Properties of Equality - ppt download - Free Printable
Educational worksheet: Properties of Equality - ppt download. Download and print for classroom or home learning activities.
PNG
612×792
16.7 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #259573
⭐
Show Answer Key & Explanations
Step-by-step solution for: Properties of Equality - ppt download
▼
Show Answer Key & Explanations
Step-by-step solution for: Properties of Equality - ppt download
Let me work through each of the 15 properties of mathematics carefully.
1) The product of any number and one is that number. For example a x 1 = a.
This is the Multiplicative Identity Property (Identity Property of Multiplication).
2) Adding 0 to any number leaves it unchanged. For example a + 0 = a.
This is the Additive Identity Property (Identity Property of Addition).
3) If you subtract the same number from both sides of an equation, the equation is still true. For example if a = b, then a - c = b - c.
This is the Subtraction Property of Equality.
4) When three or more numbers are multiplied, the product is the same regardless of the order of the multiplicands. For example (a x b) x c = a x (b x c).
Wait, let me re-read: "regardless of the order of the multiplicands" but the example shows grouping: (a x b) x c = a x (b x c). This is about grouping, not order. So this is the Associative Property of Multiplication.
Actually, looking again at the wording "regardless of the order of the multiplicands" - but the example clearly shows grouping with parentheses. The Associative Property is about grouping. Let me go with Associative Property of Multiplication.
5) When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (a + b) + c = a + (b + c).
This is the Associative Property of Addition.
6) If you add the same number to both sides of an equation, the equation is still true. For example if a = b, then a + c = b + c.
This is the Addition Property of Equality.
7) Multiplying any number by 0 yields 0. For example a x 0 = 0.
This is the Zero Property of Multiplication (or Multiplication Property of Zero).
8) If you divide the same number to both sides of an equation, the equation is still true. For example if a = b, then a/c = b/c.
This is the Division Property of Equality.
9) If you multiply the same number to both sides of an equation, the equation is still true. For example if a = b, then a x c = b x c.
This is the Multiplication Property of Equality.
10) The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example a x (b + c) = a x b + a x c.
This is the Distributive Property.
11) The multiplicative inverse of a number, a is 1/a so that a x 1/a = 1.
This is the Multiplicative Inverse Property (or Reciprocal Property).
12) When two numbers are added, the sum is the same regardless of the order of the addends. For example a + b = b + a.
This is the Commutative Property of Addition.
13) The sum of any number and zero is the original number. For example a + 0 = a.
This is the Additive Identity Property (Identity Property of Addition).
14) When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example a x b = b x a.
This is the Commutative Property of Multiplication.
15) The additive inverse of a number, a is -a so that a + -a = 0.
This is the Additive Inverse Property (or Opposite Property).
Let me verify my answers:
1) Multiplicative Identity Property ✓
2) Additive Identity Property ✓
3) Subtraction Property of Equality ✓
4) Associative Property of Multiplication ✓
5) Associative Property of Addition ✓
6) Addition Property of Equality ✓
7) Zero Property of Multiplication ✓
8) Division Property of Equality ✓
9) Multiplication Property of Equality ✓
10) Distributive Property ✓
11) Multiplicative Inverse Property ✓
12) Commutative Property of Addition ✓
13) Additive Identity Property ✓
14) Commutative Property of Multiplication ✓
15) Additive Inverse Property ✓
All answers look correct.
1) The product of any number and one is that number. For example a x 1 = a.
This is the Multiplicative Identity Property (Identity Property of Multiplication).
2) Adding 0 to any number leaves it unchanged. For example a + 0 = a.
This is the Additive Identity Property (Identity Property of Addition).
3) If you subtract the same number from both sides of an equation, the equation is still true. For example if a = b, then a - c = b - c.
This is the Subtraction Property of Equality.
4) When three or more numbers are multiplied, the product is the same regardless of the order of the multiplicands. For example (a x b) x c = a x (b x c).
Wait, let me re-read: "regardless of the order of the multiplicands" but the example shows grouping: (a x b) x c = a x (b x c). This is about grouping, not order. So this is the Associative Property of Multiplication.
Actually, looking again at the wording "regardless of the order of the multiplicands" - but the example clearly shows grouping with parentheses. The Associative Property is about grouping. Let me go with Associative Property of Multiplication.
5) When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (a + b) + c = a + (b + c).
This is the Associative Property of Addition.
6) If you add the same number to both sides of an equation, the equation is still true. For example if a = b, then a + c = b + c.
This is the Addition Property of Equality.
7) Multiplying any number by 0 yields 0. For example a x 0 = 0.
This is the Zero Property of Multiplication (or Multiplication Property of Zero).
8) If you divide the same number to both sides of an equation, the equation is still true. For example if a = b, then a/c = b/c.
This is the Division Property of Equality.
9) If you multiply the same number to both sides of an equation, the equation is still true. For example if a = b, then a x c = b x c.
This is the Multiplication Property of Equality.
10) The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example a x (b + c) = a x b + a x c.
This is the Distributive Property.
11) The multiplicative inverse of a number, a is 1/a so that a x 1/a = 1.
This is the Multiplicative Inverse Property (or Reciprocal Property).
12) When two numbers are added, the sum is the same regardless of the order of the addends. For example a + b = b + a.
This is the Commutative Property of Addition.
13) The sum of any number and zero is the original number. For example a + 0 = a.
This is the Additive Identity Property (Identity Property of Addition).
14) When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example a x b = b x a.
This is the Commutative Property of Multiplication.
15) The additive inverse of a number, a is -a so that a + -a = 0.
This is the Additive Inverse Property (or Opposite Property).
Let me verify my answers:
1) Multiplicative Identity Property ✓
2) Additive Identity Property ✓
3) Subtraction Property of Equality ✓
4) Associative Property of Multiplication ✓
5) Associative Property of Addition ✓
6) Addition Property of Equality ✓
7) Zero Property of Multiplication ✓
8) Division Property of Equality ✓
9) Multiplication Property of Equality ✓
10) Distributive Property ✓
11) Multiplicative Inverse Property ✓
12) Commutative Property of Addition ✓
13) Additive Identity Property ✓
14) Commutative Property of Multiplication ✓
15) Additive Inverse Property ✓
All answers look correct.
Parent Tip: Review the logic above to help your child master the concept of properties of equality worksheets.
