Distributive Property of Multiplication — Let's Practice!

Distributive Property of Multiplication — Let's Practice! exercise

• Solve 6$\times$15.

  Hints

  Break down the larger number into 2 smaller numbers that add to equal this larger number. For example: 7$\times$ 14 is equivalent to 7$\times$ (10 + 4)

  Next, distribute the number on the outside of the parentheses with the numbers on the inside. For example: for 7$\times$(10 + 4), we would multiply 7$\times$10 and 7$\times$4 separately.

  Finally, you add the two products you calculated in the previous step. For example: 7$\times$10 = 70, and 7$\times$4 = 28. So, you add 70 and 28 to get 98. The answer is 98.

  Solution

  15 is decomposed into 10 and 5 because we normally use the 10 and the number in the ones place:

  6$\times$15 is equivalent to 6$\times$(10 + 5)

  We distribute the 6 to the numbers inside the parentheses:

  6$\times$10 = 60, and 6$\times$ 5 = 30

  We add the 60 and the 30 and get 90

• Use the distributive property to write equivalent expressions.

  Hints

  Break down the larger number into 2 smaller numbers that add to equal this larger number. These smaller numbers are called addends. For example: in the expression 7$\times$(10 + 4), 10 and 4 are addends.

  If the larger number is greater than 10, one of its addends should be 10. There are often multiple possible addends to use, but writing one of them as 10 is usually the easiest way to solve.

  Remember, the numbers in the parentheses add (not multiply) to equal the larger number. For example: 7$\times$14 is equivalent to 7$\times$(10 + 4), not 7$\times$(7 + 2).

  Solution

  7$\times$14 is equivalent to 7$\times$(10 + 4) because 14 = 10 + 4

  18$\times$3 is equivalent to (10 + 8)$\times$3 because 18 = 10 + 8

  7$\times$8 is equivalent to 7$\times$(4 + 4) because 8 = 4 + 4

  17$\times$6 is equivalent to (10 + 7)$\times$6 because 17 = 10 + 7

• Solve the multiplication problem.

  Hints

  In order to determine how many guests Ethan has room to invite to the potluck, we need to determine how many total chairs there will be around the tables. To do this, multiply the number of tables by the number of chairs each table fits.

  There are 3 tables, and each table fits 14 chairs. Therefore, we need to multiply 3 by 14.

  Break down the 14 into two numbers that add to equal 14.

  (Setting one of these numbers as 10 is easiest for the calculation later)

  Then, distribute the 3 with these two numbers. This means multiply the 3 by these numbers.

  For example, distributing the 6 in 6$\times$(10 + 5) looks like this:

  Finally, add the two products.

  For example, from the previous hint: 6$\times$10 = 60, and 6$\times$5 = 30.

  We add 60 + 30 to calculate the final answer.

  Solution

  In order to determine how many guests Ethan has room to invite to the potluck, we need to determine how many total chairs there will be around the tables. To do this, multiply the number of tables by the number of chairs each table fits. There are 3 tables, and each table fits 14 chairs. Therefore, we need to multiply 3 by 14.

  3$\times$14 is equivalent to 3$\times$(10 + 4)

  We distribute the 3 to the numbers inside the parentheses:

  3$\times$10 = 30, and 3$\times$4 = 12

  Finally, we add the 30 and the 12 and calculate 42 guests

• Solve the multiplication problem.

  Hints

  In order to determine how much money Sara will spend on goodie bags, we need to multiply the cost of each goodie bag by the number of guests.

  Each goodie bag costs $4, and there will be 13 guests. Therefore, we need to multiply 4 by 13.

  Break down the 13 into two numbers that add to equal 13.

  (Setting one of these numbers as 10 is easiest for the calculation later)

  Then, distribute the 4 with these two numbers. This means multiply the 4 by these numbers.

  For example, distributing the 6 in 6$\times$(10 + 5) looks like this:

  Finally, add the two products.

  For example, from the previous hint: 6$\times$10 = 60, and 6$\times$5 = 30.

  We add 60 + 30 to calculate the final answer.

  Solution

  In order to determine how much money Sara will spend on goodie bags, we need to multiply the cost of each goodie bag by the number of guests. Each goodie bag costs $4, and there will be 13 guests. Therefore, we need to multiply 4 by 13.

  4$\times$13 is equivalent to 4$\times$(10 + 3)

  We distribute the 4 to the numbers inside the parentheses:

  4$\times$10 = 40, and 4$\times$3 = 12

  Finally, we add the 40 and the 12 and calculate 52 dollars

• Use the distributive property to calculate the following products.

  Hints

  Break down the larger number into two smaller numbers to write an equivalent expression.

  For example: 11$\times$9 is equivalent to (10 + 1)$\times$9

  Distribute the number on the outside of the parentheses.

  For example: (10 + 1)$\times$9 = 10$\times$9 + 1$\times$9

  Add the two products.

  For example: 10$\times$9 + 1$\times$9 = 90 + 9

  Solution

  Break down the larger number into two smaller numbers to write an equivalent expression:

  11$\times$9 is equivalent to (10 + 1)$\times$9

  Then, distribute the number on the outside of the parentheses:

  (10 + 1)$\times$9 = 10$\times$9 + 1$\times$9

  Finally, add the two products:

  90 + 9 = 99

  4$\times$12 = 4$\times$(10 + 2) = 4$\times$10 + 4$\times$2 = 40 + 8 = 48

  5$\times$20 = 5$\times$(10 + 10) = 5$\times$10 + 5$\times$10 = 50 + 50 = 100

  2$\times$13 = 2$\times$(10 + 3) = 2$\times$10 + 2$\times$3 = 20 + 6 = 26

• Solve 8$\times$21.

  Hints

  We can still use the distributive property if there are 3 or more numbers inside the parentheses.

  We can break down the 21 into 10 + 10 + 1.

  There are several options of how to break down the 21, so this is not the only approach.

  If we break down the 21 into 10 + 10 + 1...

  8$\times$21 would be equivalent to 8$\times$(10 + 10 + 1).

  8$\times$(10 + 10 + 1) = 8$\times$10 + 8$\times$10 + 8$\times$1

  Solution

  There are several options of how to break down 21. One is breaking it down into 3 numbers: 10 + 10 + 1.

  (We can still use the distributive property if there are 3 or more numbers inside the parentheses)

  So, 8$\times$21 is equivalent to 8$\times$(10 + 10 + 1).

  Distributing the 8 gives us: 8$\times$10 + 8$\times$10 + 8$\times$1 = 80 + 80 + 8 = 168.

  Other options of how to break down the 21 include 7 + 7 + 7, or 10 + 11. The 10 + 11 option is useful only if you know how to calculate 8$\times$11 easily.