An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
A current of 15.0 A flowing for 30 seconds results in a total charge of 450 C. Dividing this charge by the charge of a single electron (approximately 1.6 × 1 0 − 19 C ) reveals that about 2.81 × 1 0 21 electrons flow through the device. Thus, approximately 2.81 × 1 0 21 electrons are involved.
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Multiply the numerators and denominators: 4 11 × 7 6 = 4 × 7 11 × 6 .
Simplify the numerator and denominator: 28 66 .
Find the greatest common divisor (GCD) of 66 and 28, which is 2, and divide both by it.
Simplify the fraction: 14 33 .
Explanation
Understanding the Problem We are given the expression 4 11 × 7 6 . Our goal is to evaluate this expression and simplify the result.
Multiplying the Fractions To multiply the two fractions, we multiply the numerators together and the denominators together: 4 11 × 7 6 = 4 × 7 11 × 6
Simplifying Numerator and Denominator Now, we simplify the numerator and the denominator: 11 × 6 = 66 4 × 7 = 28 So, the expression becomes: 28 66
Simplifying the Fraction To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 66 and 28 is 2. We divide both the numerator and the denominator by 2: 28 ÷ 2 66 ÷ 2 = 14 33
Final Answer The simplified fraction is 14 33 . This is an improper fraction, and we can leave it in this form or convert it to a mixed number. To convert it to a mixed number, we divide 33 by 14: 33 ÷ 14 = 2 with a remainder of 5 So, the mixed number is 2 14 5 . The answer is 14 33
Examples
Understanding fraction multiplication is crucial in many real-life scenarios, such as scaling recipes. For instance, if a recipe calls for 2 1 cup of flour and you want to make 3 2 of the recipe, you would multiply 2 1 × 3 2 to find the new amount of flour needed, which is 3 1 cup. This same principle applies to calculating proportions in construction, adjusting chemical solutions, or determining discounts in retail.
