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Sagot :
Let's simplify each of the given fractions step-by-step and solve the equation where possible:
### 1. Simplify and Divide:
#### Given:
[tex]\[ \frac{10}{45} \div \frac{5}{5} = \frac{2}{9} \][/tex]
#### Solution:
1. Simplify the fraction [tex]\( \frac{10}{45} \)[/tex].
[tex]\[ \frac{10}{45} = \frac{2}{9} \][/tex]
(by dividing the numerator and denominator by their greatest common divisor, which is 5).
2. Recognize that [tex]\( \frac{5}{5} = 1 \)[/tex].
3. Divide [tex]\( \frac{2}{9} \)[/tex] by 1.
[tex]\[ \frac{2}{9} \div 1 = \frac{2}{9} \][/tex]
So the solution confirms:
[tex]\[ \frac{2}{9} = \frac{2}{9} \][/tex]
### 2. This fraction can’t be solved with the given data:
[tex]\[ \frac{316}{400} \][/tex]
### 3. Simplify and Divide:
#### Given:
[tex]\[ \frac{12}{28} \div \frac{6}{14} = \frac{2}{2} \][/tex]
#### Solution:
1. Simplify the fraction [tex]\( \frac{12}{28} \)[/tex].
[tex]\[ \frac{12}{28} = \frac{3}{7} \][/tex]
(by dividing the numerator and denominator by their greatest common divisor, which is 4).
2. Simplify the fraction [tex]\( \frac{6}{14} \)[/tex].
[tex]\[ \frac{6}{14} = \frac{3}{7} \][/tex]
(by dividing the numerator and denominator by their greatest common divisor, which is 2).
3. Divide [tex]\( \frac{3}{7} \)[/tex] by [tex]\( \frac{3}{7} \)[/tex].
[tex]\[ \frac{3}{7} \div \frac{3}{7} = 1 \][/tex]
4. Recognize that [tex]\( \frac{2}{2} = 1 \)[/tex].
So the solution confirms:
[tex]\[ 1 = 1 \][/tex]
### 4. This fraction can’t be solved with the given data:
[tex]\[ \frac{150}{500} \][/tex]
### 5. Simplify and Divide:
#### Given:
[tex]\[ \frac{18}{100} \div \frac{9}{50} = \frac{2}{2} \][/tex]
#### Solution:
1. Simplify the fraction [tex]\( \frac{18}{100} \)[/tex].
[tex]\[ \frac{18}{100} = \frac{9}{50} \][/tex]
(by dividing the numerator and denominator by their greatest common divisor, which is 2).
2. Recognize that the simplified fraction [tex]\( \frac{18}{100} \)[/tex] is [tex]\( \frac{9}{50} \)[/tex].
3. Divide [tex]\( \frac{9}{50} \)[/tex] by [tex]\( \frac{9}{50} \)[/tex].
[tex]\[ \frac{9}{50} \div \frac{9}{50} = 1 \][/tex]
4. Recognize that [tex]\( \frac{2}{2} = 1 \)[/tex].
So the solution confirms:
[tex]\[ 1 = 1 \][/tex]
### 6. These fractions can’t be solved with the given data:
[tex]\[ \frac{35}{75} \][/tex]
[tex]\[ \frac{2}{6} \][/tex]
[tex]\[ \frac{15}{45} \][/tex]
[tex]\[ \frac{21}{81} \][/tex]
[tex]\[ \frac{146}{254} \][/tex]
Thus, we can only solve the specified parts which confirm the results:
[tex]\[ 1 \cdot \frac{10}{45} \div \frac{5}{5} = \frac{2}{9} \][/tex]
[tex]\[ 2 \cdot \frac{12}{28} \div \frac{6}{14} = \frac{2}{2} \][/tex]
[tex]\[ 3 \cdot \frac{18}{100} \div \frac{9}{50} = \frac{2}{2} \][/tex]
The followings are the correct and solved parts of the problem:
[tex]\[ \begin{aligned} &1. &&0.22 = 0.2222222222222222 \\ &2. &&1 = 1 \\ &3. &&1 = 1 \\ \end{aligned} \][/tex]
### 1. Simplify and Divide:
#### Given:
[tex]\[ \frac{10}{45} \div \frac{5}{5} = \frac{2}{9} \][/tex]
#### Solution:
1. Simplify the fraction [tex]\( \frac{10}{45} \)[/tex].
[tex]\[ \frac{10}{45} = \frac{2}{9} \][/tex]
(by dividing the numerator and denominator by their greatest common divisor, which is 5).
2. Recognize that [tex]\( \frac{5}{5} = 1 \)[/tex].
3. Divide [tex]\( \frac{2}{9} \)[/tex] by 1.
[tex]\[ \frac{2}{9} \div 1 = \frac{2}{9} \][/tex]
So the solution confirms:
[tex]\[ \frac{2}{9} = \frac{2}{9} \][/tex]
### 2. This fraction can’t be solved with the given data:
[tex]\[ \frac{316}{400} \][/tex]
### 3. Simplify and Divide:
#### Given:
[tex]\[ \frac{12}{28} \div \frac{6}{14} = \frac{2}{2} \][/tex]
#### Solution:
1. Simplify the fraction [tex]\( \frac{12}{28} \)[/tex].
[tex]\[ \frac{12}{28} = \frac{3}{7} \][/tex]
(by dividing the numerator and denominator by their greatest common divisor, which is 4).
2. Simplify the fraction [tex]\( \frac{6}{14} \)[/tex].
[tex]\[ \frac{6}{14} = \frac{3}{7} \][/tex]
(by dividing the numerator and denominator by their greatest common divisor, which is 2).
3. Divide [tex]\( \frac{3}{7} \)[/tex] by [tex]\( \frac{3}{7} \)[/tex].
[tex]\[ \frac{3}{7} \div \frac{3}{7} = 1 \][/tex]
4. Recognize that [tex]\( \frac{2}{2} = 1 \)[/tex].
So the solution confirms:
[tex]\[ 1 = 1 \][/tex]
### 4. This fraction can’t be solved with the given data:
[tex]\[ \frac{150}{500} \][/tex]
### 5. Simplify and Divide:
#### Given:
[tex]\[ \frac{18}{100} \div \frac{9}{50} = \frac{2}{2} \][/tex]
#### Solution:
1. Simplify the fraction [tex]\( \frac{18}{100} \)[/tex].
[tex]\[ \frac{18}{100} = \frac{9}{50} \][/tex]
(by dividing the numerator and denominator by their greatest common divisor, which is 2).
2. Recognize that the simplified fraction [tex]\( \frac{18}{100} \)[/tex] is [tex]\( \frac{9}{50} \)[/tex].
3. Divide [tex]\( \frac{9}{50} \)[/tex] by [tex]\( \frac{9}{50} \)[/tex].
[tex]\[ \frac{9}{50} \div \frac{9}{50} = 1 \][/tex]
4. Recognize that [tex]\( \frac{2}{2} = 1 \)[/tex].
So the solution confirms:
[tex]\[ 1 = 1 \][/tex]
### 6. These fractions can’t be solved with the given data:
[tex]\[ \frac{35}{75} \][/tex]
[tex]\[ \frac{2}{6} \][/tex]
[tex]\[ \frac{15}{45} \][/tex]
[tex]\[ \frac{21}{81} \][/tex]
[tex]\[ \frac{146}{254} \][/tex]
Thus, we can only solve the specified parts which confirm the results:
[tex]\[ 1 \cdot \frac{10}{45} \div \frac{5}{5} = \frac{2}{9} \][/tex]
[tex]\[ 2 \cdot \frac{12}{28} \div \frac{6}{14} = \frac{2}{2} \][/tex]
[tex]\[ 3 \cdot \frac{18}{100} \div \frac{9}{50} = \frac{2}{2} \][/tex]
The followings are the correct and solved parts of the problem:
[tex]\[ \begin{aligned} &1. &&0.22 = 0.2222222222222222 \\ &2. &&1 = 1 \\ &3. &&1 = 1 \\ \end{aligned} \][/tex]
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