Properties of Operations 1
Glue into your Journal.
Commutative Property of Addition: You can add numbers in
any order.
a+b=b+a
Ex. 3 + 5 = 5 + 3
8=8
Ex. 15.3 + 21.7 = 21.7 + 15.3
37 = 37
Ex. ¾ + ¼ = ¼ + ¾
1=1
Commutative Property of Multiplication: You can multiply
numbers in any order.
axb=bxa
Ex. 3 x 5 x 2 = 2 x 5 x 3
30 = 30
Ex. 15.3 x 21.7 = 21.7 x 15.3
332.01 = 332.01
Ex. ¾ x ¼ = ¼ x ¾
3/16 = 3/16
Practice: Use the commutative property to solve. (Hint:
Group the compatible numbers together.)
1. 32 + 28 =
=
2. 2 x 15 x 5 =
=
3. ⅓ + 3 ¼ + 1⅔=
=
4. 3.4 + 12.3 + 2.6 =
=
Associative Property of Addition and Multiplication: the order
of the numbers do not change, but the grouping symbols do
change.
Ex. (18 + 13) + 17 = 18 + (13 + 17)
31 + 17 = 18 + 30
48 =
48
Ex. (17 x 5) x 2 = 17 x (5 x 2)
85 x 2 = 17 x 10
170 = 170
Your Turn Now: Use Associative Property to solve. (Hint:
Group the compatible numbers together.
1. (23 x 5) x 2
2. (9.5 + 4.9) + 5.1
a.__________________________________________________
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b.__________________________________________________
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Identity Properties
1. m + 3 = 3
3. 3m = 3
2. m + 0 = 3
4. h x 4 = 0
Tell which property is being illustrated. Then use mental math
to evaluate the expression.
1. (10.5 + 5.8) + 6.2 = 10.5 + (5.8 + 6.2)
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2. 4.2 + (2.8 + 11.95) = (4.2 + 2.8) + 11.95
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3. 1.5 + (1.74 + 3.5) = 1.5 + (3.5 + 1.74 )
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4. (3.7 + 8.9) + 6.3 = (8.9 + 3.7) + 6.3
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5. 5y = 5
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6. 5r = 0
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7. 7 + 0 = 7
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8. (27 x 2) x 5 = 27 x (2 x 5)
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9. 5 x 27 x 2 = 27 x 5 x 2
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10. Solve. Bakery. Find the total cost for a sweet roll that costs
$1.30, two hard rolls that cost $1.20 each, and a coffee cake
that costs $3.70.