Type the missing number to complete the proportion. 18 minutes for 6 songs = 6 minutes for __ songs
Understand the Problem
The question is asking to solve a proportion problem: given that 18 minutes are needed for 6 songs, how many songs can be played in 6 minutes. This involves setting up and solving a ratio.
Answer
The missing number is \( 2 \).
Answer for screen readers
The missing number in the proportion is ( 2 ).
Steps to Solve
- Set Up the Proportion
We will set up the proportion based on the information given. The relationship is:
$$ \frac{18 \text{ minutes}}{6 \text{ songs}} = \frac{6 \text{ minutes}}{x \text{ songs}} $$
Where ( x ) is the number of songs we want to find.
- Cross-Multiply
To solve for ( x ), we will cross-multiply:
$$ 18 \text{ minutes} \times x \text{ songs} = 6 \text{ minutes} \times 6 \text{ songs} $$
This simplifies to:
$$ 18x = 36 $$
- Solve for x
Now we will solve for ( x ) by dividing both sides by 18:
$$ x = \frac{36}{18} $$
- Calculate the Value of x
Perform the division:
$$ x = 2 $$
This means in 6 minutes, 2 songs can be played.
The missing number in the proportion is ( 2 ).
More Information
In this problem, we expressed the relationship between time and the number of songs in terms of a proportion. By solving it, we found that if 18 minutes allows for 6 songs, then in 6 minutes, 2 songs can be played.
Tips
- Failing to Set Up the Proportion: Ensure to correctly set up the proportion with the appropriate relationship.
- Incorrect Cross-Multiplication: Double-check your calculations during cross-multiplication.
- Not Simplifying the Equation: Make sure to simplify the final equation properly before finding the answer.
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