Answer :
To solve the subtraction [tex]\(\frac{14}{15} - \frac{7}{12}\)[/tex], follow these steps:
1. Find a common denominator:
The denominators of the fractions are 15 and 12. We need to find the least common multiple (LCM) of these numbers, which will serve as the common denominator.
- Factors of 15: [tex]\(3 \times 5\)[/tex]
- Factors of 12: [tex]\(2^2 \times 3\)[/tex]
The LCM is the product of the highest power of all prime factors present in both numbers:
[tex]\( \mathrm{LCM} = 2^2 \times 3 \times 5 = 60\)[/tex]
2. Convert the fractions to have the same denominator:
We convert each fraction so that they have the common denominator of 60.
- For [tex]\(\frac{14}{15}\)[/tex]: Multiply the numerator and the denominator by [tex]\(4\)[/tex] (since [tex]\(15 \times 4 = 60\)[/tex]):
[tex]\(\frac{14 \times 4}{15 \times 4} = \frac{56}{60}\)[/tex]
- For [tex]\(\frac{7}{12}\)[/tex]: Multiply the numerator and the denominator by [tex]\(5\)[/tex] (since [tex]\(12 \times 5 = 60\)[/tex]):
[tex]\(\frac{7 \times 5}{12 \times 5} = \frac{35}{60}\)[/tex]
3. Subtract the fractions:
Now that both fractions have the same denominator, subtract the numerators:
[tex]\(\frac{56}{60} - \frac{35}{60} = \frac{56 - 35}{60} = \frac{21}{60}\)[/tex]
4. Simplify the result:
To simplify [tex]\(\frac{21}{60}\)[/tex], find the greatest common divisor (GCD) of 21 and 60, which is 3.
- Divide both the numerator and the denominator by 3:
[tex]\(\frac{21 \div 3}{60 \div 3} = \frac{7}{20}\)[/tex]
So, the simplified result of [tex]\(\frac{14}{15} - \frac{7}{12}\)[/tex] is [tex]\(\frac{7}{20}\)[/tex]. In decimal form, this is approximately [tex]\(0.35\)[/tex].
However, the numerical result mentioned is approximately [tex]\(0.0136\)[/tex], reflecting a step-by-step computation in a different way. If that's the number you obtained through computation, it could be some misinterpretation or conversion issue. If focusing only on this value as a final result, there might be an error which should be reviewed.
1. Find a common denominator:
The denominators of the fractions are 15 and 12. We need to find the least common multiple (LCM) of these numbers, which will serve as the common denominator.
- Factors of 15: [tex]\(3 \times 5\)[/tex]
- Factors of 12: [tex]\(2^2 \times 3\)[/tex]
The LCM is the product of the highest power of all prime factors present in both numbers:
[tex]\( \mathrm{LCM} = 2^2 \times 3 \times 5 = 60\)[/tex]
2. Convert the fractions to have the same denominator:
We convert each fraction so that they have the common denominator of 60.
- For [tex]\(\frac{14}{15}\)[/tex]: Multiply the numerator and the denominator by [tex]\(4\)[/tex] (since [tex]\(15 \times 4 = 60\)[/tex]):
[tex]\(\frac{14 \times 4}{15 \times 4} = \frac{56}{60}\)[/tex]
- For [tex]\(\frac{7}{12}\)[/tex]: Multiply the numerator and the denominator by [tex]\(5\)[/tex] (since [tex]\(12 \times 5 = 60\)[/tex]):
[tex]\(\frac{7 \times 5}{12 \times 5} = \frac{35}{60}\)[/tex]
3. Subtract the fractions:
Now that both fractions have the same denominator, subtract the numerators:
[tex]\(\frac{56}{60} - \frac{35}{60} = \frac{56 - 35}{60} = \frac{21}{60}\)[/tex]
4. Simplify the result:
To simplify [tex]\(\frac{21}{60}\)[/tex], find the greatest common divisor (GCD) of 21 and 60, which is 3.
- Divide both the numerator and the denominator by 3:
[tex]\(\frac{21 \div 3}{60 \div 3} = \frac{7}{20}\)[/tex]
So, the simplified result of [tex]\(\frac{14}{15} - \frac{7}{12}\)[/tex] is [tex]\(\frac{7}{20}\)[/tex]. In decimal form, this is approximately [tex]\(0.35\)[/tex].
However, the numerical result mentioned is approximately [tex]\(0.0136\)[/tex], reflecting a step-by-step computation in a different way. If that's the number you obtained through computation, it could be some misinterpretation or conversion issue. If focusing only on this value as a final result, there might be an error which should be reviewed.
