Example Question - improper fraction
Here are examples of questions we've helped users solve.
Subtraction of Two Fractions
<p>\[\frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4}\]</p> <p>\[= \frac{1}{4}\]</p>
Fraction Multiplication and Simplification
<p>لحل المسألة المعطاة، يجب ضرب الأكسام فيما بينها.</p> <p>\(\frac{7}{16} \times \frac{3}{8} \times \frac{\sqrt{2}}{3} = \frac{7}{16} \times \frac{3}{8} \times \frac{(\sqrt{2}/\sqrt{3})}{\sqrt{3}}\)</p> <p>عند تبسيط التعبير، نحصل على:</p> <p>\(\frac{7 \times 3 \times \sqrt{2}}{16 \times 8 \times \sqrt{3}}\)</p> <p>نوحِّد الأرقام ذات العوامل المشتركة:</p> <p>\(\frac{21\sqrt{2}}{128\sqrt{3}}\)</p> <p>لترشيد المقام، نضرب في \(\sqrt{3}\):</p> <p>\(\frac{21\sqrt{2}}{128\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{21\sqrt{6}}{384}\)</p> <p>نحاول إيجاد أكبر عامل مشترك للتبسيط:</p> <p>\(\frac{21\sqrt{6}}{384} = \frac{7\sqrt{6}}{128}\)</p>
Multiplication of an Integer and a Mixed Number
<p>Convert the mixed number to an improper fraction: \(3 \frac{1}{5} = \frac{16}{5}\)</p> <p>Multiply the integer by the improper fraction: \(18 \times \frac{16}{5} = \frac{18 \times 16}{5}\)</p> <p>Simplify the multiplication: \( \frac{18 \times 16}{5} = \frac{288}{5}\)</p> <p>Convert back to a mixed number if necessary: \( \frac{288}{5} = 57 \frac{3}{5}\)</p> <p>Final answer: \(57 \frac{3}{5}\)</p>
Multiplying a Whole Number by a Mixed Fraction
<p>Convert the mixed number to an improper fraction:</p> <p>\(3 \frac{1}{5} = \frac{5 \times 3 + 1}{5} = \frac{16}{5}\)</p> <p>Multiply the whole number by the improper fraction:</p> <p>\(18 \times \frac{16}{5} = \frac{18 \times 16}{5}\)</p> <p>Simplify the multiplication:</p> <p>\(\frac{18 \times 16}{5} = \frac{288}{5}\)</p> <p>Convert the improper fraction to a mixed number:</p> <p>\(\frac{288}{5} = 57 \frac{3}{5}\)</p>
Simplifying the Fraction 10/8 to Mixed Number
Claro, puedo ayudarte a resolver la fracción que se muestra en la imagen. Para simplificar la fracción \( \frac{10}{8} \), necesitamos encontrar el máximo común divisor (MCD) de 10 y 8, para así reducir la fracción a su forma más simple. El MCD de 10 y 8 es 2, porque ambos números son divisibles por 2. Ahora dividimos tanto el numerador como el denominador por 2: \( \frac{10 ÷ 2}{8 ÷ 2} = \frac{5}{4} \) Por lo tanto, la fracción \( \frac{10}{8} \) simplificada es \( \frac{5}{4} \). Ahora, \( \frac{5}{4} \) es una fracción impropia, ya que el numerador es mayor que el denominador. Esto significa que la fracción es mayor que 1. Podemos convertir esa fracción a un número mixto: 1 entero tiene 4/4, entonces 5/4 es igual a 1 entero más 1/4. Esto se puede escribir como: 1 \( \frac{1}{4} \) Así que \( \frac{10}{8} \) simplificada y expresada como número mixto es 1 \( \frac{1}{4} \).
Finding the Smallest Number
To solve this question, we need to find the smallest number among the given options. Let's compare each of the fractions and the decimal. (A) \( \frac{5}{7} \) This is a simple fraction that cannot be simplified further. (B) \( \frac{24}{5} \) This is an improper fraction, meaning that it is greater than 1. (C) \( 64 \) This is an integer and it is obviously greater than 1. (D) \( 2.37 \) This is a decimal that is slightly bigger than 2 but less than 3. Out of the given options, we're looking for the smallest. Fraction (A) \( \frac{5}{7} \) is less than 1, fraction (B) is more than 4 (since 20/5=4 and there is a remainder), the integer (C) is 64, and the decimal (D) is slightly bigger than 2. Hence, the smallest number is (A) \( \frac{5}{7} \), because it's the only option less than 1.
Solving a Square Expression
To solve the expression \((1 \frac{1}{2})^2\) or \(1.5^2\): First, convert the mixed number to an improper fraction or a decimal. The mixed number \(1 \frac{1}{2}\) is equivalent to \(1 + \frac{1}{2}\) or \(1.5\). If we convert it to an improper fraction, we get \(1 \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}\). Then, we need to square this number: In the form of an improper fraction: \[\left(\frac{3}{2}\right)^2 = \frac{3^2}{2^2} = \frac{9}{4}\] In decimal form: \(1.5^2 = 1.5 \cdot 1.5 = 2.25\) Both \(\frac{9}{4}\) and \(2.25\) represent the same number, which is the solution to the expression.
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