Example Question - mathematical calculation steps
Here are examples of questions we've helped users solve.
Solving a Mathematical Expression Using PEMDAS
To solve the mathematical expression in the image, you have to follow the order of operations, sometimes remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). The division symbol ":" here is equivalent to "÷". Starting with the given expression: \( 9 - 3 \div \frac{1}{3} + 1 \) Perform the division first: \( 3 \div \frac{1}{3} \) is the same as \( 3 \times 3 \) (because dividing by a fraction is the same as multiplying by its reciprocal), which equals \( 9 \). The expression now simplifies to: \( 9 - 9 + 1 \) Now proceed from left to right with subtraction and addition: \( 9 - 9 = 0 \) Now add 1: \( 0 + 1 = 1 \) So, the solution to the expression is: \( 1 \)
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)
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