Example Question - order of operations
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Solving a Mixed Arithmetic Operation Equation
Para resolver la ecuación dada, debemos seguir el orden de las operaciones, conocido como PEMDAS (Paréntesis, Exponentes, Multiplicación y División de izquierda a derecha, Adición y Sustracción de izquierda a derecha). <p>La ecuación es: \( 32 + 15 - 42 \cdot 3 + 25 \div 5 \).</p> <p>Primero, realizaremos la multiplicación y la división en el orden en que aparecen:</p> <p>\( 42 \cdot 3 = 126 \)</p> <p>\( 25 \div 5 = 5 \)</p> <p>Reemplazamos estos resultados en la ecuación original:</p> <p>\( 32 + 15 - 126 + 5 \)</p> <p>Ahora, procedemos con la adición y sustracción en el orden que aparecen:</p> <p>\( 32 + 15 = 47 \)</p> <p>\( 47 - 126 = -79 \)</p> <p>\( -79 + 5 = -74 \)</p> <p>Por lo tanto, el resultado final de la ecuación es \(-74\).</p>
Fraction Operations and Order of Operations
<p>Первое действие:</p> <p>\[ \frac{12}{19} - \left( \frac{7}{12} - \frac{4 \cdot 13}{21} \right) \]</p> <p>\[ \frac{12}{19} - \left( \frac{7}{12} - \frac{52}{21} \right) \]</p> <p>Найти общий знаменатель для \(\frac{7}{12}\) и \(\frac{52}{21}\):</p> <p>\[ 12 \cdot 21 = 252 \]</p> <p>\[ \frac{12}{19} - \left( \frac{7 \cdot 21}{252} - \frac{52 \cdot 12}{252} \right) \]</p> <p>\[ \frac{12}{19} - \left( \frac{147}{252} - \frac{624}{252} \right) \]</p> <p>\[ \frac{12}{19} - \left( -\frac{477}{252} \right) \]</p> <p>\[ \frac{12}{19} + \frac{477}{252} \]</p> <p>Теперь найдем общий знаменатель для \(\frac{12}{19}\) и \(\frac{477}{252}\):</p> <p>\[ 19 \cdot 252 = 4788 \]</p> <p>\[ \frac{12 \cdot 252}{4788} + \frac{477 \cdot 19}{4788} \]</p> <p>\[ \frac{3024}{4788} + \frac{9063}{4788} \]</p> <p>\[ \frac{12087}{4788} \]</p> <p>Упрощаем дробь:</p> <p>\[ \frac{12087 \div 3}{4788 \div 3} \]</p> <p>\[ \frac{4029}{1596} \]</p> <p>Упрощаем дробь:</p> <p>\[ \frac{4029 \div 3}{1596 \div 3} \]</p> <p>\[ \frac{1343}{532} \]</p> <p>Далее применяем деление с остатком:</p> <p>\[ 1343 = 532 \cdot 2 + 279 \]</p> <p>\[ \frac{1343}{532} = 2 \frac{279}{532} \]</p> <p>Второе действие:</p> <p>\[ \left( 3 \frac{2}{7} - 25,8 \right) \cdot \frac{7}{23} \]</p> <p>Преобразуем смешанное число в неправильную дробь:</p> <p>\[ 3 \frac{2}{7} = \frac{3 \cdot 7 + 2}{7} = \frac{21 + 2}{7} = \frac{23}{7} \]</p> <p>\[ \left( \frac{23}{7} - 25,8 \right) \cdot \frac{7}{23} \]</p> <p>Переведем 25,8 в дробь:</p> <p>\[ 25,8 = \frac{258}{10} = \frac{129}{5} \]</p> <p>Теперь найдем общий знаменатель для \(\frac{23}{7}\) и \(\frac{129}{5}\):</p> <p>\[ 7 \cdot 5 = 35 \]</p> <p>\[ \left( \frac{23 \cdot 5}{35} - \frac{129 \cdot 7}{35} \right) \cdot \frac{7}{23} \]</p> <p>\[ \left( \frac{115}{35} - \frac{903}{35} \right) \cdot \frac{7}{23} \]</p> <p>\[ \left( -\frac{788}{35} \right) \cdot \frac{7}{23} \]</p> <p>\[ -\frac{5516}{35 \cdot 23} \]</p> <p>\[ -\frac{5516}{805} \]</p> <p>Применяем деление с остатком:</p> <p>\[ 5516 = 805 \cdot 6 + 746 \]</p> <p>\[ -\frac{5516}{805} = -6 \frac{746}{805} \]</p> <p>Ответы на задания:</p> <p>1) \( 2 \frac{279}{532} \)</p> <p>2) \( -6 \frac{746}{805} \)</p>
Solving a Multistep Arithmetic Problem
<p>The expression to simplify is:</p> <p>\[ 5 \times (0.6) + 3 \times (7) + 4 - 6 \times \left(\frac{2}{3}\right) \]</p> <p>To solve this, follow the order of operations, PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):</p> <p>Multiply within the parentheses first:</p> <p>\[ 5 \times 0.6 = 3 \]</p> <p>\[ 3 \times 7 = 21 \]</p> <p>\[ 6 \times \frac{2}{3} = 4 \]</p> <p>Then perform the addition and subtraction:</p> <p>\[ 3 + 21 + 4 - 4 \]</p> <p>Finally, add and subtract the numbers:</p> <p>\[ 24 + 4 = 28 \]</p> <p>\[ 28 - 4 = 24 \]</p> <p>The simplified result is 24.</p>
Order of Operations Problem
<p>Solución para el número 5:</p> <p>\begin{align*} 10 \times 5 + 25 : 5 & = 50 + 5 \\ & = 55 \end{align*}</p> <p>Solución para el número 6:</p> <p>\begin{align*} 54 : 6 - 2 \times 3 & = 9 - 6 \\ & = 3 \end{align*}</p>
Order of Operations in Mathematical Expressions
<p>Problema 1:</p> <p>Paso 1: Realizar primero la operación de división en la expresión \( 7 + \frac{54}{3} \)</p> <p>\( \frac{54}{3} = 18 \)</p> <p>Paso 2: Sumar el resultado al número 7</p> <p>\( 7 + 18 = 25 \)</p> <p>Problema 2:</p> <p>Paso 1: Realizar primero la operación de multiplicación en la expresión \( 3 + 9 \times 5 \)</p> <p>\( 9 \times 5 = 45 \)</p> <p>Paso 2: Sumar el resultado al número 3</p> <p>\( 3 + 45 = 48 \)</p>
Solving Arithmetic Operations Involving Addition, Subtraction, Multiplication, and Division
Para la pregunta 3, aplicamos el orden de las operaciones, también conocido como PEMDAS/BODMAS (Paréntesis, Exponentes, Multiplicación y División, Adición y Sustracción): <p>\( 24 - 8 \div 2 + 9 - 10 \)</p> Primero realizamos la división: <p>\( 24 - 4 + 9 - 10 \)</p> Después, realizamos las operaciones de izquierda a derecha, comenzando con la resta y luego la suma: <p>\( 20 + 9 - 10 \)</p> <p>\( 29 - 10 \)</p> <p>\( 19 \)</p> Por lo tanto, la solución para la pregunta 3 es 19. Para la pregunta 4, nuevamente aplicamos el orden de las operaciones: <p>\( 10 + 3 \times 4 - 9 \)</p> Primero realizamos la multiplicación: <p>\( 10 + 12 - 9 \)</p> Luego, realizamos las operaciones de suma y resta de izquierda a derecha: <p>\( 22 - 9 \)</p> <p>\( 13 \)</p> Así, la solución para la pregunta 4 es 13.
Solving a Mathematical Expression Following Order of Operations
当然，解决这个数学问题，我们需要遵循运算法则顺序，即乘法和除法优先于加法和减法。 1. 6 - (1×0) + (2÷2) 2. 6 - 0 + 1 3. 6 + 1 4. 7 答案是7。
Solving Arithmetic Expression with Division and Addition/Subtraction
To solve the expression, follow the order of operations (PEMDAS/BODMAS): 1. Perform any calculations inside parentheses first. 2. Solve multiplication and division from left to right. 3. Solve addition and subtraction from left to right. The given expression: \(9 - 3 \div \frac{1}{3} + 1\) There are no parentheses, so we move to division: \(9 - (3 \div \frac{1}{3}) + 1\) \(3 \div \frac{1}{3}\) is the same as \(3 \times 3\), which equals 9. Now replace this in the original expression: \(9 - 9 + 1\) Now we solve the subtraction and addition from left to right: \(9 - 9 = 0\) \(0 + 1 = 1\) So the final solution is: \(1\)
How to Solve Mathematical Expressions Using PEMDAS/BODMAS
To solve the given mathematical expression, you should follow the order of operations, often remembered by the acronym PEMDAS/BODMAS, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Here's how you solve the expression step by step: 1. Calculate the expression inside the parentheses first. \[ 1 + 2 = 3 \] 2. Multiply or divide from left to right. Since there is no multiplication or exponentiation to perform first, we move to division, which must account for the entire term \( 2(1+2) \), as it is common in mathematics to consider the multiplication part of the term "glued" to its next element, meaning it has to be taken as a whole. \[ 6 ÷ 2(3) = 6 ÷ 6 \] 3. Finally, divide 6 by 6. \[ 6 ÷ 6 = 1 \] The answer to the expression is 1.
Solving a simple equation using PEMDAS
To solve the equation in the image, you should follow the order of operations, often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). The equation is 4 + (6 × 2). According to the order of operations, you must first do the multiplication inside the parentheses: 6 × 2 = 12 Then, you add the result to 4: 4 + 12 = 16 So the solution to the equation is 16.
Solving Mathematical Expressions with PEMDAS
To solve the mathematical expression in the image correctly, you need to follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). The expression given is: \[ 8 \div 2(2+2) \] First, solve the operation inside the parentheses: \[ 2+2 = 4 \] Then the expression becomes: \[ 8 \div 2(4) \] \[ 8 \div 2 \times 4 \] According to PEMDAS, division and multiplication should be performed from left to right: \[ 4 \times 4 = 16 \] Therefore, the correct result of the expression is: \[ 16 \]
Order of Operations and Ambiguity in Math
This math problem is a classic example that can lead to two different answers depending on the interpretation of the order of operations. To solve it according to the standard mathematical order of operations (PEMDAS/BODMAS), you solve any expressions within parentheses first, then do multiplication and division from left to right, followed by addition and subtraction from left to right. The equation is: \[6 \div 2(1+2)\] First, solve the expression inside the parentheses. \[1+2 = 3\] Now, the equation becomes: \[6 \div 2 \times 3\] According to the order of operations, you should divide and multiply from left to right. \[6 \div 2 = 3\] \[3 \times 3= 9\] So the solution is 9. However, some people might interpret the problem differently, suggesting that the 2 should be distributed to the terms inside the parentheses first (which would be the case if the division sign was replaced with a fraction). But following the standard order of operations, the solution is 9.
Solving a Linear Equation by Order of Operations
Por supuesto, te ayudaré a resolver la ecuación que aparece en la imagen: \( x + 48 \times -20 = 0 \) Primero, debemos resolver la operación de multiplicación antes de proceder con la suma, de acuerdo con el orden de las operaciones (primero multiplicaciones y divisiones, luego sumas y restas). Entonces multiplicamos 48 por -20: \( 48 \times -20 = -960 \) Ahora sustituimos este resultado en la ecuación original: \( x - 960 = 0 \) Para despejar \( x \), necesitamos sumar 960 a ambos lados de la ecuación para aislar la variable \( x \): \( x - 960 + 960 = 0 + 960 \) \( x = 960 \) Por lo tanto, el valor de \( x \) es 960.
Solving Mathematical Expression with Order of Operations
Para resolver la expresión matemática dada en la imagen, primero sigamos las reglas de jerarquía de las operaciones, realizando primero las potencias y luego las sumas y restas en orden. La expresión es: \[ 1 + \left(\frac{6}{2}\right)^2 - \frac{5}{2} - (-3)^3 \] Empecemos con las potencias: El término \(\left(\frac{6}{2}\right)^2\) es igual a \(\left(3\right)^2\) porque \( \frac{6}{2} = 3 \), y \(3^2 = 9\). El término \((-3)^3\) es igual a \(-27\), porque \( -3 \times -3 \times -3 = -27 \). Reemplacemos esos valores en la expresión original: \[ 1 + 9 - \frac{5}{2} - (-27) \] Ahora, resolvamos la resta y la suma: El término \(- \frac{5}{2}\) es equivalente a \(-2.5\) en forma decimal. La expresión ahora es: \[ 1 + 9 - 2.5 + 27 \] Sumemos y restemos en orden: \[ 10 - 2.5 + 27 \] Ahora, 10 menos 2.5 es 7.5, así que nos queda: \[ 7.5 + 27 \] Finalmente, sumamos 7.5 y 27 para obtener: \[ 34.5 \] Por lo tanto, el resultado de la expresión es 34.5.
Solving a Multiplication and Addition Expression
To solve the expression given in the image, \(25 \times 4 + 10\), you need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). First, you should do the multiplication part: \(25 \times 4 = 100\). Then, you add 10 to the result: \(100 + 10 = 110\). So, \(25 \times 4 + 10 = 110\). The correct answer is 110.
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