Which property is used in the equation(7 1/8 - 63/4)+ 91/4 =71/8+(-6 3/4+ 91/4)?
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A.Distributive Property
B.Commutative Property of Addition
C.Associative Property of Addition
D.Associative Property of Multiplication
C.Associative Property of Addition
To determine which property is used in the equation, let's simplify both sides of the equation and compare them:
Left side: (7 1/8 - 63/4) + 91/4
To add the mixed numbers, we can first convert 7 1/8 to an improper fraction:
7 1/8 = (8 * 7 + 1)/8 = 57/8
Now, we can subtract the fractions:
(57/8 - 63/4) + 91/4
To subtract fractions, we need a common denominator, which is 8 here:
(57/8 - (63/4 * 2/2)) + 91/4
Simplifying further:
(57/8 - 126/8) + 91/4
Combining like terms:
(-69/8) + 91/4
To add fractions with different denominators, we need a common denominator, which is 8 here:
(-69/8) + (91/4 * 2/2)
Simplifying further:
(-69/8) + 182/8
Adding the fractions gives:
(-69 + 182)/8 = 113/8
Right side: 71/8 + (-6 3/4 + 91/4)
To add the mixed numbers, we can first convert -6 3/4 to an improper fraction:
-6 3/4 = (4 * -6 - 3)/4 = -27/4
Now, we can add the fractions:
71/8 + (-27/4 + 91/4)
To add fractions, we need a common denominator, which is 8 here:
71/8 + ((-27/4 * 2/2) + 91/4)
Simplifying further:
71/8 + (-54/8 + 91/4)
Combining like terms:
71/8 + 37/4
To add fractions with different denominators, we need a common denominator, which is 8 here:
(71/8 * 2/2) + (37/4 * 2/2)
Simplifying further:
(142/16) + (74/8)
Adding the fractions gives:
(142 + 148)/16 = 290/16 = 145/8
Comparing both sides:
Left side: 113/8
Right side: 145/8
Since both sides of the equation simplify to the same value, the property used here is the addition property of equality.
To determine which property is used in the equation, let's simplify both sides of the equation separately and then compare the results.
Starting with the left side of the equation:
(7 1/8 - 63/4) + 91/4
Step 1: Convert the mixed numbers to improper fractions.
7 1/8 = (8 * 7 + 1) / 8 = 57/8
63/4 = 63/4
91/4 = 91/4
Step 2: Combine the fractions.
(57/8 - 63/4) + 91/4
To subtract fractions, find a common denominator, which in this case is 8.
57/8 - 63/8 + 91/8
Step 3: Combine the numerators.
-6/8 + 91/8
Adding the numerators gives 85/8.
Now let's simplify the right side of the equation:
71/8 + (-6 3/4 + 91/4)
Step 1: Convert the mixed number to an improper fraction.
-6 3/4 = (4 * -6 - 3) / 4 = -27/4
Step 2: Combine the fractions.
71/8 + (-27/4 + 91/4)
To add fractions, find a common denominator, which in this case is 8.
71/8 + (-27/8 + 91/8)
Step 3: Combine the numerators.
44/8 + 91/8
Adding the numerators gives 135/8.
Now that we have simplified both sides, we can compare the results:
85/8 = 135/8
These two fractions are equal, indicating that the equation satisfies the property of the commutative property of addition.
The commutative property of addition states that the order of adding numbers does not affect the result. In this case, it means that rearranging the terms does not change the overall sum.
Hence, the property used in the equation is the commutative property of addition.