# 3rd Grade - Multiplication And Division Are Opposites

 Grade Level: 3rd Skill: Multiplication and Division Topic: Multiplication and Division Are Opposites Goal: Use the inverse relationship of multiplication and division to compute and check results. Skill Description: Number Sense: Inverse relationship of multiplication and division The ability to use the information that division is the opposite of multiplication (and visa-versa) to check the results of computations.

## Building Blocks/Prerequisites

### Sample Problems

 (1) How are division and multiplication related? Division is the inverse (opposite) operation of multiplication: axb=c so a=c/b. (2) How are inverse relationships used? This principle can be used for a child to check his or her work. For example, after completing a division problem the answer can be multiplied by the divisor to get the third number. (3) How are division problems written? There are two common ways to indicate division: c divided by b can be written as c/b or c÷b. (4) What are the names for the numbers in a division problem? a=c ÷b, a is the quotient, c is the dividend, and b is the divisor. Quotient=dividend÷divisor or quotient=dividend divisor (5) Is the order of numbers important? When dividing the order of the numbers is important: 40/5 does not equal 5/40. (6) Are there any special rules when dividing? Division is special when dividing by 0 and 1. A number divided by zero is not defined. Any number divided by one is equal to that number.

### Online Resources

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### Extra Help Problems

 (1) 81 divided by 9= (9) 9 x 9= (81) (2) 1,000 x 8 = (8,000) 8,000 divided by 8 = (1,000) (3) 25 ÷ 5= (5); 5 x 5= (25) (4) 78 ÷ 6 = (13); 13 x 6 = (78) (5) 45 ÷ 9 = (5); 5 x 9= (45) (6) 35 ÷ 5=(7); 5 x 7 = (35) (7) 72 ÷4=(18); 18 x 4 = (72) (8) 91 ÷7=(13); 13 x 7=91 (9) 60 ÷4 = (15); 15 x 4 = (60) (10) 88 ÷ 4 = (22); 22 x 4 = (88) (11) 84 ÷ 6 = (14); 14 x 6 = (84) (12) 70 ÷ 7 = (10); 10 x 7 = (70) (13) 65 ÷ 5 = (13); 13 x 5 = 65 (14) 30 ÷ 1= (30); 30 x 1 = 30 (15) 60 ÷ 2 = (30); 30 x 2 = 60 (16) 27 ÷ 3 = (9); 9 x 3 = (27) (17) 48 ÷ 8 = (6); 6 x 8 = (48) (18) 99 ÷ 9 = (11); 11 x 9 = (99) (19) 90 ÷ 6 = (15); 15 x 6 = (90) (20) 64 ÷ 8 = (8); 8 x 8 = (64) (21) 72 ÷ 9 = 8); 8 x 9 = (72) (22) 7 x 9 = (63); 63 ÷ 7 = (9) (23) 63 ÷ 3 = (21); 21 x 3 = (63) (24) 42 ÷ 3 = (14); 14 x 3 = (42) (25) 52 ÷ 4 = (13); 13 x 4 = (52)