25 divided by 1/5 = ?
125
Understanding Division by Fractions
The question asks us to calculate the value of 25 divided by 1/5. Dividing by a fraction is equivalent to multiplying by the reciprocal of that fraction.
What is a Reciprocal?
The reciprocal of a fraction is found by flipping the numerator and the denominator. For example, the reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$. The reciprocal of a whole number can be found by considering it as a fraction with a denominator of 1. For instance, the number 5 can be written as $\frac{5}{1}$, and its reciprocal is $\frac{1}{5}$. Similarly, the number 1/5 is a fraction, and its reciprocal is found by swapping the numerator (1) and the denominator (5), which gives us 5/1, or simply 5.
Calculating 25 Divided by 1/5
We need to solve the expression:
$\text{25} \div \frac{1}{5}$
According to the rule of dividing by fractions, we change the division operation ($\div$) to multiplication ($\times$) and use the reciprocal of the divisor (1/5). The reciprocal of 1/5 is 5.
So, the expression becomes:
$\text{25} \times 5$
Now, we simply multiply 25 by 5:
$25 \times 5 = 125$
Therefore, 25 divided by 1/5 is equal to 125.
Summary of the Calculation
- Identify the numbers involved: 25 and 1/5.
- Identify the operation: Division ($\div$).
- Recall the rule for dividing by a fraction: Multiply by the reciprocal of the divisor.
- Find the reciprocal of the divisor (1/5): It is 5.
- Rewrite the problem as multiplication: $25 \times 5$.
- Perform the multiplication: $25 \times 5 = 125$.
| Original Problem | Operation Change | Divisor Reciprocal | Equivalent Multiplication | Result |
|---|---|---|---|---|
| $25 \div \frac{1}{5}$ | Division to Multiplication | Reciprocal of $\frac{1}{5}$ is 5 | $25 \times 5$ | 125 |
Revision Table: Dividing by Fractions
| Concept | Explanation | Example |
|---|---|---|
| Dividing by a fraction | Equivalent to multiplying by the reciprocal of the fraction. | $a \div \frac{b}{c} = a \times \frac{c}{b}$ |
| Reciprocal of a fraction | Flip the numerator and denominator ($\frac{b}{c} \to \frac{c}{b}$). | Reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. |
| Reciprocal of a whole number | Write the number as $\frac{\text{number}}{1}$ and flip ($\frac{n}{1} \to \frac{1}{n}$). | Reciprocal of 7 is $\frac{1}{7}$. |
Additional Information: Inverse Operations
Division and multiplication are inverse operations. This means that one operation can 'undo' the other. The rule for dividing by a fraction using its reciprocal stems from this relationship. Multiplying by the reciprocal of a number is the same as dividing by that number. For example, multiplying by $\frac{1}{5}$ is the same as dividing by 5. Conversely, dividing by $\frac{1}{5}$ is the same as multiplying by 5 (the reciprocal).
Understanding reciprocals and inverse operations is fundamental for solving problems involving fractions and division.
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Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
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d.
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iv.
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