Which correctly applies the distributive property to show an equivalent expression to (–2.1)(3.4)? (2)(3) – (0.1)(0.4) (–2)(3) + (–0.1)(0.4) (2.1)(3) – (2.1)(0.4) (–2.1)(3) + (–2.1)(0.4)
Answers
Answer:
Correct choice is option 4.
Step-by-step explanation:
The Distributive Property says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately:
a\cdot (b+c)=a\cdot b+a\cdot c.a⋅(b+c)=a⋅b+a⋅c.
Note that 3.4=3+0.4, then
(-2.1)\cdot 3.4=(-2.1)\cdot (3+0.4)=(-2.1)\cdot 3+(-2.1)\cdot 0.4.(−2.1)⋅3.4=(−2.1)⋅(3+0.4)=(−2.1)⋅3+(−2.1)⋅0.4.
As you can see this result is the same as in option 4.
Given : (–2.1)(3.4)
To Find : Which correctly applies the distributive property
(2)(3) – (0.1)(0.4)
(–2)(3) + (–0.1)(0.4)
(2.1)(3) – (2.1)(0.4)
(–2.1)(3) + (–2.1)(0.4)
Solution:
(a + b) c = ac + bc
a ( b + c) = ab + ac
(–2.1)(3.4)
= (-2 - 0.1)(3.4)
= (-2)(3.4) + (-0.1)(3.4)
or
(–2.1)(3.4)
= (-2.1) (3 + 0.4)
= (-2.1) (3) + (-2.1)(0.4)
Matches with the last option:
(–2.1)(3.4) = (–2.1)(3) + (–2.1)(0.4)
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