Is 22/32 the same as 3/4?
Understand the Problem
The question is asking whether the fraction 22/32 is equivalent to 3/4. To determine this, we will compare the two fractions by simplifying 22/32 and checking if it equals 3/4.
Answer
No, $ \frac{22}{32} \neq \frac{3}{4} $.
Answer for screen readers
No, the fraction $ \frac{22}{32} $ is not equivalent to $ \frac{3}{4} $.
Steps to Solve
- Simplifying the fraction 22/32
To simplify the fraction $ \frac{22}{32} $, we need to find the greatest common divisor (GCD) of the numerator (22) and the denominator (32). The GCD of 22 and 32 is 2.
Now, we divide both the numerator and the denominator by their GCD:
$$ \frac{22 \div 2}{32 \div 2} = \frac{11}{16} $$
- Checking equivalence with 3/4
Now, we need to check if $ \frac{11}{16} $ is equal to $ \frac{3}{4} $.
To compare these fractions, we can cross-multiply:
$$ 11 \times 4 \quad \text{and} \quad 3 \times 16 $$
Calculating:
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$ 11 \times 4 = 44 $
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$ 3 \times 16 = 48 $
- Comparing the results
Now we compare:
Since $ 44 \neq 48 $, the two fractions are not equal.
Thus, $ \frac{22}{32} $ is not equivalent to $ \frac{3}{4} $.
No, the fraction $ \frac{22}{32} $ is not equivalent to $ \frac{3}{4} $.
More Information
When comparing fractions, simplifying them and using cross-multiplication is a reliable method. In this case, simplifying $ \frac{22}{32} $ showed that it reduced to $ \frac{11}{16} $, which is not equivalent to $ \frac{3}{4} $.
Tips
- A common mistake is failing to simplify the fraction correctly. Always ensure to find the GCD accurately before simplifying.
- Another mistake is forgetting to compare fractions using cross-multiplication properly. Ensure you calculate both products accurately.
