IM 6.6.9 Practice: The Distributive Property, Part 1

Select [b]all[/b] the expressions that represent the area of the large, outer rectangle.[br][img]data:image/png;base64,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[/img]

[math]5(2+4)[/math] [math]5+2+4[/math] [math]5\cdot6[/math] [math]5\cdot2\cdot4[/math] [math]5\cdot2+4[/math] [math]5\cdot2+5\cdot4[/math]

Draw and label diagrams that shows these two methods for calculating 19 ᐧ 50: (1) First find 10 ᐧ 50 and then add 9 ᐧ 50.

Draw and label diagrams that shows these two methods for calculating 19 ᐧ 50: (2) First find 20 ᐧ 50 and then take away 50.

Complete each calculation using the distributive property.

[math]98\cdot24[/math][br][math]\left(100-2\right)\cdot24[/math][br]...

[math]21\cdot15[/math][br][math]\left(20+1\right)\cdot15[/math][br]...

[math]0.51\cdot40[/math][br][math]\left(0.5+0.01\right)\cdot40[/math][br]...

A group of 8 friends go to the movies. A bag of popcorn costs $2.99. How much will it cost to get one bag of popcorn for each friend? Explain how you can calculate this amount mentally.

Draw diagrams of a+a+a+a and 4a when a is 1, 2, and 3. What do you notice?

Do [math]a+a+a+a[/math] and [math]4a[/math] have the same value for any value of [math]a[/math]? Explain how you know.

120% of x is equal to 78.

Write an equation that shows the relationship of 120%, [math]x[/math] , and 78.

Use your equation to find [math]x[/math]. Show your reasoning.

Kiran’s aunt is 17 years older than Kiran.

How old will Kiran’s aunt be when Kiran is: 15 years old?

How old will Kiran’s aunt be when Kiran is: 30 years old?

How old will Kiran’s aunt be when Kiran is: [math]x[/math] years old?

How old will Kiran be when his aunt is 60 years old?