For which expressions would you use the Distributive Property? Select two answers.
A. 6.5(11.5)
B. 2.1(5.3 + 6.9)
C. -8.4(1.5 - 7.3****
D. −12.5(3.9) + 5.1
E. 1.9 − 6.2(9.4)****
C and also B
not E
better review the distributive property.
To determine which expressions require the use of the Distributive Property, we need to look for expressions that involve the multiplication of terms within parentheses. The Distributive Property states that for any numbers a, b, and c, the expression a(b + c) is equivalent to ab + ac.
Let's analyze each option:
A. 6.5(11.5): This expression involves multiplying two numbers, but there are no parentheses or terms to distribute. Therefore, the Distributive Property is not applicable here.
B. 2.1(5.3 + 6.9): This expression contains terms within parentheses that need to be distributed. Using the Distributive Property, we have:
2.1(5.3) + 2.1(6.9)
This simplifies to:
11.13 + 14.49
C. -8.4(1.5 - 7.3): Similar to option B, this expression has terms within parentheses that need to be distributed. Applying the Distributive Property, we get:
(-8.4)(1.5) + (-8.4)(-7.3)
This simplifies to:
-12.6 + 61.32
D. −12.5(3.9) + 5.1: There are no terms within parentheses that need to be distributed; instead, we have two separate multiplication operations. The Distributive Property is not applicable here.
E. 1.9 − 6.2(9.4): This expression involves multiplying a number by a term within parentheses. Using the Distributive Property, we have:
1.9 - (6.2)(9.4)
This simplifies to:
1.9 - 57.88
So, the options that require the use of the Distributive Property are B. 2.1(5.3 + 6.9) and E. 1.9 − 6.2(9.4).