$2.35 \cdot \frac{2}{3} = \newline \frac{7}{30} \newline \frac{7}{15} \newline \frac{27}{30}
Answer (1)
Convert the decimal to a fraction: 2.35 = 20 47 .
Multiply the fraction by 3 2 : 20 47 × 3 2 = 20 × 3 47 × 2 .
Simplify the resulting fraction: 60 94 = 30 47 .
The final answer is 30 47 .
Explanation
Understanding the Problem We are asked to evaluate the expression 2.35 × 3 2 and choose the correct answer from the given options.
Converting Decimal to Fraction First, let's convert the decimal 2.35 to a fraction. We have 2.35 = 100 235 . We can simplify this fraction by dividing both the numerator and the denominator by 5, which gives us 100 235 = 20 47 .
Multiplying Fractions Now, we multiply the resulting fraction by 3 2 : 20 47 × 3 2 = 20 × 3 47 × 2 = 60 94 .
Simplifying the Fraction We can simplify the fraction 60 94 by dividing both the numerator and the denominator by 2, which gives us 60 94 = 30 47 .
Comparing to Options Now, we compare the simplified fraction 30 47 to the given options: 30 7 , 15 7 , 30 27 , 47. We can see that 30 47 is the correct answer.
Final Answer Therefore, 2.35 × 3 2 = 30 47 .
Examples
Understanding fractions and decimals is crucial in everyday situations, such as calculating discounts while shopping. For instance, if an item costs 2.35 an d i so n s a l e f or \frac{2}{3}$ of the original price, you would calculate 2.35 × 3 2 to find the sale price. This calculation helps you determine the actual cost you'll pay, enabling you to make informed purchasing decisions and manage your budget effectively.
