ORDER OF OPERATIONS

When we are adding numbers, it makes no difference in what order the numbers are taken. The best way to check the addition of a column of figures is to add in the reverse order: if you have already added up the column, then check by adding down.

Numbers may also be multiplied in any order, and a good check for multiplying 378 by 597 is to multiply 597 by 378.

When an example calls for additions and also subtractions, we may perform the operations in any order we like. 12 - 20+18 is the same as - 12 + 18 - 20; x² - 5 + 3x may be written x² +3x - 5.

In a more complicated example like 5+2 X 7 - 12 : 6 the multiplications and divisions must be performed before the additions, and subtractions:

5 + 2 × 7- 12 : 6 = 5+14 -2 = 19 - 2 = 17.

To find the value of such an expression as 5a² + 2ab - a³ when a = 3, b=4, the value of each term is first obtained separately:

5a² + 2ab - a³ = 5 • 3² +2 • 3 • 4 - 3³ = 5 • 9 +2 • 12 - 27 = 45 + 24 - 27 = 69 - 27 = 42.

The parentheses in 4 (5+3) is a symbol of grouping, and the expression within the parentheses must be handled as a single number. In any example, the operation inside the parentheses must be done first of all.

add складывать

addend слагаемое

addition сложение

check проверять

difference разность

divide делить

dividend делимое

division деление

divisor делитель

factor множитель, фактор

in column столбиком

by means of при помощи

minuend уменьшаемое

minus минус

multiplicand множимое

multiplication умножение

multiplier множитель

multiply умножать

number of places число разрядов

numeral цифра

parentheses скобки

perform производить, совершать

plus плюс

problem задача

product продукт

quotient частное

reverse order обратный порядок

sign знак, символ

space расстояние, промежуток

subtract вычитать

subtraction вычитание

subtrahend вычитаемое

sum сумма

term член

two- (three-, four-) place number двух-, трех-, четырехзначное число

unit единица

value величина

whole number целое число