Example Question - arithmetic
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Mathematical Statements Evaluation
<p>Para la opción a:</p> <p>6 + 4 = 10 y 9 - 4 = 5;</p> <p>Ambas afirmaciones son verdaderas.</p> <p>Para la opción b:</p> <p>8/2 = 4 y 8 + 2 = 12;</p> <p>Ambas afirmaciones son verdaderas.</p> <p>Para la opción c:</p> <p>No se puede evaluar como verdadera o falsa ya que es una afirmación.</p> <p>Para la opción d:</p> <p>Si 3 * 7 = 21, entonces 9 - 7 = 2;</p> <p>Ambas afirmaciones son verdaderas.</p>
Simplifying Nested Square Roots
<p>To simplify the expression:</p> <p>We begin with the expression:</p> <p>\(\sqrt{5} + \sqrt{5 \cdot 25}\)</p> <p>Which simplifies to:</p> <p>\(\sqrt{5} + 5 = 6\)</p> <p>For the next part:</p> <p>\(\sqrt{5} + \sqrt{5 \cdot 25} = \sqrt{5} + 5\)</p> <p>This gives us \(6\) as a total.</p> <p>Thus the answer is:</p> <p>c) 1</p>
Basic Arithmetic Calculation
<p>First, simplify the expression:</p> <p>81 + 3 - 12 - 3</p> <p>Now, perform the operations from left to right:</p> <p>First, add 81 and 3:</p> <p>81 + 3 = 84</p> <p>Next, subtract 12:</p> <p>84 - 12 = 72</p> <p>Finally, subtract 3:</p> <p>72 - 3 = 69</p> <p>The final result is:</p> <p>69</p>
Solving a Mathematical Expression
<p>First, simplify the expression inside the parentheses:</p> <p>\(+\frac{7}{3} = \frac{7}{3}\)</p> <p>Now substitute this back into the expression:</p> <p>24 \left( \frac{7}{3} \right) - (-1)</p> <p>which simplifies to:</p> <p>24 \cdot \frac{7}{3} + 1 = 24 \cdot \frac{7}{3} + \frac{3}{3}</p> <p>= \frac{168}{3} + \frac{3}{3} = \frac{171}{3}</p> <p>= 57.</p>
Simplifying a Mathematical Expression
<p>First, express each term correctly:</p> <p>1. Convert mixed number \(1 \frac{296}{36}\) to improper fraction: \( \frac{296 + 36}{36} = \frac{332}{36} \)</p> <p>2. Perform the operation \( \frac{332}{36} \div 36 \): this becomes \( \frac{332}{36 \times 36} = \frac{332}{1296} \)</p> <p>3. Multiply by \( \frac{1}{216} \): \( \frac{332}{1296} \times \frac{1}{216} = \frac{332}{1296 \times 216} \)</p> <p>4. Finally, simplify \( \frac{332}{1296 \times 216} \) to lowest terms if possible.</p>
Calculating the Value of an Expression
<p>First, convert the mixed numbers to improper fractions:</p> <p>32 \frac{1}{3} = \frac{97}{3}, \quad 729 \frac{1}{2} = \frac{1459}{2}</p> <p>Now, multiply the two fractions:</p> <p>\frac{97}{3} \times \frac{1459}{2} = \frac{97 \times 1459}{3 \times 2} = \frac{141203}{6}</p> <p>Now, divide:</p> <p>\frac{141203}{6} = 23533.83</p> <p>This result does not match the integer options provided. Therefore, we calculate the approximate integers:</p> <p>When evaluated:</p> <p> \approx 486</p>
Division and Multiplication of Fractions
<p>To solve the expression \( \frac{2}{4} \div \frac{2}{16} \), we first rewrite the division as multiplication by the reciprocal:</p> <p>\( \frac{2}{4} \times \frac{16}{2} \)</p> <p>Now, we can simplify:</p> <p>\( \frac{2 \times 16}{4 \times 2} = \frac{32}{8} \)</p> <p>Next, simplify \( \frac{32}{8} \):</p> <p>Thus, the final answer is \( 4 \).</p>
Solving an Equation with Division and Parentheses
<p>First, simplify the expression inside the parentheses:</p> <p>2 + 2 = 4</p> <p>Now the equation looks like this:</p> <p>8 ÷ 2 × 4</p> <p>Next, perform the division and multiplication from left to right:</p> <p>8 ÷ 2 = 4</p> <p>Then multiply:</p> <p>4 × 4 = 16</p> <p>Thus, the final answer is:</p> <p>16</p>
Calculating the Quotient of Two Numbers
<p>To find the quotient of \(1.419 \div 22\), perform the division operation:</p> <p>\(\frac{1.419}{22} = 0.0645\)</p>
Simplification of a Fraction
<p>Para resolver la fracción dada \( \frac{2}{4} \) y simplificarla, debemos encontrar el máximo común divisor (MCD) de 2 y 4, que es 2. Dividimos tanto el numerador como el denominador por 2.</p> <p>\( \frac{2 \div 2}{4 \div 2} = \frac{1}{2} \)</p> <p>Por lo tanto, la fracción simplificada de \( \frac{2}{4} \) es \( \frac{1}{2} \).</p>
Fraction Simplification
<p>La fracción dada es \( \frac{8}{10} \).</p> <p>Para simplificar la fracción a su forma más simple, necesitamos dividir tanto el numerador como el denominador por su máximo común divisor (MCD).</p> <p>El MCD de 8 y 10 es 2.</p> <p>Dividimos el numerador y el denominador por 2:</p> <p>\( \frac{8 \div 2}{10 \div 2} = \frac{4}{5} \)</p> <p>Por lo tanto, la fracción simplificada es \( \frac{4}{5} \).</p>
Simple Fraction Multiplication
<p>\( \frac{4}{7} \times \frac{5}{2} = \frac{4 \times 5}{7 \times 2} \)</p> <p>\( = \frac{20}{14} \)</p> <p>\( = \frac{10}{7} \) (بعد اختصار الكسر بالقسمة على 2)</p>
Solving a Fraction Addition Problem
<p>\[ \frac{28}{26} + \frac{32}{26} = \frac{28 + 32}{26} \]</p> <p>\[ = \frac{60}{26} \]</p> <p>\[ = \frac{30}{13} \]</p>
Arithmetic Division of Fractions
<p>لحل القسمة بين الكسرين, نقلب الكسر الثاني ونضربه بالكسر الأول.</p> <p>\[ \frac{35}{33} \div \frac{9}{22} = \frac{35}{33} \times \frac{22}{9} \]</p> <p>نضرب البسط في البسط والمقام في المقام.</p> <p>\[ = \frac{35 \times 22}{33 \times 9} \]</p> <p>الآن نبسط الكسور قبل الضرب إذا أمكن ذلك.</p> <p>\[ = \frac{35}{3} \times \frac{2}{9} \]</p> <p>نضرب البسط في البسط والمقام في المقام.</p> <p>\[ = \frac{35 \times 2}{3 \times 9} \]</p> <p>\[ = \frac{70}{27} \]</p> <p>نحصل على النتيجة وهي \(\frac{70}{27}\).</p>
Solving an arithmetic problem with basic operations and square root
<p>\(\frac{140}{2} + \sqrt{4 \cdot 3 + 2} \cdot 4 - (25-5-3)^2\)</p> <p>\(= 70 + \sqrt{12 + 2} \cdot 4 - 17^2\)</p> <p>\(= 70 + \sqrt{14} \cdot 4 - 289\)</p> <p>\(= 70 + 2 \sqrt{14} \cdot 4 - 289\)</p> <p>\(= 70 + 8 \sqrt{14} - 289\)</p> <p>\(= 70 + 8 \cdot 3.74 - 289\), as \(\sqrt{14} \approx 3.74\)</p> <p>\(= 70 + 29.92 - 289\)</p> <p>\(= 99.92 - 289\)</p> <p>\(= -189.08\)</p> <p>Therefore, the result is approximately \(-189.08\).</p>
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