Example Question - solving mathematical expression
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Solving a Mathematical Expression Using PEMDAS
To solve the mathematical expression in the image, you have to follow the order of operations, sometimes remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). The division symbol ":" here is equivalent to "÷". Starting with the given expression: \( 9 - 3 \div \frac{1}{3} + 1 \) Perform the division first: \( 3 \div \frac{1}{3} \) is the same as \( 3 \times 3 \) (because dividing by a fraction is the same as multiplying by its reciprocal), which equals \( 9 \). The expression now simplifies to: \( 9 - 9 + 1 \) Now proceed from left to right with subtraction and addition: \( 9 - 9 = 0 \) Now add 1: \( 0 + 1 = 1 \) So, the solution to the expression is: \( 1 \)
Solving Mathematical Expression with Multiplication and Division
Para resolver esta expresión matemática, debemos seguir el orden de las operaciones, que es paréntesis, exponentes, multiplicación y división de izquierda a derecha, y luego suma y resta de izquierda a derecha. Esta expresión no tiene paréntesis ni exponentes, así que vamos directamente a la multiplicación y división: 3 + 15 - 28 + 17 - 63 - 70 ÷ 5 + 142 Primero, realizamos la división: 70 ÷ 5 = 14 Reemplazamos el resultado de la división en la expresión: 3 + 15 - 28 + 17 - 63 - 14 + 142 Ahora, realizamos las operaciones de suma y resta de izquierda a derecha: 3 + 15 = 18 18 - 28 = -10 -10 + 17 = 7 7 - 63 = -56 -56 - 14 = -70 -70 + 142 = 72 La respuesta final es 72.
Solving Mathematical Expression with Cube Roots
Claro, vamos a resolver la expresión matemática proporcionada en la imagen: \[ (4 \cdot \left(\frac{4}{3}\right)^3) \cdot (5 \cdot \sqrt[3]{\frac{8}{5}}) \] Primero, calculamos el cubo de \( \frac{4}{3} \): \[ \left(\frac{4}{3}\right)^3 = \frac{4^3}{3^3} = \frac{64}{27} \] Luego, calculamos la raíz cúbica de \( \frac{8}{5} \): \[ \sqrt[3]{\frac{8}{5}} = \frac{\sqrt[3]{8}}{\sqrt[3]{5}} = \frac{2}{\sqrt[3]{5}} \] Ahora multiplicamos 4 por \( \frac{64}{27} \): \[ 4 \cdot \frac{64}{27} = \frac{256}{27} \] Y multiplicamos 5 por \( \frac{2}{\sqrt[3]{5}} \): \[ 5 \cdot \frac{2}{\sqrt[3]{5}} = \frac{10}{\sqrt[3]{5}} \] Por último, multiplicamos ambos resultados: \[ \frac{256}{27} \cdot \frac{10}{\sqrt[3]{5}} = \frac{2560}{27 \sqrt[3]{5}} \] Este es el resultado de la expresión que se muestra en la imagen.
Solving a Complex Mathematical Expression Step by Step
Давайте решим представленное математическое выражение пошагово: Дано выражение: \(\frac{7}{3 / \frac{2}{1 + \frac{1}{3}}}\) Шаг 1: Решим самое внутреннее выражение в знаменателе, то есть \(1 + \frac{1}{3}\). \(1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3}\) Таким образом, наше выражение теперь имеет вид: \(\frac{7}{3 / \frac{2}{\frac{4}{3}}}\) Шаг 2: Далее решим деление дробей в знаменателе, используя основное свойство деления дробей - умножения на обратное число. То есть, разделим 3 на \(\frac{2}{\frac{4}{3}}\) или умножим 3 на обратную дробь от \(\frac{2}{\frac{4}{3}}\). Для этого сначала найдем обратную дробь. Обратная дробь для \(\frac{2}{\frac{4}{3}}\) равна \(\frac{\frac{4}{3}}{2}\), что равно \(\frac{4}{3} \cdot \frac{1}{2} = \frac{4}{6} = \frac{2}{3}\). Теперь умножим 3 на обратную дробь \(\frac{2}{3}\): \(3 \cdot \frac{2}{3} = 2\) Таким образом, наше выражение теперь имеет вид: \(\frac{7}{2}\) Шаг 3: Теперь, когда у нас есть деление числа 7 на 2, просто выполним это деление: \(\frac{7}{2} = 3,5\) Таким образом, результат выражения равен 3,5.
Solving a Mathematical Expression Step by Step
Pour résoudre l'expression mathématique donnée dans l'image, procédons étape par étape : 1. Calculons d'abord \(5^0\). Par définition, n'importe quel nombre (autre que zéro) élevé à la puissance de zéro est égal à 1. Donc, \(5^0 = 1\). 2. Ensuite, calculons \((-3)^2\). Lorsque nous élevons un nombre négatif au carré, le résultat est positif, car le produit de deux nombres négatifs est positif. Donc, \((-3)^2 = (-3) \times (-3) = 9\). 3. Puis, calculons \(4^1\). N'importe quel nombre élevé à la puissance de un est égal à lui-même. Donc, \(4^1 = 4\). Maintenant, ajoutons les résultats : \(5^0 + (-3)^2 + 4^1 = 1 + 9 + 4\) Faisons l'addition : \(1 + 9 + 4 = 14\) La réponse finale à l'expression donnée est 14.
Solving a Mathematical Expression Involving Fractions and Exponents
To solve the expression given in the image, we follow these steps: First, simplify the expression inside the parentheses: \[\left(\sqrt{\frac{4}{25}} - 1\right)\] Since the square root of a fraction is the square root of the numerator divided by the square root of the denominator, we have: \[\sqrt{\frac{4}{25}} = \frac{\sqrt{4}}{\sqrt{25}} = \frac{2}{5}\] Now, replace the square root with its simplified form in the original expression: \[\left(\frac{2}{5} - 1\right)\] To subtract 1 (which is the same as 5/5) from 2/5, we express 1 with a common denominator: \[\left(\frac{2}{5} - \frac{5}{5}\right)\] Now subtract the numerators while keeping the common denominator: \[\frac{2 - 5}{5} = \frac{-3}{5}\] Finally, raise this fraction to the power of 3: \[\left(\frac{-3}{5}\right)^3 = \frac{-3^3}{5^3} = \frac{-27}{125}\] So, the solution to the expression is \(-\frac{27}{125}\).
Solving Mathematical Expression with Multiplication and Division
Để giải quyết bài toán trong hình ảnh bạn cung cấp, chúng ta cần thực hiện phép nhân và phép chia cho các số đã cho. Dưới đây là cách làm: Phép nhân: \[ 132 \times 145 = 19140 \] Sau đó, ta nhân kết quả này với 100 (theo qui tắc khi nhân một số với 100, chúng ta chỉ cần thêm hai số 0 vào cuối số đó): \[ 19140 \times 100 = 1914000 \] Tiếp theo, chúng ta thực hiện phép chia: \[ 145 \times 133 - 46 = 19285 - 46 = 19239 \] Cuối cùng, để tìm kết quả của biểu thức bạn cung cấp, chúng ta cần chia hai kết quả mà ta đã tìm được ở trên: \[ \frac{1914000}{19239} \approx 99.565 \] Vậy kết quả xấp xỉ của biểu thức sau khi thực hiện các phép tính là khoảng 99.565.
Solving a Mathematical Expression with Division and Multiplication
This mathematical expression involves the basic operations: division and multiplication. To solve this, we will follow the order of operations, commonly remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). First, solve the expression inside the parentheses: \(1 + 2 = 3\) Now the original expression simplifies to: \(6 \div 2(3)\) Following the order of operations, we perform the division and multiplication from left to right: \(3(3) = 9\) Thus, the result of the expression \(6 \div 2(1+2)\) is \(9\).
Solving a Mathematical Expression with Subtraction and Multiplication
好的，让我们一步一步解决这个问题。 首先，我们需要计算括号里面的表达式，然后根据减法和乘法的顺序进行运算。 首先计算括号内的 \((-3\frac{2}{3})^2\)，将混合数转换为假分数处理： \[-3\frac{2}{3} = -\frac{11}{3}\] 对它平方得到： \[\left(-\frac{11}{3}\right)^2 = \frac{11^2}{3^2} = \frac{121}{9}\] 然后，计算括号内的另一个部分。 将 \(\frac{121}{9}\) 和 \(-\frac{1}{4}\) 相减，我们首先找到共同分母，即 36，然后相减： \[\frac{121}{9}-\frac{1}{4} = \frac{121*4}{36}-\frac{1*9}{36} = \frac{484}{36}-\frac{9}{36} = \frac{475}{36}\] 现在，我们可以计算给定表达式的剩余部分： \[8\frac{8}{9} - \left(\frac{475}{36}\right)\] 将混合数转换为假分数： \[8\frac{8}{9} = \frac{80}{9}\] 现在将80/9与475/36相减。我们再次找到共同的分母，即 36，然后相减，所以先将80/9扩大到相同的分母： \[\frac{80}{9} * \frac{4}{4} = \frac{320}{36}\] 现在减去： \[\frac{320}{36} - \frac{475}{36} = \frac{320 - 475}{36} = \frac{-155}{36}\] 结果是 \(-\frac{155}{36}\)，它也可以写作一个混合数：-4\(-\frac{11}{36}\)。 所以，解答是 \(-4\)-\(\frac{11}{36}\)。
Solving a Logarithmic Equation for a Mathematical Expression
El problema nos da la ecuación \( ab = c \) y la siguiente igualdad de logaritmos: \[ \log_c a + \log_c b = \frac{32}{5} \] Se nos pide calcular el valor de \( F \), que está dado por: \[ F = \frac{\log a^3 + \log b^3 + \log c^3}{\log a \cdot \log b \cdot \log c} \] Primero, reescribiremos la fracción con las propiedades de los logaritmos. Sabemos que \(\log x^n = n \log x\), así podemos simplificar el numerador: \[ F = \frac{3 \log a + 3 \log b + 3 \log c}{\log a \cdot \log b \cdot \log c} \] Ahora, sabemos que \(\log a = \log_c a \cdot \log c\) y similarmente para los otros logaritmos. Vamos a reescribir el denominador utilizando esta propiedad y el hecho de que \( \log_c a + \log_c b = \frac{32}{5} \): \[ \log a \cdot \log b \cdot \log c = (\log_c a \cdot \log c) \cdot (\log_c b \cdot \log c) \cdot \log c \] \[ = (\log_c a \cdot \log_c b) \cdot (\log c)^3 \] \[ = \frac{32}{5} \cdot (\log c)^3 \] Entonces: \[ F = \frac{3(\log a + \log b + \log c)}{\frac{32}{5} \cdot (\log c)^3} \] Pero aquí estamos atascados porque no tenemos suficiente información sobre \(\log a\), \(\log b\), y \ log c\ directamente para simplificar más. Necesitamos averiguar cómo relacionar \(\log_c a\), \(\log_c b\), y \(\log c\) para poder avanzar. De la relación dada \( ab = c \), si tomamos el logaritmo natural (o logaritmo en cualquier base), tenemos: \[ \log ab = \log c \] Por las propiedades de los logaritmos, esta ecuación es equivalente a: \[ \log a + \log b = \log c \] Podemos usar esta información para reescribir \(\log a + \log b + \log c\) como \(2 \log c\). Por lo tanto, el numerador se convierte en: \[ 3(2 \log c) = 6 \log c \] Ahora, sustituimos esto de vuelta en la ecuación de \( F \) y simplificamos: \[ F = \frac{6 \log c}{\frac{32}{5} \cdot (\log c)^3} \] \[ F = \frac{6 \cdot 5}{32} \cdot \frac{1}{(\log c)^2} \] \[ F = \frac{30}{32} \cdot \frac{1}{(\log c)^2} \] Reduzcamos esta fracción para simplificarla: \[ F = \frac{15}{16} \cdot \frac{1}{(\log c)^2} \] Dado que no tenemos más información específica sobre \( \log c \), no podemos simplificar más. Por lo tanto, el valor de \( F \) es: \[ F = \frac{15}{16} \cdot \frac{1}{(\log c)^2} \] Podríamos buscar expresar \( \log c \) de alguna manera con la información dada, pero sin información adicional sobre los valores de \( a \), \( b \), y \( c \), no podemos determinar un valor numérico específico para \( F \).
Solving a Complex Mathematical Expression Step-by-Step
The image appears to be upside down; however, I can still read the content. It shows a mathematical problem which seems to be: \[ \frac{-9b^2 - 4 \times (12)(155)}{2 \times (12)} \] To solve this problem, follow these steps: 1. Multiply \(4 \times 12 \times 155\) to find the product in the numerator. 2. Once you've found the product, you will subtract it from \(-9b^2\) (still in the numerator). 3. Lastly, divide the result by \(2 \times 12\), which is the division in the denominator. Let's solve it step-by-step: 1. Compute \(4 \times 12 \times 155\) \[ 4 \times 12 = 48 \] \[ 48 \times 155 = 7440 \] 2. Subtract that product from \(-9b^2\) to calculate the new numerator. \[ -9b^2 - 7440 \] 3. Divide the new numerator by \(2 \times 12\), which is 24. \[ \frac{-9b^2 - 7440}{24} \] To simplify further, you can separate the fraction: \[ \frac{-9b^2}{24} - \frac{7440}{24} \] The terms may simplify depending on whether there are common factors. For the constant term: \[ \frac{7440}{24} = 310 \] Leaving us with: \[ \frac{-9b^2}{24} - 310 \] The fraction \(\frac{-9b^2}{24}\) can also be simplified by dividing both numerator and denominator by their greatest common divisor which is 3: \[ \frac{-9b^2}{24} = \frac{-3b^2}{8} \] So the simplified form of the expression would be: \[ \frac{-3b^2}{8} - 310 \] Please note that this expression may not simplify further without specific information about the variable \(b\).
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