Continued Four Operations-Division Lesson 3 Continued Four Operations-Division

The Whole Numbers Division Definition: if a. b. and c represent whole numbers and if A/B=C, then it must be true that A=B x C Example: 72÷9 = 8 72/9=8 Dividend is the number being divided; 72 Divisor is the number doing the dividing; 9 Quotient is the answer; 8 Whatever is “left over” is indicated as a Remainder, usually denoted by the letter R. Example: 45/7=6 R 3 Note: the remainder cannot be larger than the divisor. 34453 ÷ 23 = 1497 R22 23 114 92 225 207 183 161 22

The Decimal Numbers Division The decimal number divide by the whole number: Rule: to divide a decimal number by a whole number use the long-division algorithm and place the decimal in the quotient directly above the decimal in the dividend. Rule: to divide a decimal number by a power of ten move the decimal point to left a number of places equal to the number of zero in the power of ten. Example: 231.5 / 10=23.15 Rule: if a division is to be rounded to certain # of decimal places. The quotient must be carried to one more place to correctly round to desired place.

Divide by decimal numbers (both of dividend and divisor are decimals): Rules: to divide a decimal number or whole number by a decimal number move the decimal point of the divisor all the way to right until the divisor is a whole number. Examples: 7.834 /. 02 2. 50 / .0025 (be careful the location o decimal points is) Then move the decimal point the same digits of the places in the dividend to the right. If the question asks you to round the place value you have to round the number as the questions ask for

Continued Tips: Should be careful the format of; Where the decimal point is if the dividend is a whole number;

Grouping Symbols Symbols: Exponent, Parentheses (1), Brackets [ 2 ], and Braces { 3 } . Name other examples

Grouping numbers without symbols Rule: if an expression without grouping symbols contains only additions and subtractions, these operations are performed in order from left to right. Example: 10+5-3+8 or 8-4+9-4

Continued Rule: if an expression without grouping symbols contains multiplication, division, additions, and subtractions, these operations are performed by MSAD or DMSA in order from left to right. Name examples:

Continued Rule: if no grouping symbols occur in an expression, multiplication and division are performed from left to right, and then addition and subtraction from left to right. Example: 4X3÷2-2+5 12 ÷6X2+2-4

Four operations with the grouping symbols Four operations with the grouping symbols are first and Parentheses are most commonly use when no other grouping symbols are involved.  Exponent, Parentheses (1), Brackets [ 2 ], and Braces { 3 } EPMDAS or EPDMSA Left to Right

Continued Rule: when simplifying an expression containing grouping symbols with grouping symbols, remove the innermost set of symbols first ( 1 ) [ 2 ] { 3 } and follow EPMDAS or EPDMSA from left to right No sign between a number and any parentheses that means Multiplication Examples: 5+ [ 8- (3+1) ] 18-{5+ [4 (5-2) -7] } 3 [4+ (3-1) ] + 5 [12- (8+2) ]

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