(-6/5) \left[ (4/3) + (1/4) \right] = \left( (-6/5) \times (4/3) \right) + \left( (-6/5) \times (1/4) \right)
Answer (2)
The equation demonstrates the distributive property of multiplication over addition in mathematics. After performing the calculations on both sides, we find they are equal, which confirms the validity of the property. Thus, the expression holds true as stated.
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The equation you provided is an example of the distributive property in mathematics. The distributive property allows you to multiply a sum by a factor by distributing, or spreading, the multiplication over each of the addends within the parentheses.
Here's a step-by-step explanation of how the distributive property is applied in your question:
Firstly, look at the expression on the left side of the equation:
( − 5 6 ) ( 3 4 + 4 1 )
This can be distributed as follows:
= ( ( − 5 6 ) × 3 4 ) + ( ( − 5 6 ) × 4 1 )
This is the expression on the right side of your equation. Both expressions are equal because of the distributive property, which states that:
a ( b + c ) = ab + a c
In your example:
a = − 5 6
b = 3 4
c = 4 1
Now we can evaluate each part:
Calculate ( − 5 6 ) × 3 4 :
= − 5 6 × 3 4 = − 15 24 = − 5 8
Calculate ( − 5 6 ) × 4 1 :
= − 5 6 × 4 1 = − 20 6 = − 10 3
Now, combine the results of the two products:
− 5 8 + ( − 10 3 )
To add these fractions, find a common denominator, which is 10:
− 5 8 = − 10 16
Adding the fractions, we get:
− 10 16 + ( − 10 3 ) = − 10 19
So, the equation confirms that both the left and right sides are equivalent, as shown through the correct application of the distributive property.
