Example Question - simplified fraction
Here are examples of questions we've helped users solve.
Multiplication of Fractions
Para resolver la operación dada en la imagen, necesitas multiplicar dos fracciones. La operación mostrada es \( \frac{7}{5} \times \frac{2}{3} \). Para multiplicar fracciones, simplemente multiplica los numeradores entre sí y los denominadores entre sí. En este caso: Numeradores: \( 7 \times 2 = 14 \) Denominadores: \( 5 \times 3 = 15 \) Por lo tanto, la fracción resultante de la multiplicación es \( \frac{14}{15} \). Esta es ya la forma más simplificada de la fracción, por lo que \( \frac{7}{5} \times \frac{2}{3} = \frac{14}{15} \).
Calculating Probability of Drawing Cards from a Set
The question displayed in the image asks for the probability of picking an even number first and then picking an 8 when drawing cards labeled with the numbers 7, 8, and 9. Since the problem states that the card is put back before the second draw, the events are independent. To find the probability of both events happening, we calculate the probability of each event separately and then multiply them together. The probability of drawing an even number (which could only be the 8 in this case) on the first draw is 1 out of 3, since there is one even number and three cards overall. The probability of drawing an 8 on the second draw is again 1 out of 3, because after replacing the card, all three cards are available for selection again. Therefore, the combined probability is: Probability of even number (8) then an 8 = (1/3) * (1/3) = 1/9 The answer, as a simplified fraction, is 1/9.
Solving a Fraction Problem
Let's denote the numerator of the original fraction as \( n \) and the denominator as \( d \). According to the problem, the denominator is four more than the numerator, so: \( d = n + 4 \) The problem also states that if both the numerator and denominator are increased by one, the resulting fraction is simplified to \( \frac{5}{7} \): \( \frac{n + 1}{d + 1} = \frac{5}{7} \) Now we have a system of two equations to solve for the values of \( n \) and \( d \): 1) \( d = n + 4 \) 2) \( \frac{n + 1}{n + 5} = \frac{5}{7} \) (since \( d = n + 4 \), we replaced \( d \) with \( n + 4 \) in the second equation) Next, we can cross-multiply in the second equation to solve for \( n \): \( 7(n + 1) = 5(n + 5) \) Expand both sides: \( 7n + 7 = 5n + 25 \) Subtract \( 5n \) from both sides: \( 2n + 7 = 25 \) Subtract 7 from both sides: \( 2n = 18 \) Divide by 2: \( n = 9 \) Now that we have \( n \), we can find \( d \) using either of the original equations. Let's use the first one: \( d = n + 4 \) Replace \( n \) with 9: \( d = 9 + 4 \) Thus: \( d = 13 \) The original fraction is \( \frac{n}{d} = \frac{9}{13} \).
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