+ Plus, indicates addition; thus, 10 + 5 is 15.

- Minus, indicates subtraction; thus, 10 - 5 is 5.

X Multiplied by, indicates multiplication; thus, 10 X 5 is 50.

÷ Divided by, indicates division; thus, 10 -5- 5 is 2.

= Equal to, indicates equality; thus, 12 in. = 1 ft.

( ), [ ], { }, called parenthesis, bracket, and brace, respectively, have the same meaning, and signify that the operations indicated within them are to be performed first; or, if more than one is used, that indicated in the inner one is to be effected first. Thus, in the expression 5(7 - 2), the subtraction is to be made before multiplying by 5. Again, in the expression 1/2[ a + ( b -c/4)], the subtraction indicated within the parenthesis is made first; the remainder is added to a, and one-half the sum found.

-, called the vinculum, is used for the same purpose as the parenthesis, but chiefly in connection with the sign

√; thus, √¯.

. , called the decimal point, is placed in a number containing decimals, to fix the value of the number; thus, 12.5 is 12 and 5/10; 1.25 is 1 and 25/100 etc.

82 means that the number 8 is to be squared; thus, 82 = 8 X 8 = 64.

83 means that the number 8 is to be cubed; thus, 83 = 8 X 8 X 8 = 512.

√¯, called the radical sign, means that some root of the expression under it is to be found; if used without a small index figure, it means square root; thus,√64 = 8.

mean that the cube or the fourth root is to be found, the index figure indicating the root; thus, = 3.

: : : : means proportion; thus, 3:4 :: 6: 8 is read 3 is to 4 as 6 is to 8. Instead of the : : sign, the equality sign = often substituted; thus, 3:4 = 6:8.

° ' " mean degrees, minutes, and seconds; as, 60° 15' 15" which is read 60 degrees, 15 minutes, 15 seconds.

' " also mean feet and inches; thus, 7' 6" is read 7 feet 6 inches.

(read pi) means the ratio of the circumference of a circle to the diameter and = 3.1416.

(read sigma) means summation; thus, (a+ 6) means that there are several values for both a and 6, and that the sum of all is to be found.