What ratios are equivalent to 14/12
The Correct Answer and Explanation is:
To find ratios equivalent to ( \frac{14}{12} ), we can simplify the fraction and then generate equivalent ratios by multiplying or dividing both the numerator and the denominator by the same number.
Simplifying ( \frac{14}{12} )
First, we simplify ( \frac{14}{12} ):
- Find the Greatest Common Divisor (GCD): The GCD of 14 and 12 is 2.
- Divide both numerator and denominator by the GCD:
[
\frac{14 \div 2}{12 \div 2} = \frac{7}{6}
]
Thus, ( \frac{14}{12} ) simplifies to ( \frac{7}{6} ).
Finding Equivalent Ratios
Now that we have ( \frac{7}{6} ), we can find equivalent ratios by multiplying both the numerator and the denominator by any non-zero integer.
- Multiply by 1:
[
\frac{7 \times 1}{6 \times 1} = \frac{7}{6}
] - Multiply by 2:
[
\frac{7 \times 2}{6 \times 2} = \frac{14}{12}
] - Multiply by 3:
[
\frac{7 \times 3}{6 \times 3} = \frac{21}{18}
] - Multiply by 4:
[
\frac{7 \times 4}{6 \times 4} = \frac{28}{24}
] - Multiply by 5:
[
\frac{7 \times 5}{6 \times 5} = \frac{35}{30}
]
Summary of Equivalent Ratios
From the calculations above, we find that the ratios equivalent to ( \frac{14}{12} ) include:
- ( \frac{7}{6} )
- ( \frac{21}{18} )
- ( \frac{28}{24} )
- ( \frac{35}{30} )
These ratios all represent the same proportion, meaning they express the same relationship between two quantities. Equivalent ratios are essential in various mathematical applications, such as scaling recipes, converting units, and solving real-world problems involving proportions. Understanding how to find and use equivalent ratios enhances problem-solving skills in both academic and everyday contexts.