Fill in the blank to make the fractions equivalent.
Understand the Problem
The question is asking us to find a number that will make the fraction 2/3 equivalent to the fraction represented by the blank over 12. To do this, we will use the concept of equivalent fractions, where we can set up a proportion between the two fractions.
Answer
The value for the blank is \( x = 8 \).
Answer for screen readers
The number that makes the fractions equivalent is ( x = 8 ).
Steps to Solve
- Set up the proportion
We start by setting up the proportion between the two fractions:
$$ \frac{2}{3} = \frac{x}{12} $$
where (x) is the number we want to find.
- Cross-multiply
Next, we cross-multiply to eliminate the fraction:
$$ 2 \cdot 12 = 3 \cdot x $$
This simplifies to:
$$ 24 = 3x $$
- Solve for (x)
Now, we solve for (x) by dividing both sides by 3:
$$ x = \frac{24}{3} $$
This simplifies to:
$$ x = 8 $$
The number that makes the fractions equivalent is ( x = 8 ).
More Information
The concept of equivalent fractions is based on the idea that if two fractions are equal, then cross-multiplying will yield the same result.
Tips
- Not cross-multiplying correctly: Ensure you multiply diagonally across the equal sign.
- Forgetting to simplify: Always simplify your final answer if possible.
AI-generated content may contain errors. Please verify critical information
