4 divided by 1/5 = n
The correct answer and explanation is:
Answer:
4÷15=204 \div \frac{1}{5} = 20
So, n = 20
Explanation (300 words):
To solve the expression 4÷154 \div \frac{1}{5}, we need to understand what it means to divide by a fraction.
Step 1: Division by a Fraction
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is simply switching the numerator and the denominator. So, the reciprocal of 15\frac{1}{5} is 51\frac{5}{1}, which is just 5.
So, 4÷15=4×514 \div \frac{1}{5} = 4 \times \frac{5}{1}
Step 2: Multiply
4×51=4×51=201=204 \times \frac{5}{1} = \frac{4 \times 5}{1} = \frac{20}{1} = 20
Therefore, n=20n = 20.
Conceptual Understanding
Let’s think about what this really means. If you have 4 whole units and you want to find out how many one-fifths fit into 4, you’re essentially asking:
“How many 15\frac{1}{5}s are there in 4?”
Since each whole number contains 5 fifths:
- 1 has 5 fifths
- 2 has 10 fifths
- 3 has 15 fifths
- 4 has 20 fifths
So, there are 20 parts of size 15\frac{1}{5} in the number 4.
Real-Life Example
Imagine you have 4 whole pizzas and you cut each one into 5 equal slices. How many slices do you have in total?
- 4 pizzas × 5 slices each = 20 slices
Each slice represents 15\frac{1}{5} of a pizza. So, you have 20 slices of size 15\frac{1}{5}, confirming again that: 4÷15=204 \div \frac{1}{5} = 20
Summary:
Dividing by a fraction flips the fraction (takes its reciprocal) and turns the division into multiplication. It’s a common rule in arithmetic and a useful tool in math and real-life problem-solving.