Fill in the blanks. Also write the name of the property used.
a. 3193 × 1 = ______ ( )
b. 4234 × 0 = ______ ( )
c. 2513 × 5216 = ______ × 2513 ( )
d. 9062 × ______ = 807 × ______ ( )
e. 4023 × ______ = 0 ( )
f. 9128 × ______ = 9128 ( )
g. 314 × (63 × 23) = ( ______ × ______ ) × 23 ( )
h. 403 × (100 × 15) = (403 × ______ ) × ______ ( )
Answer (2)
In mathematics, multiplication has several important properties that are consistently used to simplify and solve problems. Let's address each part of your question by filling in the blanks and identifying the properties used:
(a) 3193 × 1 = 3193 (Identity Property of Multiplication)
The Identity Property of Multiplication states that any number multiplied by 1 stays the same.
(b) 4234 × 0 = 0 (Zero Property of Multiplication)
The Zero Property of Multiplication tells us that any number multiplied by zero is zero.
(c) 2513 × 5216 = 5216 × 2513 (Commutative Property of Multiplication)
The Commutative Property of Multiplication indicates that changing the order of the factors does not change the product.
(d) 9062 × 807 = 807 × 9062 (Commutative Property of Multiplication)
Again, this is the Commutative Property of Multiplication, showing that the order of multiplication can be switched.
(e) 4023 × 0 = 0 (Zero Property of Multiplication)
Here, the Zero Property of Multiplication is applied, confirming that multiplying any number by zero results in zero.
(f) 9128 × 1 = 9128 (Identity Property of Multiplication)
The Identity Property of Multiplication is used here to show that multiplying by 1 keeps the number unchanged.
(g) 314 × ( 63 × 23 ) = ( 314 × 63 ) × 23 (Associative Property of Multiplication)
The Associative Property of Multiplication states that the grouping of numbers does not affect the product.
(h) 403 × ( 100 × 15 ) = ( 403 × 100 ) × 15 (Associative Property of Multiplication)
Once again, the Associative Property of Multiplication shows that how numbers are grouped in an operation does not change the result.
These properties are fundamental in mathematics and often help simplify complex calculations and bolster understanding of the underlying structure of arithmetic.
The answer consists of completing multiplication equations and identifying their properties. Each equation demonstrates properties such as the Identity Property, Zero Property, Commutative Property, and Associative Property of Multiplication. These properties are fundamental in mathematics for understanding multiplication.
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