Order of operations with fractions and brackets

0:00What is the value of this expression with fractions and brackets?

0:05The order of operations is the agreed order for working out an expression.

0:09Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.

0:18Brackets group a part to work out first. Here it is seven minus four fifths.

0:24Write seven with denominator five, the bottom number. Seven times five is thirty-five, so seven is thirty-five fifths.

0:34The denominators match, so subtract the numerators, the top numbers: thirty-five minus four is thirty-one.

0:42So the brackets are worth thirty-one fifths.

0:46Division and multiplication have equal priority, so go from left to right.

0:52A common mistake is to multiply first. The division is on the left, so it comes first.

0:59To divide by a fraction, multiply by its reciprocal: flip it so the numerator and denominator swap places.

1:07Nine sixths flips to six ninths.

1:10Multiply tops and bottoms: one times six is six, and two times nine is eighteen.

1:18Divide the top and bottom by six: six eighteenths is one third.

1:25Now multiply one third by thirty-one fifths.

1:29One times thirty-one is thirty-one, and three times five is fifteen: thirty-one fifteenths.

1:37Fifteen goes into thirty-one two times, with one left over.

1:42As a mixed number, a whole number and a fraction, the answer is two and one fifteenth.

1:49Brackets first, then multiply and divide from left to right.