1.03 Properties of number operations
Determine whether the following statements are true or false:
96 + 12 + 4 = 96 + \left(12 + 4\right)
96 - 12 - 4 = 96 - \left(12 - 4\right)
96 \times 12 \times 4 = 96 \times \left( 12 \times 4\right)
96 \div 12 \div 4 = 96 \div \left( 12 \div 4\right)
Rewrite the expression 27 + 39 + 11 using the associative property.
Rewrite the expression 13 \times 4 \times 5 using the associative property.
For each of the following, complete the work using the associative property:
\begin{aligned} 36+29+11&= 36+(⬚+⬚)\\&=36+⬚\\&=⬚ \end{aligned}
\begin{aligned} 13 \times 4 \times5&= 13\times(⬚\times ⬚)\\&=13 \times ⬚\\&=⬚ \end{aligned}
Determine whether the following statements are true or false:
24 + 6 = 6 + 24
24 - 6 = 6 - 24
24 \times 6 = 6 \times 24
24 \div 6 = 6 \div 24
Rewrite the expression 27 + 48 + 13 using the commutative property.
Rewrite the expression 4 \times 13 \times 5 using the commutative property.
Neville is evaluating 4 \times 17 \times 5. He noticed that it would be easier to multiply 4 and 5 together first and rearranged the numbers by reordering using the commutative property.
Complete his work:
\begin{aligned} 4 \times 17 \times 5&= 4 \times 5 \times 17\\&=⬚\times 17\\&=⬚ \end{aligned}
Consider 27 + 49 + 13.
Which pair of numbers will be easiest to add together first?
Complete the following work:
\begin{aligned} 27+49+13&= 49+⬚+⬚\\&=49+⬚\\&=⬚ \end{aligned}
Consider 4 \times 13 \times 5.
Which pair of numbers will be easiest to multiply together first?
Complete the following work:
\begin{aligned} 4 \times 13 \times 5 &= 4 \times ⬚ \times ⬚ \\&= ⬚ \times ⬚ \\&= ⬚ \end{aligned}
Evaluate the expression 28 + 39 + 12 by reordering using the commutative property.
Evaluate 4 \times 17 \times 5 using regrouping.
Determine whether the following statements are true or false:
120 + \left(4 + 5\right) = \left(120 + 4\right) + \left(120 + 5\right)
120 - \left(4 + 5\right) = \left(120 - 4\right) + \left(120 - 5\right)
\left(15 + 10\right) \times 5 = \left( 15 \times 5\right) + \left( 10 \times 5\right)
\left(15 + 10\right) \div 5 = \left( 15 \div 5\right) + \left( 10 \div 5\right)
120 \times \left(4 + 5\right) = \left( 120 \times 4\right) + \left( 120 \times 5\right)
120 \div \left(4 + 5\right) = \left( 120 \div 4\right) + \left( 120 \div 5\right)
Consider the expression 16 \times 23.
Complete the following statement:
16 \times 23 is the same as 16 \times ( 20 +⬚).
Complete the following statement:
16 \times \left(20 + 3\right) is the same as 16 \times ⬚ + 16 \times 3.
Evaluate the expression 16 \times 23.
Consider the expression 26 \times 29.
Complete the following statement:
26 \times 29 is the same as 26 \times ( ⬚ - 1 ).
Complete the following statement:
26 \times \left(30 - 1\right) is the same as 26 \times 30 - 26 \times ⬚.
Evaluate the expression 26 \times 29.
Consider the expression 42 \div 3.
Complete the following statement:
42 \div 3 is the same as(30+⬚ )\div 3.
Complete the following statement:
\left(30 + 12\right) \div 3 is the same as 30 \div 3 + ⬚ \div 3.
Evaluate the expression 42 \div 3.
Consider the expression 87 \div 3.
Complete the following statement:
87 \div 3 is the same as ( 90 -⬚)\div 3 .
Complete the following statement:
\left(90 - 3\right) \div 3 is the same as 90 \div 3-3 \div ⬚ .
Evaluate the expression 87 \div 3.
Evaluate the following using the distributive property:
6 \times 94
8 \times 1003
7 \times 996
9 \times 998
7 \times 1002
11 \times 124
6 \times 412
8 \times 1997
Consider the following rectangle:
Find the area of Area 1.
Find the area of Area 2.
Find the total area of the rectangle.
Consider the following rectangle:
Find the total area of the rectangle.
Find the unshaded area of the rectangle.
Find the shaded area of the rectangle.
