Type the missing number to complete the proportion. 20 newspapers in 4 piles = 10 newspapers in ___ piles.
Understand the Problem
The question asks for the missing number in a proportion where 20 newspapers are in 4 piles and we need to find out how many piles correspond to 10 newspapers. This involves setting up a ratio and solving for the unknown.
Answer
The missing number is $2$.
Answer for screen readers
The missing number is $2$.
Steps to Solve
- Set up the proportion
We set up the proportion based on the information given. We know that 20 newspapers correspond to 4 piles, and we need to find how many piles (let's call it $x$) correspond to 10 newspapers.
The proportion can be expressed as: $$ \frac{20 \text{ newspapers}}{4 \text{ piles}} = \frac{10 \text{ newspapers}}{x \text{ piles}} $$
- Cross-multiply the proportion
To solve for $x$, we cross-multiply: $$ 20 \cdot x = 10 \cdot 4 $$
This simplifies to: $$ 20x = 40 $$
- Solve for the unknown
Now, we solve for $x$ by dividing both sides by 20: $$ x = \frac{40}{20} $$
- Calculate the value of $x$
Calculating the value gives: $$ x = 2 $$
Thus, the number of piles for 10 newspapers is 2.
The missing number is $2$.
More Information
In this problem, we used a proportion to relate the number of newspapers to the number of piles. Proportions are useful in many real-world situations where two ratios are equal.
Tips
- Forgetting to set up the proportion correctly can lead to an incorrect answer. Always ensure the corresponding quantities are aligned properly.
- Not simplifying the equation when solving can lead to errors; always perform arithmetic operations carefully.
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