$2.35 \cdot \frac{2}{3}=$
A. $\frac{7}{30}$
B. $\frac{7}{15}$
C. $\frac{27}{30}$
D. $\frac{47}{30}$
Answer (2)
Convert the decimal to a fraction: 2.35 = 100 235 .
Simplify the fraction: 100 235 = 20 47 .
Multiply by 3 2 : 20 47 ⋅ 3 2 = 60 94 .
Simplify the result: 60 94 = 30 47 .
The final answer is 30 47 .
Explanation
Convert decimal to fraction First, we need to convert the decimal 2.35 into a fraction. Since 2.35 has two decimal places, we can write it as a fraction with a denominator of 100: 2.35 = 100 235 .
Simplify the fraction Next, we simplify the fraction 100 235 by dividing both the numerator and the denominator by their greatest common divisor, which is 5: 100 235 = 100 ÷ 5 235 ÷ 5 = 20 47 .
Multiply the fractions Now, we multiply the simplified fraction 20 47 by 3 2 : 20 47 \t ⋅ 3 2 = 20 \t ⋅ 3 47 \t ⋅ 2 = 60 94 .
Simplify the result We simplify the resulting fraction 60 94 by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 60 94 = 60 ÷ 2 94 ÷ 2 = 30 47 .
Find the correct answer Finally, we compare the simplified fraction 30 47 with the given options. The correct answer is 30 47 .
Examples
Understanding fractions and decimals is crucial in everyday situations, such as calculating discounts while shopping. For instance, if an item costs 2.35 an d i so n s a l e f or \frac{2}{3}$ of the original price, you would calculate 2.35 ⋅ 3 2 to find the sale price. Converting decimals to fractions and performing multiplication helps you determine the final cost, ensuring you're getting the correct discount.
The answer to the problem 2.35 ⋅ 3 2 is 30 47 . This was determined by first converting 2.35 to a fraction, simplifying, multiplying by 3 2 , and then simplifying the result. The correct choice from the options provided is D : 30 47 .
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