What should you divide by first: the whole number or the fraction? This question often arises in various mathematical calculations and can lead to confusion if not addressed properly. Understanding the order of operations and the significance of dividing by whole numbers and fractions is crucial for accurate mathematical computations.
In mathematics, the order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed. These rules are commonly remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). According to this order, division should be performed before addition and subtraction, and before multiplication.
When dealing with a whole number and a fraction, it is essential to consider the context of the problem. If the problem requires dividing the whole number by the fraction, you should follow the order of operations by dividing the whole number first. For instance, if you are given the expression 6 divided by 2/3, you would divide 6 by 2/3, resulting in 9. This is because division is performed before multiplication, and the whole number is divided by the fraction.
On the other hand, if the problem requires dividing the fraction by the whole number, you should also follow the order of operations. In this case, you would divide the fraction by the whole number, and then perform the resulting division. For example, if you are given the expression 2/3 divided by 6, you would divide 2/3 by 6, resulting in 1/9.
It is important to note that when dividing a fraction by a whole number, you can simplify the expression by multiplying the numerator by the reciprocal of the whole number. For instance, dividing 2/3 by 6 can be rewritten as 2/3 multiplied by 1/6, which equals 1/9.
In conclusion, when faced with the question of what should you divide by first, the whole number or the fraction, it is crucial to consider the context of the problem and the order of operations. By following the rules of PEMDAS, you can ensure accurate mathematical computations and avoid confusion. Remember that division should be performed before multiplication and before addition and subtraction, and that dividing a fraction by a whole number can be simplified by multiplying the numerator by the reciprocal of the whole number.
