Question

At a ski resort, 1/4 of the 300 skiers are beginners,and 1/4 of the 260 snowboarders are beginners.The resort staff used the distributive property to make the calculation of the total number of beginners on the ski slopes. Write an expression demonstrates the distributive property? Explain your answer with at least 5 sentences. * 16 points

Answer 1

The expression demonstrating distributive property to make calculation of the total number of beginners on the ski slopes is
`(1)/(4) * 300 + (1)/(4) * 260 = (1)/(4)(300 + 260)`

Solution:

From given question,

`(1)/(4)` of the 300 skiers are beginners

`(1)/(4)` of the 260 snowboarders are beginners

The resort staff used the distributive property to make the calculation of the total number of beginners on the ski slopes

Let us first understand about distributive property

The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum

a(b + c) = ab + bc

Beginners in skiers =
`(1)/(4)` of 300

Beginners in snowboarders =
`(1)/(4)` of the 260

Total number of beginners = Beginners in skiers + Beginners in snowboarders

`\text{ Total number of beginners } = (1)/(4)(300) + (1)/(4)(260)`

Now let us apply distributive property

Factor out
`(1)/(4)` to get the distributive property

`(1)/(4)(300) + (1)/(4)(260) = (1)/(4)(300+260)`

`(1)/(4) * 300 + (1)/(4) * 260 = (1)/(4)(300 + 260)`

Thus the expression demonstrating distributive property is found