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Chapter 2: Q5. (page 72)

Evaluate the expression using the distributive property and mental math.

4  (105)

Short Answer

Expert verified

4(105)=420.

Step by step solution

01

Step-1 – What are real numbers? 

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

02

Step-2 – Distributive Property of Multiplication 

Suppose a, b, and c is three real numbers.

Distributive Property of Multiplication

Property: a  (b  +  c  )  =  a  ·  b  +  a  ·  c  

Example: 12  (3  +  4  )  =  12  ·  3  +  12  ·  4  =  36  +  48  =  84

03

Step-3:  Evaluate the expression using the distributive property and mental math.        

We can write 105 as 100+ 5, to evaluate the expression 4(105), we can use the distributive method of multiplication.

Distributive Property of Multiplication

Property: a  (b  +  c  )  =  a  ·  b  +  a  ·  c  

4 ( 105 ) â¶Ä‰= â¶Ä‰4 â¶Ä‰( â¶Ä‰100 â¶Ä‰+ â¶Ä‰5 â¶Ä‰) â¶Ä‰= â¶Ä‰4 â¶Ä‰Â·â€‰â¶Ä‰100 â¶Ä‰+ â¶Ä‰4 â¶Ä‰Â·â€‰â¶Ä‰5 â¶Ä‰= â¶Ä‰400 â¶Ä‰+ â¶Ä‰20 â¶Ä‰= â¶Ä‰420 4(105)=420

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Most popular questions from this chapter

Simplify the expression.

-2+y+8

Extended Problem Solving For a cylindrical corn silo with the dimensions shown, the weight W (in pounds) of the corn silage inside is typically given by W  =  4400  (  40  -  d), where d is the distance (in feet) from the top of the corn to the top of the silo.

a. Use the distributive property to write the given formula without parentheses.

b. Calculate Suppose d 15 feet. What is the weight of the corn in the silo?

c. Interpret and apply how many days will the amount of corn from part (b) last if it is used to feed a herd of 100 cows and each cow eats 10 pounds of corn a day?

Are 2(x+1)  and  2x+1 equivalent variable expressions? Explain.

Use the distributive property to write an equivalent variable expression.

( s  +  20  ) (- 7)

Use the distributive property to evaluate the expression.

3  -14  (-5)
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