What expression has a value of 7/12
The Correct Answer and Explanation is:
To find an expression that has a value of ( \frac{7}{12} ), consider the following expression:
[
\frac{7}{12} = \frac{7 \times 1}{12 \times 1}
]
This expression is already in its simplest form, as the numerator (7) and the denominator (12) have no common factors other than 1.
Explanation:
The fraction ( \frac{7}{12} ) represents a ratio or division of two numbers. It indicates that if you have 12 equal parts, 7 of them are considered. Fractions can be simplified if the numerator and denominator have a common factor, but in this case, the greatest common divisor (GCD) of 7 and 12 is 1, meaning it’s already in its lowest terms.
Understanding the Components:
- Numerator (7): This is the top part of the fraction and tells how many parts you have.
- Denominator (12): This is the bottom part and represents the total number of equal parts.
Operations Leading to ( \frac{7}{12} ):
- Addition of Fractions: One way to get this value is through adding smaller fractions that result in ( \frac{7}{12} ). For instance:
[
\frac{1}{12} + \frac{6}{12} = \frac{7}{12}
]
Here, the fractions are combined by adding their numerators while keeping the denominator the same. - Multiplication of a Number by a Fraction: Another approach is multiplying a number by a fraction, which gives:
[
\frac{7}{12} \times 1 = \frac{7}{12}
]
Use in Real-Life Situations:
Fractions like ( \frac{7}{12} ) often appear in real-life scenarios, such as dividing objects into parts. For instance, if a pizza is cut into 12 equal slices and someone eats 7 slices, they have consumed ( \frac{7}{12} ) of the pizza.
In conclusion, ( \frac{7}{12} ) is a fundamental expression in mathematics, representing a ratio that can be used in various contexts like addition or practical division problems.