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Answer :
- Find equivalent fractions by multiplying the numerator and denominator by the same number.
- For $\frac{1}{2}$, multiply by 2 to get $\frac{2}{4}$, by 3 to get $\frac{3}{6}$, and convert to decimal to get $0.5$.
- For $\frac{1}{25}$, multiply by 2 to get $\frac{2}{50}$, by 4 to get $\frac{4}{100}$, and convert to decimal to get $0.04$.
- The equivalent fractions are: $\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = 0.5$ and $\frac{1}{25} = \frac{2}{50} = \frac{4}{100} = 0.04$.
### Explanation
1. Problem Analysis
We need to find three equivalent fractions for both $\frac{1}{2}$ and $\frac{1}{25}$, with one of them being a decimal if possible. Equivalent fractions represent the same value but have different numerators and denominators. We can find equivalent fractions by multiplying or dividing both the numerator and denominator by the same non-zero number.
2. Finding Equivalent Fraction for 1/2
For the fraction $\frac{1}{2}$, we can multiply the numerator and the denominator by 2 to get $\frac{1 \times 2}{2 \times 2} = \frac{2}{4}$.
3. Finding Another Equivalent Fraction for 1/2
Next, we can multiply the numerator and the denominator of $\frac{1}{2}$ by 3 to get $\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.
4. Finding Decimal Equivalent for 1/2
To find a decimal equivalent, we can divide the numerator by the denominator: $1 \div 2 = 0.5$. We can also express this as a fraction: $\frac{5}{10}$.
5. Equivalent Fractions for 1/2
So, three equivalent fractions for $\frac{1}{2}$ are $\frac{2}{4}$, $\frac{3}{6}$, and $0.5$.
6. Finding Equivalent Fraction for 1/25
Now, let's find three equivalent fractions for $\frac{1}{25}$. We can multiply the numerator and the denominator by 2 to get $\frac{1 \times 2}{25 \times 2} = \frac{2}{50}$.
7. Finding Another Equivalent Fraction for 1/25
Next, we can multiply the numerator and the denominator of $\frac{1}{25}$ by 4 to get $\frac{1 \times 4}{25 \times 4} = \frac{4}{100}$.
8. Finding Decimal Equivalent for 1/25
To find a decimal equivalent, we can divide the numerator by the denominator: $1 \div 25 = 0.04$.
9. Equivalent Fractions for 1/25
So, three equivalent fractions for $\frac{1}{25}$ are $\frac{2}{50}$, $\frac{4}{100}$, and $0.04$.
10. Final Answer
Therefore, the equivalent fractions are:
$\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = 0.5$
$\frac{1}{25} = \frac{2}{50} = \frac{4}{100} = 0.04$
### Examples
Understanding equivalent fractions is useful in everyday situations, such as when you're cooking and need to adjust recipe quantities. For instance, if a recipe calls for $\frac{1}{2}$ cup of flour but you want to double the recipe, you need to know that $\frac{1}{2}$ is equivalent to $\frac{2}{4}$ or $\frac{3}{6}$ to measure the correct amount. Similarly, when dealing with money, knowing that $\frac{1}{25}$ of a dollar is the same as 4 cents ($0.04) helps in calculating discounts or understanding proportions.
- For $\frac{1}{2}$, multiply by 2 to get $\frac{2}{4}$, by 3 to get $\frac{3}{6}$, and convert to decimal to get $0.5$.
- For $\frac{1}{25}$, multiply by 2 to get $\frac{2}{50}$, by 4 to get $\frac{4}{100}$, and convert to decimal to get $0.04$.
- The equivalent fractions are: $\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = 0.5$ and $\frac{1}{25} = \frac{2}{50} = \frac{4}{100} = 0.04$.
### Explanation
1. Problem Analysis
We need to find three equivalent fractions for both $\frac{1}{2}$ and $\frac{1}{25}$, with one of them being a decimal if possible. Equivalent fractions represent the same value but have different numerators and denominators. We can find equivalent fractions by multiplying or dividing both the numerator and denominator by the same non-zero number.
2. Finding Equivalent Fraction for 1/2
For the fraction $\frac{1}{2}$, we can multiply the numerator and the denominator by 2 to get $\frac{1 \times 2}{2 \times 2} = \frac{2}{4}$.
3. Finding Another Equivalent Fraction for 1/2
Next, we can multiply the numerator and the denominator of $\frac{1}{2}$ by 3 to get $\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.
4. Finding Decimal Equivalent for 1/2
To find a decimal equivalent, we can divide the numerator by the denominator: $1 \div 2 = 0.5$. We can also express this as a fraction: $\frac{5}{10}$.
5. Equivalent Fractions for 1/2
So, three equivalent fractions for $\frac{1}{2}$ are $\frac{2}{4}$, $\frac{3}{6}$, and $0.5$.
6. Finding Equivalent Fraction for 1/25
Now, let's find three equivalent fractions for $\frac{1}{25}$. We can multiply the numerator and the denominator by 2 to get $\frac{1 \times 2}{25 \times 2} = \frac{2}{50}$.
7. Finding Another Equivalent Fraction for 1/25
Next, we can multiply the numerator and the denominator of $\frac{1}{25}$ by 4 to get $\frac{1 \times 4}{25 \times 4} = \frac{4}{100}$.
8. Finding Decimal Equivalent for 1/25
To find a decimal equivalent, we can divide the numerator by the denominator: $1 \div 25 = 0.04$.
9. Equivalent Fractions for 1/25
So, three equivalent fractions for $\frac{1}{25}$ are $\frac{2}{50}$, $\frac{4}{100}$, and $0.04$.
10. Final Answer
Therefore, the equivalent fractions are:
$\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = 0.5$
$\frac{1}{25} = \frac{2}{50} = \frac{4}{100} = 0.04$
### Examples
Understanding equivalent fractions is useful in everyday situations, such as when you're cooking and need to adjust recipe quantities. For instance, if a recipe calls for $\frac{1}{2}$ cup of flour but you want to double the recipe, you need to know that $\frac{1}{2}$ is equivalent to $\frac{2}{4}$ or $\frac{3}{6}$ to measure the correct amount. Similarly, when dealing with money, knowing that $\frac{1}{25}$ of a dollar is the same as 4 cents ($0.04) helps in calculating discounts or understanding proportions.
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