Is 15/32 the same as 5/8?
Understand the Problem
The question is asking whether the fraction 15/32 is equivalent to the fraction 5/8. To determine if two fractions are equal, we can cross-multiply and compare the results.
Answer
The fractions \( \frac{15}{32} \) and \( \frac{5}{8} \) are not equivalent.
Answer for screen readers
The fractions ( \frac{15}{32} ) and ( \frac{5}{8} ) are not equivalent.
Steps to Solve
- Set up the fractions for cross-multiplication
To determine if the two fractions ( \frac{15}{32} ) and ( \frac{5}{8} ) are equivalent, we can cross-multiply:
$$ 15 \cdot 8 \quad \text{and} \quad 5 \cdot 32 $$
- Calculate the products
Next, we will calculate the products from the cross-multiplication:
First, calculate ( 15 \cdot 8 ):
$$ 15 \cdot 8 = 120 $$
Then calculate ( 5 \cdot 32 ):
$$ 5 \cdot 32 = 160 $$
- Compare the results
Now, we compare the two results from the cross-multiplication:
We have ( 120 ) on one side and ( 160 ) on the other side.
Since ( 120 \neq 160 ), we conclude that the fractions are not equivalent.
The fractions ( \frac{15}{32} ) and ( \frac{5}{8} ) are not equivalent.
More Information
When comparing fractions, cross-multiplication is an effective method. It helps in discovering whether two fractions represent the same value. In this case, we found that the fractions differ significantly, indicating they are not the same quantity.
Tips
A common mistake is forgetting to carry out both multiplications correctly or misinterpreting the equality of the products. To avoid this, double-check your multiplication and ensure you are comparing the correct values.