1.04 The distributive property
Consider the addition 33 + 27.
Find the greatest common factor of 33 and 27.
By completing the following work, rewrite 33 + 27 as an equivalent multiplication using the distributive property:
\begin{aligned} 33+27 & = 3 \times (⬚+⬚) \\& =⬚ \times 20 \end{aligned}
Consider the subtraction 96 - 80.
Find the greatest common factor of 96 and 80.
By completing the following work, rewrite 96 - 80 as an equivalent multiplication using the distributive property:
\begin{aligned} 96-80 & = 16 \times (⬚-⬚) \\& =16 \times ⬚ \end{aligned}
Complete the following statements using the distributive property:
11 \times \left(8 - 3\right) = 88 - ⬚
6 \times \left(10 + 9\right) = ⬚ + 54
7 \times \left(7 - 2\right) = 49 - ⬚
3 \times \left(5 + 17\right) = 15 + ⬚
Complete the following statements using the distributive property:
42 + 39 = 3 \times \left( ⬚ + ⬚ \right)
72 + 26 = ⬚ \times \left( ⬚ + 13 \right)
24 - 15 = ⬚ \times \left( 8 - ⬚ \right)
63 - 49 = 7 \times \left( ⬚ - ⬚ \right)
Complete the following statements:
\left(⬚ + 6\right) \times \left(⬚ - 3\right) = 15 \left(7 - 3\right)
\left(⬚ + 11\right) \times \left(⬚ - 5\right) = 21 \left(9 - 5\right)
\left(11 + ⬚\right) \times \left(7 + ⬚\right) = 15 \left(7 + 2\right)
\left(⬚ - 2\right) \times \left(⬚ + 3\right) = 10 \left(8 + 3\right)
Vanessa is making bouquets of roses and lilies. She has 18 red roses and 99 white lilies and wants to use all of them with none left over.
Find the largest number of bouquets she can make if all bouquets are identical.
How many of each type of flower will go in each bouquet?
Rewrite the scenario as an equivalent statement in terms of the number of bouquets using the distributive property.
Amy is splitting a number of students into groups for a treasure hunt. She has 63 boys and 81 girls and doesn't want any boys or girls left out.
Find the largest number of groups she can make if each group has the same number of boys and the same number of girls.
How many males and females need to go into each group?
Rewrite the scenario as an equivalent statement in terms of the number of groups using the distributive property.
Valentina is making decorations her school's gym for a party. She has 25 yellow balloons and 15 green balloons and she wants the balloons to be divided into equal groups so that each group contains the same number of green balloons and same number of yellow balloons.
Find the largest number of groups she can make if all groups are identical.
How many of each balloon color will go in each group?
Rewrite the scenario as an equivalent statement in terms of the number of groups using the distributive property.
Hermione and Yuri both earn \$11 per hour in their casual job. In a day where one works for 7 hours and the other works for 2 hours, write a number sentence that can be used to evaluate the difference in their wages.
Avril and Quiana played a game of tennis over 4 days. Each day, Avril won 7 sets and Quiana won 5 sets. Quiana wanted to keep playing until she won more sets in a single day, but over the next 2 days, the same thing happened. Each day, Avril won 7 sets and Quiana won 5 sets.
Write a number sentence that can be used to calculate how many more sets did Avril win over the entire 6 days.