Example Question - improper fractions
Here are examples of questions we've helped users solve.
Multiplication of Mixed Numbers and Improper Fractions
<p>Convert the mixed number to an improper fraction:</p> <p>2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}</p> <p>Now, multiply:</p> <p>\frac{7}{3} \times \frac{4 \times 3 + 3}{7} = \frac{7}{3} \times \frac{15}{7}</p> <p>Cancel the 7s:</p> <p> \frac{15}{3} = 5</p> <p>Thus, the solution is 5.</p>
Simplifying Fraction and Converting to Mixed Number
Claro, la imagen muestra una fracción: \( \frac{10}{8} \) Para simplificar la fracción, debemos encontrar el máximo común divisor de 10 y 8, que es 2. Luego, dividimos tanto el numerador como el denominador por 2. \( \frac{10 \div 2}{8 \div 2} = \frac{5}{4} \) La fracción simplificada de \( \frac{10}{8} \) es \( \frac{5}{4} \). Además, podemos observar que \( \frac{5}{4} \) es una fracción impropia porque el numerador es mayor que el denominador, lo que significa que representa un número mayor que 1. Si deseamos convertir la fracción impropia a un número mixto, dividimos 5 entre 4. El resultado es 1 y sobra 1. Por lo tanto, como número mixto, \( \frac{5}{4} \) se expresa como \( 1 \frac{1}{4} \). Esta fracción representa un número mezclado, lo que indica que hay un entero y una parte fraccionaria. En contexto, si la imagen representa una pizza, \( 1 \frac{1}{4} \) sugiere que hay una pizza completa y un cuarto de otra pizza.
Adding Fractions by Finding a Common Denominator
Para resolver la suma de fracciones \( \frac{4}{5} + \frac{1}{3} \), primero necesitamos encontrar un denominador común entre 5 y 3. El mínimo común denominador (MCD) de 5 y 3 es 15, porque 15 es el número más pequeño que es divisible tanto por 5 como por 3. Luego convertimos cada fracción a equivalentes con el denominador común de 15: Para \( \frac{4}{5} \), multiplicamos el numerador y el denominador por 3 (ya que 15 dividido por 5 es 3): \[ \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15} \] Para \( \frac{1}{3} \), multiplicamos el numerador y el denominador por 5 (ya que 15 dividido por 3 es 5): \[ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \] Ahora sumamos las dos nuevas fracciones con el mismo denominador: \[ \frac{12}{15} + \frac{5}{15} = \frac{12 + 5}{15} = \frac{17}{15} \] La suma de esas dos fracciones es \( \frac{17}{15} \), que es una fracción impropia. Si quieres convertirla en una fracción mixta, puedes hacerlo así: \( \frac{17}{15} \) equivale a \( 1 \frac{2}{15} \), ya que 17 dividido por 15 es 1 con un residuo de 2. En la imagen, la opción marcada es \( \frac{7}{15} \), pero esa no es la respuesta correcta al problema. La respuesta correcta al problema presentado sería \( 1 \frac{2}{15} \) o \( \frac{17}{15} \) si permaneciera como una fracción impropia, lo cual no está entre las opciones presentadas.
Identifying Fraction Greater than 1
Dựa trên câu hỏi được cho trong hình ảnh, chúng ta cần tìm phân số lớn hơn 1 từ các phân số đã cho: \( \frac{4}{5}, \frac{3}{5}, \frac{5}{4}, \frac{4}{6} \). Phân số nào có tử số lớn hơn mẫu số thì nó sẽ lớn hơn 1. Nhìn qua các phân số ta có thể thấy ngay phân số \( \frac{5}{4} \) có tử số lớn hơn mẫu số và do đó nó lớn hơn 1. Các phân số còn lại đều có tử số nhỏ hơn hoặc bằng mẫu số nên chúng đều nhỏ hơn hoặc bằng 1. Vậy phần trả lời đúng là \( \frac{5}{4} \), tương ứng với phương án C.
Converting Mixed Numbers to Improper Fractions and Adding/Subtracting
Para resolver esta expresión con números mixtos, primero convirtamos cada número mixto a una fracción impropia. Luego, haremos la suma y resta de estas fracciones. 1. Convertimos los números mixtos a fracciones impropias: La fracción impropia de \( \left( +\dfrac{4}{2} \right) = +2 \) ya que \( 4/2 \) es simplemente \( 2 \). La fracción impropia de \( -\left( +\dfrac{2}{3} \right) = -\dfrac{2}{3} \) puesto que el signo negativo aplica al número entero. La fracción impropia de \( -\left( -\dfrac{1}{6} \right) = +\dfrac{1}{6} \) ya que dos signos negativos se convierten en un signo positivo (ley de los signos). 2. Realizamos las operaciones con las fracciones: \[ +2 - \left(-\dfrac{2}{3}\right) + \left(+\dfrac{1}{6}\right) \] Para poder sumar y restar las fracciones, necesitamos un denominador común. El mínimo común denominador (MCD) entre 2, 3 y 6 es 6. Convertimos todas las fracciones a tener denominador 6. \[ +2 = +\dfrac{2 \cdot 3}{3 \cdot 3} = \dfrac{6}{3} = \dfrac{12}{6} \] \[ -\dfrac{2}{3} = -\dfrac{2 \cdot 2}{3 \cdot 2} = -\dfrac{4}{6} \] \[ +\dfrac{1}{6} = +\dfrac{1}{6} \] (ya tiene el denominador 6, así que no se cambia) Ahora sumamos y restamos las fracciones con el mismo denominador: \[ \dfrac{12}{6} + \left(-\dfrac{4}{6}\right) + \dfrac{1}{6} \] \[ = \dfrac{12 - 4 + 1}{6} \] \[ = \dfrac{8 + 1}{6} \] \[ = \dfrac{9}{6} \] Finalmente, simplificamos la fracción. \( \dfrac{9}{6} \) se puede simplificar dividiendo tanto el numerador como el denominador por 3: \[ \dfrac{9 \div 3}{6 \div 3} = \dfrac{3}{2} \] Por lo tanto, el resultado de sumar y restar las fracciones es \( \dfrac{3}{2} \) o \( 1\dfrac{1}{2} \) en forma de número mixto.
Comparing Mixed Numbers and Improper Fractions
Для начала переведем смешанные числа в неправильные дроби, чтобы было проще сравнить их. 1) -4 7/9 преобразовывается в неправильную дробь путем умножения целой части на знаменатель и прибавления числителя: -4 * 9 = -36 -36 + 7 = -29 Итак, -4 7/9 = -29/9. -4 5/9 преобразовывается аналогично: -4 * 9 = -36 -36 + 5 = -31 Итак, -4 5/9 = -31/9. Таким образом, -29/9 больше, чем -31/9, потому что чем меньше отрицательное число, тем оно "меньше". Поэтому в первом пункте меньшим числом будет -4 5/9. 2) 3 2/3 также преобразовывается в неправильную дробь: 3 * 3 = 9 9 + 2 = 11 Итак, 3 2/3 = 11/3. Сравним 11/3 и -9,6. В данном случае 11/3 - это положительное число, а -9,6 - отрицательное. Положительное число всегда будет больше отрицательного, поэтому 3 2/3 больше, чем -9,6. Следовательно, меньшим числом будет -9,6. Ответы: 1) -4 5/9 2) -9,6
Solving Measurement Problem
I see there are two separate problems labeled b) and d) in the provided image. Let's solve problem d), since it's the one without a completed answer: 6 1/2 in. x 2 1/2 in. First, convert the mixed numbers into improper fractions: 6 1/2 in = (6*2 + 1) / 2 = 13/2 in 2 1/2 in = (2*2 + 1) / 2 = 5/2 in Now multiply the improper fractions: (13/2) * (5/2) = 65/4 This result is still an improper fraction, and it needs to be converted back into a mixed number. To convert it, divide 65 by 4: 65 ÷ 4 = 16 with a remainder of 1. This gives us: 16 1/4 inches. So, the solution to problem d) is: 6 1/2 in. x 2 1/2 in. = 16 1/4 in.
Solving Area Problems with Mixed Numbers
The image shows two mixed numbers: 4 and 5/6 feet by 2 and 1/3 feet. To solve problems like these, typically involving the dimensions of an area, you multiply the length by the width. First, convert each mixed number to an improper fraction: \[ 4 \frac{5}{6} = \frac{4 \times 6 + 5}{6} = \frac{24 + 5}{6} = \frac{29}{6} \] \[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \] Now multiply the two improper fractions together: \[ \frac{29}{6} \times \frac{7}{3} = \frac{29 \times 7}{6 \times 3} \] \[ = \frac{203}{18} \] Now we will convert this improper fraction back to a mixed number and simplify if necessary: \[ \frac{203}{18} = 11 \frac{7}{18} \] (11 is the whole number part, because 203 divided by 18 is 11 with a remainder of 7.) So, the area covered is 11 and 7/18 square feet.
Subtracting Mixed Numbers
The image displays a fraction subtraction problem, which is part (iii) of a larger set of problems. Here's how to solve it: \( 1\frac{1}{5} - 1\frac{2}{3} \) First, convert the mixed numbers into improper fractions to make subtraction easier. For the first number: \( 1\frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} \) For the second number: \( 1\frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \) Now, subtract the second improper fraction from the first: \( \frac{6}{5} - \frac{5}{3} \) To subtract fractions, they must have a common denominator. The least common multiple (LCM) of the denominators 5 and 3 is 15, so convert each fraction to have the same denominator: \( \frac{6}{5} \times \frac{3}{3} = \frac{18}{15} \) \( \frac{5}{3} \times \frac{5}{5} = \frac{25}{15} \) Now perform the subtraction: \( \frac{18}{15} - \frac{25}{15} = \frac{18 - 25}{15} = \frac{-7}{15} \) The answer is a negative fraction because the second number was larger than the first one. Therefore, \( 1\frac{1}{5} - 1\frac{2}{3} = -\frac{7}{15} \).
Multiplication of Fractions and Conversion to Mixed Number
The image shows the multiplication of two fractions: \( \frac{5}{3} \times \frac{10}{7} \). To solve this, you simply multiply the numerators (top numbers) together and then multiply the denominators (bottom numbers) together: Numerator: \( 5 \times 10 = 50 \) Denominator: \( 3 \times 7 = 21 \) So the product of the two fractions is: \( \frac{50}{21} \) This is the exact answer and it is an improper fraction (the numerator is larger than the denominator). If you wish to convert it to a mixed number, you can divide 50 by 21: \( 50 \div 21 = 2 \) with a remainder of \( 8 \). Thus, the mixed number would be: \( 2 \frac{8}{21} \).
Adding and Converting Mixed Numbers
To solve this problem, we need to add the two amounts of newspapers collected by the two sections of Payapa School: First, let's convert the mixed numbers to improper fractions so that we can add them easily. For 18 2/5, we have: \( 18 + \frac{2}{5} = \frac{18 \times 5}{5} + \frac{2}{5} = \frac{90}{5} + \frac{2}{5} = \frac{92}{5} \) For 22 1/2, we have: \( 22 + \frac{1}{2} = \frac{22 \times 2}{2} + \frac{1}{2} = \frac{44}{2} + \frac{1}{2} = \frac{45}{2} \) Now, we need to add these two improper fractions: \( \frac{92}{5} + \frac{45}{2} \) To add them, we need a common denominator, which for 2 and 5 is 10. We need to convert each fraction to have this common denominator: \( \frac{92}{5} = \frac{92 \times 2}{5 \times 2} = \frac{184}{10} \) \( \frac{45}{2} = \frac{45 \times 5}{2 \times 5} = \frac{225}{10} \) Now we can add the two fractions: \( \frac{184}{10} + \frac{225}{10} = \frac{184+225}{10} = \frac{409}{10} \) Now, we convert this improper fraction back to a mixed number: \( \frac{409}{10} = 40 + \frac{9}{10} = 40 \frac{9}{10} \) The correct answer is C) \( 40 \frac{9}{10} \) kg.
Solving Mixed-Number Subtraction for Dragonfly and Mayfly Wingspans
To solve this problem, we will subtract the wingspan of the mayfly from the wingspan of the dragonfly. The dragonfly's wingspan is given as 6 2/7 centimeters, and it is said to be 1 3/10 centimeters wider than the wingspan of the mayfly. Let's perform the subtraction: Dragonfly's wingspan: 6 2/7 cm Wingspan wider than mayfly's wingspan: 1 3/10 cm To subtract these mixed numbers, first convert them to improper fractions. For 6 2/7: 6 * 7 = 42 42 + 2 = 44 So, 6 2/7 = 44/7 For 1 3/10: 1 * 10 = 10 10 + 3 = 13 So, 1 3/10 = 13/10 Now we need to have a common denominator to subtract the fractions. The lowest common denominator for 7 and 10 is 70. Convert the fractions to equivalent fractions with a denominator of 70: 44/7 becomes (44 * 10)/(7 * 10) = 440/70 13/10 becomes (13 * 7)/(10 * 7) = 91/70 Now, subtract the wingspan difference from the dragonfly's wingspan: 440/70 (dragonfly's wingspan in cm) - 91/70 (difference in cm) = 349/70 Now we convert this improper fraction back to a mixed number: 349 divided by 70 equals 4 with a remainder of 69. Convert the remainder to a fraction by placing it over the original denominator: The mayfly's wingspan = 4 69/70 centimeters a. The whole box would show the number 4 because that's the whole number part of the wingspan for the mayfly. b. Number model with unknown: Let the wingspan of the mayfly be W. W + 1 3/10 = 6 2/7 Convert fractions to equivalent fractions with a common denominator and solve for W. Using the working above, we get the wingspan of the mayfly, W = 4 69/70 cm. c. A different way to solve a mixed-number subtraction problem could involve a visual fraction model or using a calculator that can handle mixed numbers. Additionally, it's sometimes easier to convert mixed numbers to improper fractions, perform the subtraction, and then convert the result back to a mixed number, as done above.
Multiplication of Mixed Numbers and Fractions
The image shows a multiplication problem involving two mixed numbers: \( 2\frac{1}{4} \times 5\frac{2}{3} \) To solve this problem, we should first convert each mixed number to an improper fraction. For \( 2\frac{1}{4} \): Multiply the whole number by the denominator of the fraction and then add the numerator: \( 2 \times 4 + 1 = 8 + 1 = 9 \) So \( 2\frac{1}{4} \) becomes \( \frac{9}{4} \). For \( 5\frac{2}{3} \): Multiply the whole number by the denominator of the fraction and then add the numerator: \( 5 \times 3 + 2 = 15 + 2 = 17 \) So \( 5\frac{2}{3} \) becomes \( \frac{17}{3} \). Now we multiply the two improper fractions: \( \frac{9}{4} \times \frac{17}{3} = \frac{9 \times 17}{4 \times 3} \) Calculate the multiplication: \( 9 \times 17 = 153 \) \( 4 \times 3 = 12 \) Thus, the expression becomes: \( \frac{153}{12} \) To simplify the fraction, divide both the numerator and denominator by their greatest common divisor, which is 3 in this case: \( \frac{153 \div 3}{12 \div 3} = \frac{51}{4} \) The fraction \( \frac{51}{4} \) can also be written as a mixed number. To convert it back to a mixed number, divide 51 by 4: \( 51 \div 4 = 12 \) with a remainder of 3. So the mixed number is \( 12\frac{3}{4} \), which is the product of the original problem.
Mathematical Calculation of Mixed Numbers
The problem in the image is: \[ 4 \frac{1}{2} (5 \frac{5}{8} - 15\frac{5}{8}) + (1 \frac{1}{2} - 3\frac{1}{4}) \] First, let's convert the mixed numbers into improper fractions: For \( 4 \frac{1}{2} \), we have \( 4 \times 2 + 1 = 9/2 \). For \( 5 \frac{5}{8} \), we have \( 5 \times 8 + 5 = 45/8 \). For \( 15 \frac{5}{8} \), we have \( 15 \times 8 + 5 = 125/8 \). For \( 1 \frac{1}{2} \), we have \( 1 \times 2 + 1 = 3/2 \). For \( 3 \frac{1}{4} \), we have \( 3 \times 4 + 1 = 13/4 \). Then the expression becomes: \[ \frac{9}{2} \left( \frac{45}{8} - \frac{125}{8} \right) + \left( \frac{3}{2} - \frac{13}{4} \right) \] Now we'll do the operations within the parentheses: \[ \frac{45}{8} - \frac{125}{8} = -\frac{80}{8} = -10 \] \[ \frac{3}{2} - \frac{13}{4} = \frac{6}{4} - \frac{13}{4} = -\frac{7}{4} \] Now our expression is: \[ \frac{9}{2} \times -10 + -\frac{7}{4} \] Multiplying \( \frac{9}{2} \) by -10: \[ \frac{9}{2} \times -10 = \frac{9 \times -10}{2} = -\frac{90}{2} = -45 \] We now have: \[ -45 - \frac{7}{4} \] To subtract these, we'll express -45 as a fraction with a denominator of 4: \[ -45 = -\frac{180}{4} \] Now subtract: \[ -\frac{180}{4} - \frac{7}{4} = -\frac{187}{4} \] The answer is \(-\frac{187}{4}\), which can be left as an improper fraction or converted back into a mixed number: \[ -\frac{187}{4} = -46 \frac{3}{4} \] So the final answer is \( -46 \frac{3}{4} \).
Multiplication of Mixed Fractions
To solve the multiplication of mixed fractions, you first convert each mixed fraction into an improper fraction. For the first mixed fraction \(1 \frac{6}{7}\): Multiply the whole number by the denominator and add the numerator to this product. This gives you the new numerator, while the denominator remains the same. So, \(1 \times 7 + 6 = 7 + 6 = 13\), making the improper fraction \(\frac{13}{7}\). For the second mixed fraction \(2 \frac{2}{3}\): Multiply the whole number by the denominator and then add the numerator to get the new numerator. So, \(2 \times 3 + 2 = 6 + 2 = 8\), which makes the improper fraction \(\frac{8}{3}\). Now multiply the improper fractions together: \(\frac{13}{7} \times \frac{8}{3}\) Multiply the numerators together and the denominators together: Numerator: \(13 \times 8 = 104\) Denominator: \(7 \times 3 = 21\) The product is \(\frac{104}{21}\). This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor if possible. In this case, 104 and 21 don't have a common divisor other than 1, so the fraction is already in its simplest form. Since the numerator is larger than the denominator, you can also convert it back into a mixed number: \(104 \div 21 = 4\) with a remainder of \(16\). So the mixed number is \(4 \frac{16}{21}\). If you want to check whether the fraction \(\frac{16}{21}\) can be simplified, you can look for common factors. In this case, there are none, and the final answer is: \(4 \frac{16}{21}\)
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com