What the equivalent rational number for -15/36 denominator 12 numerator -75
The Correct Answer and Explanation is:
To find the equivalent rational number for −1536-\frac{15}{36}−3615 with the denominator as 12 and numerator as -75, we need to follow these steps:
Step 1: Simplify the Original Fraction −1536-\frac{15}{36}−3615
Start by simplifying the fraction −1536-\frac{15}{36}−3615. Both 15 and 36 have common factors that can be divided to simplify the fraction. The greatest common divisor (GCD) of 15 and 36 is 3.
Now, divide both the numerator and the denominator by 3:−1536=−15÷336÷3=−512\frac{-15}{36} = \frac{-15 \div 3}{36 \div 3} = \frac{-5}{12}36−15=36÷3−15÷3=12−5
So, the simplified form of −1536-\frac{15}{36}−3615 is −512-\frac{5}{12}−125.
Step 2: Compare to the New Fraction −7512\frac{-75}{12}12−75
Now, we are asked to express the same fraction with a denominator of 12 and a numerator of -75. We need to check if the simplified form of −512-\frac{5}{12}−125 can match −7512\frac{-75}{12}12−75.
Since both fractions have the same denominator (12), the key step here is to check if the numerators are equivalent. Let’s compare the numerators:−5 and −75-5 \text{ and } -75−5 and −75
To get −75-75−75 from −5-5−5, we multiply the numerator −5-5−5 by 15:−5×15=−75-5 \times 15 = -75−5×15=−75
Thus, −512-\frac{5}{12}−125 is equivalent to −7512\frac{-75}{12}12−75.
Step 3: Conclusion
Therefore, the fraction −1536-\frac{15}{36}−3615 simplifies to −512-\frac{5}{12}−125, which is equivalent to −7512\frac{-75}{12}12−75. Both expressions represent the same rational number.
In summary, to express −1536-\frac{15}{36}−3615 with a numerator of −75-75−75 and denominator 12, the equivalent rational number is −7512\frac{-75}{12}12−75, which was derived by scaling the simplified form of −512-\frac{5}{12}−125 by a factor of 15.
