Evaluate the arithmetic expression

In this video, we will solve this numerical expression step by step. It involves fractions, the order of operations, and periodic decimals.

Let's first write down the expression clearly. We have twenty-five over four-hundred-eighty minus the product of eleven over forty and sixteen over thirty-three, plus the quotient of fifteen over eighty and three fifths, all divided by zero point four five periodic times ninety minus one.

First, let's simplify the individual terms. Twenty-five and four-hundred-eighty can both be divided by five.

Now, let's look at the multiplication. We can cancel eleven and thirty-three by eleven to get one and three. We can also simplify sixteen and forty by dividing by eight.

Next, the division. Dividing by three fifths is the same as multiplying by five thirds. After simplifying, we get five sixteenths.

Now let's convert the periodic decimal zero point four five periodic into a fraction. The formula for a mixed periodic decimal gives us forty-five minus four over ninety.

With this, we can rewrite the second part of our expression.