Complete the sentence to explain how to use mental math to express 12/25 as a percent.
Multiply the numerator and the denominator by______ to get ———
100
which is the same as _%
The Correct answer and Explanation is :
To express ( \frac{12}{25} ) as a percent using mental math, we can complete the sentence as follows:
Multiply the numerator and the denominator by 4 to get 48 over 100, which is the same as 48%.
Explanation
To convert a fraction to a percentage, the goal is to express it as a fraction out of 100. This can be done using mental math, which simplifies the process. Here’s a step-by-step breakdown of how to convert ( \frac{12}{25} ) to a percentage.
- Understanding the Fraction: The fraction ( \frac{12}{25} ) means 12 parts out of a total of 25 parts. To convert it to a percentage, we need to find an equivalent fraction with a denominator of 100.
- Finding the Multiplier: To change the denominator from 25 to 100, we determine what number we need to multiply 25 by to reach 100. This can be calculated by dividing 100 by 25:
[
100 \div 25 = 4
]
Therefore, we multiply both the numerator and the denominator by 4. - Performing the Multiplication:
- Multiply the numerator: ( 12 \times 4 = 48 )
- Multiply the denominator: ( 25 \times 4 = 100 ) This gives us the new fraction:
[
\frac{48}{100}
]
- Interpreting the Result: The fraction ( \frac{48}{100} ) indicates that 48 out of 100 parts are represented, which directly translates to the percentage. Therefore, we can say that:
[
\frac{12}{25} = 48\%
] - Using Mental Math: This process demonstrates how effective mental math can be. Instead of using a calculator or more complicated methods, we utilized basic multiplication and understanding of fractions to quickly arrive at the answer.
In summary, by multiplying both the numerator and denominator of ( \frac{12}{25} ) by 4, we efficiently transformed the fraction into its percentage equivalent, which is 48%. This mental math technique is particularly useful for quickly converting fractions to percentages in everyday calculations.