Example Question - order of operations pemdas
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Solving a Complex Arithmetic Expression
To solve the expression given in the image, follow the order of operations, commonly remembered by the acronym PEMDAS (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right). The expression to solve is: \[ 4 \times \frac{10 - 27 \times 2}{1+1 \times 5} \div \frac{6}{3} \] Step 1: Solve multiplication and divisions as they appear from left to right. For the numerator of the fraction: \[ 27 \times 2 = 54 \] Step 2: Continue with the subtraction in the numerator and the addition in the denominator: For the numerator: \[ 10 - 54 = -44 \] For the denominator: \[ 1 + 1 \times 5 = 1 + 5 = 6 \] Step 3: Now you have the fraction: \[ 4 \times \frac{-44}{6} \] However, the division by 6 is not finished yet. At this point, divide 6 into the numerator -44: \[ \frac{-44}{6} = -\frac{44}{6} = -\frac{22}{3} \] Step 4: Now multiply 4 by the result of the fraction: \[ 4 \times -\frac{22}{3} \] Divide 4 by 3 before multiplying to simplify the computation: \[ \frac{4}{3} \times -22 = -\frac{88}{3} \] Step 5: Solve the division by the fraction \(\frac{6}{3}\): \[ \frac{6}{3} = 2 \] Step 6: Now put together the multiplication and the division: \[ -\frac{88}{3} \div 2 = -\frac{88}{3} \times \frac{1}{2} = -\frac{88}{6} \] Step 7: Simplify the fraction by dividing both the numerator and the denominator by 2: \[ -\frac{88}{6} = -\frac{44}{3} \] Thus, the answer to the given expression is: \[ -\frac{44}{3} \] or in decimal form: \[ -14.67 \] (rounded to two decimal places)
Solving Arithmetic Expression with Fractions
To solve the expression shown in the image, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). The expression is as follows: \( \frac{3}{5} - \left( \frac{8}{3} - \frac{9}{2} \right) + \frac{1}{4} \) Step 1: Solve the parentheses first. Inside the parentheses, we have two fractions that need to be subtracted: \[ \frac{8}{3} - \frac{9}{2} \] To subtract these fractions, we need a common denominator, which in this case would be 6 (the least common multiple of 3 and 2). First, convert both fractions to have the same denominator: \[ \frac{8}{3} \times \frac{2}{2} = \frac{16}{6} \] \[ \frac{9}{2} \times \frac{3}{3} = \frac{27}{6} \] Now subtract the second fraction from the first: \[ \frac{16}{6} - \frac{27}{6} = -\frac{11}{6} \] Step 2: Apply the result back into the expression with the correct sign (negative, since we are subtracting the result of the parentheses): \[ \frac{3}{5} - (-\frac{11}{6}) + \frac{1}{4} \] Step 3: Add \(-(-\frac{11}{6})\) to \(\frac{3}{5}\). First, find a common denominator for \(\frac{3}{5}\) and \(\frac{11}{6}\), which is 30: \[ \frac{3}{5} \times \frac{6}{6} = \frac{18}{30} \] \[ \frac{11}{6} \times \frac{5}{5} = \frac{55}{30} \] Now convert the subtraction of a negative to addition and add the two fractions: \[ \frac{18}{30} + \frac{55}{30} = \frac{73}{30} \] Step 4: Add the remaining fraction \(\frac{1}{4}\) to the result. Again, we need a common denominator, which is 120 for 30 and 4: \[ \frac{73}{30} \times \frac{4}{4} = \frac{292}{120} \] \[ \frac{1}{4} \times \frac{30}{30} = \frac{30}{120} \] Now add them: \[ \frac{292}{120} + \frac{30}{120} = \frac{322}{120} \] Step 5: Reduce the fraction to its simplest form: \[ \frac{322}{120} \text{ can be simplified by dividing by 2:} \frac{161}{60} \] Therefore, the final simplified answer is: \[ \frac{161}{60} \] This fraction can be left as an improper fraction, or it can be converted to a mixed number by dividing the numerator by the denominator (161 ÷ 60), which would be 2 remainder 41, resulting in: \[ 2 \frac{41}{60} \] So the expression simplifies to \( 2 \frac{41}{60} \).
Solving a Division and Multiplication Equation with Parentheses
To solve the equation 8 ÷ 2(2 + 2), you need to follow the order of operations, often remembered by the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Here's how you solve the equation step-by-step: 1. First, solve the expression within the parentheses: \(2 + 2 = 4\) 2. Now, rewrite the equation with the sum: \(8 ÷ 2(4)\) Since there are no parentheses containing an operation to perform or exponents to simplify, proceed with multiplication and division from left to right. 3. Perform the division followed by multiplication: \(8 ÷ 2 = 4\) \(4 × 4 = 16\) Therefore, the solution to the equation \(8 ÷ 2(2 + 2)\) is \(16\).
Solving a Division and Multiplication Expression with Parentheses
To solve the expression \( 8 \div 2(2+2) \), you need to follow the order of operations, which is commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Here are the steps: 1. Parentheses: Calculate the expression within the parentheses first. \( 2+2 = 4 \) 2. Multiplication and Division: Next, you perform multiplication and division from left to right. \( 8 \div 2 \times 4 \) We do the division first because it comes before multiplication as we read from left to right. \( 4 \times 4 \) 3. Finally, you multiply the result. \( 4 \times 4 = 16 \) So the answer to the expression is \( 16 \).
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