 \div 15 = 1$ with a remainder of $20 - (15 \times 1) = 20 - 15 = 5$.
- Mixed number: $1 \frac{5}{15}$.
- Simplify $\frac{5}{15}$: Both 5 and 15 are divisible by 5.
$$ \frac{5}{15} = \frac{5 \div 5}{15 \div 5} = \frac{1}{3} $$
- Final answer: $1 \frac{1}{3}$.

28. $\frac{152}{40}$:
- Divide: $152 \div 40 = 3$ with a remainder of $152 - (40 \times 3) = 152 - 120 = 32$.
- Mixed number: $3 \frac{32}{40}$.
- Simplify $\frac{32}{40}$: Both 32 and 40 are divisible by 8.
$$ \frac{32}{40} = \frac{32 \div 8}{40 \div 8} = \frac{4}{5} $$
- Final answer: $3 \frac{4}{5}$.

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Eighth Row:

29. $\frac{333}{72}$:
- Divide: $333 \div 72 = 4$ with a remainder of $333 - (72 \times 4) = 333 - 288 = 45$.
- Mixed number: $4 \frac{45}{72}$.
- Simplify $\frac{45}{72}$: Both 45 and 72 are divisible by 9.
$$ \frac{45}{72} = \frac{45 \div 9}{72 \div 9} = \frac{5}{8} $$
- Final answer: $4 \frac{5}{8}$.

30. $\frac{14}{10}$:
- Divide: $14 \div 10 = 1$ with a remainder of $14 - (10 \times 1) = 14 - 10 = 4$.
- Mixed number: $1 \frac{4}{10}$.
- Simplify $\frac{4}{10}$: Both 4 and 10 are divisible by 2.
$$ \frac{4}{10} = \frac{4 \div 2}{10 \div 2} = \frac{2}{5} $$
- Final answer: $1 \frac{2}{5}$.

31. $\frac{18}{12}$:
- Divide: $18 \div 12 = 1$ with a remainder of $18 - (12 \times 1) = 18 - 12 = 6$.
- Mixed number: $1 \frac{6}{12}$.
- Simplify $\frac{6}{12}$: Both 6 and 12 are divisible by 6.
$$ \frac{6}{12} = \frac{6 \div 6}{12 \div 6} = \frac{1}{2} $$
- Final answer: $1 \frac{1}{2}$.

32. $\frac{35}{10}$:
- Divide: $35 \div 10 = 3$ with a remainder of $35 - (10 \times 3) = 35 - 30 = 5$.
- Mixed number: $3 \frac{5}{10}$.
- Simplify $\frac{5}{10}$: Both 5 and 10 are divisible by 5.
$$ \frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2} $$
- Final answer: $3 \frac{1}{2}$.

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Final Answers:

$$
\boxed{
\begin{array}{cccc}
4 \frac{3}{4} & 3 & 3 \frac{5}{7} & 1 \frac{1}{12} \\
5 \frac{1}{4} & 1 \frac{1}{4} & 1 \frac{1}{4} & 5 \frac{1}{3} \\
2 \frac{1}{12} & 1 & 1 \frac{8}{9} & 3 \frac{1}{3} \\
1 \frac{7}{10} & 5 \frac{4}{5} & 5 \frac{1}{3} & 3 \frac{3}{4} \\
5 \frac{1}{8} & 2 \frac{5}{12} & 5 \frac{3}{10} & 4 \frac{3}{4} \\
3 & 1 \frac{1}{6} & 3 & 4 \frac{1}{2} \\
3 \frac{7}{12} & 2 \frac{3}{4} & 1 \frac{1}{3} & 3 \frac{4}{5} \\
4 \frac{5}{8} & 1 \frac{2}{5} & 1 \frac{1}{2} & 3 \frac{1}{2}
\end{array}
}
$$