Answer :
- Find the greatest common divisor (GCD) of 45 and 12, which is 3.
- Divide both the numerator and the denominator by the GCD: $\frac{45 \div 3}{12 \div 3} = \frac{15}{4}$.
- Convert the improper fraction $\frac{15}{4}$ to a mixed number: $3 \frac{3}{4}$.
- The simplified fraction is $\boxed{3 \frac{3}{4}}$.
### Explanation
1. Problem Analysis
We are asked to simplify the fraction $\frac{45}{12}$. To do this, we need to find the greatest common divisor (GCD) of the numerator (45) and the denominator (12).
2. Finding the GCD
The greatest common divisor (GCD) is the largest number that divides both 45 and 12 without leaving a remainder. We can find the GCD using the Euclidean algorithm or by listing the factors of each number.
3. Determining the GCD
The factors of 45 are 1, 3, 5, 9, 15, and 45. The factors of 12 are 1, 2, 3, 4, 6, and 12. The largest number that appears in both lists is 3. Therefore, the GCD of 45 and 12 is 3.
4. Simplifying the Fraction
Now we divide both the numerator and the denominator by the GCD:$$\frac{45}{12} = \frac{45 \div 3}{12 \div 3} = \frac{15}{4}$$
5. Converting to a Mixed Number
The simplified fraction is $\frac{15}{4}$. We can also express this as a mixed number. To do this, we divide 15 by 4:$$15 \div 4 = 3 \text{ with a remainder of } 3$$This means that $\frac{15}{4} = 3 \frac{3}{4}$.
6. Final Answer
Therefore, $\frac{45}{12} = \frac{15}{4} = 3 \frac{3}{4}$.
### Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Simplifying fractions makes it easier to understand and work with these quantities. For example, if you have a recipe that calls for $\frac{45}{12}$ cups of flour, you can simplify this to $3 \frac{3}{4}$ cups, which is easier to measure.
- Divide both the numerator and the denominator by the GCD: $\frac{45 \div 3}{12 \div 3} = \frac{15}{4}$.
- Convert the improper fraction $\frac{15}{4}$ to a mixed number: $3 \frac{3}{4}$.
- The simplified fraction is $\boxed{3 \frac{3}{4}}$.
### Explanation
1. Problem Analysis
We are asked to simplify the fraction $\frac{45}{12}$. To do this, we need to find the greatest common divisor (GCD) of the numerator (45) and the denominator (12).
2. Finding the GCD
The greatest common divisor (GCD) is the largest number that divides both 45 and 12 without leaving a remainder. We can find the GCD using the Euclidean algorithm or by listing the factors of each number.
3. Determining the GCD
The factors of 45 are 1, 3, 5, 9, 15, and 45. The factors of 12 are 1, 2, 3, 4, 6, and 12. The largest number that appears in both lists is 3. Therefore, the GCD of 45 and 12 is 3.
4. Simplifying the Fraction
Now we divide both the numerator and the denominator by the GCD:$$\frac{45}{12} = \frac{45 \div 3}{12 \div 3} = \frac{15}{4}$$
5. Converting to a Mixed Number
The simplified fraction is $\frac{15}{4}$. We can also express this as a mixed number. To do this, we divide 15 by 4:$$15 \div 4 = 3 \text{ with a remainder of } 3$$This means that $\frac{15}{4} = 3 \frac{3}{4}$.
6. Final Answer
Therefore, $\frac{45}{12} = \frac{15}{4} = 3 \frac{3}{4}$.
### Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Simplifying fractions makes it easier to understand and work with these quantities. For example, if you have a recipe that calls for $\frac{45}{12}$ cups of flour, you can simplify this to $3 \frac{3}{4}$ cups, which is easier to measure.
