Example Question - arithmetic operations
Here are examples of questions we've helped users solve.
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>
Solving for a number based on given arithmetic operations
Seja \( x \) o número desconhecido. Primeiro, a pessoa subtrai 4 do número desconhecido: <p>\( x - 4 \)</p> Em seguida, ela divide a diferença por 3 e o quociente é 2: <p>\( \frac{x - 4}{3} = 2 \)</p> Para encontrar o valor de \( x \), multiplicamos ambos os lados da equação por 3: <p>\( x - 4 = 2 \times 3 \)</p> <p>\( x - 4 = 6 \)</p> Agora, adicionamos 4 a ambos os lados para isolar \( x \): <p>\( x = 6 + 4 \)</p> <p>\( x = 10 \)</p> Portanto, o número desconhecido é 10.
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>
Simplifying Complex Fractions
<p>Для первого задания:</p> <p>\[\frac{\frac{12}{19}}{\frac{7}{12} - \frac{4}{13} + \frac{13}{21}}\]</p> <p>Найдем общий знаменатель для выражения в знаменателе:</p> <p>\[Кратное(12, 13, 21) = 2^2 \cdot 3 \cdot 7 \cdot 13 = 1092\]</p> <p>Перепишем выражение с общим знаменателем:</p> <p>\[\frac{\frac{12}{19}}{\frac{7 \cdot 91}{1092} - \frac{4 \cdot 84}{1092} + \frac{13 \cdot 52}{1092}}\]</p> <p>\[\frac{\frac{12}{19}}{\frac{637 - 336 + 676}{1092}}\]</p> <p>\[\frac{\frac{12}{19}}{\frac{977}{1092}}\]</p> <p>Выразим сложную дробь как деление:</p> <p>\[\frac{12}{19} \cdot \frac{1092}{977}\]</p> <p>Сократим дробь:</p> <p>\[\frac{12 \cdot 1092}{19 \cdot 977}\]</p> <p>Так как нет общих делителей между числителем и знаменателем, это конечный ответ.</p> <p>Для второго задания:</p> <p>\[\frac{\left(\frac{3}{7} - 2,\!8\right) \cdot \frac{5}{8}}{\frac{7}{23}}\]</p> <p>Преобразуем смешанное число в неправильную дробь:</p> <p>\[2,\!8 = 2 + \frac{4}{5} = \frac{14}{5}\]</p> <p>Теперь вычтем эту дробь из \[\frac{3}{7}\]:</p> <p>\[\frac{3}{7} - \frac{14}{5} = \frac{3 \cdot 5}{35} - \frac{14 \cdot 7}{35}\]</p> <p>\[\frac{15 - 98}{35} = -\frac{83}{35}\]</p> <p>Теперь умножим результат на \[\frac{5}{8}\]:</p> <p>\[-\frac{83}{35} \cdot \frac{5}{8} = -\frac{83 \cdot 5}{35 \cdot 8}\]</p> <p>Упростим дробь:</p> <p>\[-\frac{415}{280}\]</p> <p>Затем разделим на \[\frac{7}{23}\]:</p> <p>\[-\frac{415}{280} \cdot \frac{23}{7} = -\frac{415 \cdot 23}{280 \cdot 7}\]</p> <p>Сократим дробь где это возможно (обратите внимание на числа 280 и 7):</p> <p>\[-\frac{415 \cdot 23}{40 \cdot 1} = -\frac{9545}{40}\]</p> <p>\[-\frac{9545}{40} = -238,\!625\]</p> <p>Это конечный ответ второго выражения.</p>
Simplifying a Fractional Expression
<p>\[ 6 \left( \frac{2}{3} \times \frac{4}{7} - \frac{1}{2} \right) + \frac{5}{6} \times \frac{7}{5} \]</p> <p>\[ = 6 \left( \frac{8}{21} - \frac{1}{2} \right) + \frac{35}{30} \]</p> <p>\[ = 6 \left( \frac{8}{21} - \frac{10.5}{21} \right) + \frac{7}{6} \]</p> <p>\[ = 6 \left( -\frac{2.5}{21} \right) + \frac{7}{6} \]</p> <p>\[ = -\frac{15}{21} + \frac{7}{6} \]</p> <p>\[ = -\frac{5}{7} + \frac{7}{6} \]</p> <p>\[ = -\frac{30}{42} + \frac{49}{42} \]</p> <p>\[ = \frac{19}{42} \]</p>
Solving a Math Problem Involving Basic Arithmetic Operations and Logical Reasoning
<p>From the provided image, it looks like we are to solve for the value of \( K \) in question number 4.</p> <p>The given number pattern is:</p> <p>\( \frac{1}{5} , \frac{3}{5} , \frac{5}{5} , K \frac{1}{5} \)</p> <p>To find the pattern, observe the numerators:</p> <p>The sequence of numerators is increasing by 2 each time: 1, 3, 5, ...</p> <p>Thus, the next term after 5 in the sequence is 5 + 2 = 7.</p> <p>The denominator remains constant at 5, so the next term is:</p> <p>\( \frac{7}{5} \)</p> <p>Therefore, the value of \( K \) is \( \frac{7}{5} \) or 1.4.</p>
Solving an Algebraic Equation Involving Basic Arithmetic Operations
<p>The image displays an equation with a missing number which needs to be found:</p> <p>\( (5 \times 8) + (\boxed{?} \times 8) = 40 + \boxed{?} \)</p> <p>Since \( 5 \times 8 = 40 \), the equation simplifies to:</p> <p>\( 40 + (\boxed{?} \times 8) = 40 + \boxed{?} \)</p> <p>To find the missing number, let's denote it as \( x \):</p> <p>\( 40 + (x \times 8) = 40 + x \)</p> <p>Subtract \( 40 \) from both sides:</p> <p>\( (x \times 8) = x \)</p> <p>Divide both sides by \( x \) (assuming \( x \neq 0 \)):</p> <p>\( 8 = 1 \)</p> <p>This leads to a contradiction, as \( 8 \) does not equal \( 1 \). The problem seems to be constructed erroneously, as the equation provided does not hold true for any real number \( x \). We would need additional information or a correction to the equation to proceed.</p>
Simplifying a Radical Expression
<p>\sqrt{8} + \sqrt{72} - \sqrt{32} - \sqrt{50} - \sqrt{2}</p> <p>\sqrt{4 \cdot 2} + \sqrt{36 \cdot 2} - \sqrt{16 \cdot 2} - \sqrt{25 \cdot 2} - \sqrt{2}</p> <p>2\sqrt{2} + 6\sqrt{2} - 4\sqrt{2} - 5\sqrt{2} - \sqrt{2}</p> <p>(2 + 6 - 4 - 5 - 1)\sqrt{2}</p> <p>-2\sqrt{2}</p>
Basic Arithmetic Operations Problem
<p>The given expression is: \( b - 15 + 63 \div 3 \times 5 \)</p> <p>According to the order of operations, we first need to divide and then multiply before performing addition and subtraction.</p> <p>Step 1: Calculate \( 63 \div 3 = 21 \)</p> <p>Step 2: Calculate \( 21 \times 5 = 105 \)</p> <p>Step 3: Now we perform the subtraction and addition \( b - 15 + 105 \)</p> <p>Step 4: Combine like terms by adding the numerical values: \( 105 - 15 = 90 \)</p> <p>Step 5: Now we have \( b + 90 \)</p> <p>Therefore, the simplified expression is \( b + 90 \).</p>
Arithmetic Operations with Positive and Negative Numbers
<p>25 - (-14) - 6 + (-30)</p> <p>Applying the operation of subtracting a negative, which is the same as addition:</p> <p>25 + 14 - 6 - 30</p> <p>Now, combine like terms (positive and negative separately):</p> <p>(25 + 14) - (6 + 30)</p> <p>39 - 36</p> <p>The final result is:</p> <p>3</p>
Solving a Multiplication Problem Involving Decimals
<p>To solve the multiplication problem \( 3.2 \times 6.4 \times 4.8 \), first multiply the two first numbers.</p> <p>\( 3.2 \times 6.4 = 20.48 \)</p> <p>Next, multiply the result by the last number.</p> <p>\( 20.48 \times 4.8 = 98.304 \)</p> <p>Therefore, the solution to \( 3.2 \times 6.4 \times 4.8 \) is \( 98.304 \).</p>
Calculating Monthly Earnings from Coffee Sales
<p>\textbf{For part (b)}:</p> <p>\text{January Cups Sold: }850</p> <p>\text{March Cups Sold: }587</p> <p>\text{Price per Cup in March: }$1.98</p> <p>\text{Revenue in March: }587 \times 1.98</p> <p>\text{Revenue in March: }$1162.26</p> <p>\textbf{For part (c)}:</p> <p>\text{May Cups Sold: }387</p> <p>\text{Price per Cup in May after Increase: }$2.25</p> <p>\text{Revenue in May: }387 \times 2.25</p> <p>\text{Revenue in May: }$871.25</p>
Solving Basic Arithmetic Operations
<p>Para resolver la operación dada en la imagen:</p> <p>\[10 \times 5 + 25 \div 5\]</p> <p>Debemos seguir la jerarquía de operaciones o regla del orden de operaciones (PEMDAS/BIDMAS), donde se realizan primero las multiplicaciones y divisiones de izquierda a derecha y luego las sumas y restas. Por lo tanto, comenzamos con la multiplicación y la división:</p> <p>\[10 \times 5 = 50\]</p> <p>\[25 \div 5 = 5\]</p> <p>Luego sumamos los resultados:</p> <p>\[50 + 5 = 55\]</p> <p>Así que la solución es 55.</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.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com