Order of operations with rational numbers and powers

0:00What is one minus two times four fifths squared?

0:04All three numbers are rational: each can be written as a fraction of two integers.

0:10This part is a power. Its exponent, the small two, squares the whole fraction in the brackets.

0:18The order of operations is the agreed order: brackets, then powers, then multiplication and division, then addition and subtraction, each pair from left to right.

0:30Brackets first. Inside is just four fifths, so there is nothing to work out.

0:36Next, the power: four fifths times four fifths. Multiply the numerators, the tops, to get sixteen, and the denominators, the bottoms, to get twenty-five.

0:49Then multiply before you subtract: two times sixteen twenty-fifths is thirty-two twenty-fifths.

0:57Last, subtract. Use the same denominator: one is twenty-five twenty-fifths.

1:04Twenty-five minus thirty-two is negative seven, so the answer is negative seven twenty-fifths.

1:11Check with decimals: four fifths is 0.8, and 0.8 squared is 0.64.

1:191 minus 2 times 0.64 is 1 minus 1.28, which is negative 0.28, the same as negative 7 over 25.

1:31A common mistake is to work left to right: one minus two is negative one.

1:37Negative one times sixteen twenty-fifths is negative sixteen twenty-fifths, which is wrong: multiply before you subtract.

1:46To recap, the order is brackets, then powers, then multiply and divide, then add and subtract.