1.08 Number operation properties
State whether each expression is an example of the associative law, commutative law, reordering or distributive law.
54 \div 9 = 9 \div 54
126 \div 3 = (120 + 6)\div3
State whether the following statements are true or false.
4 \times \left(3 + 5\right) = 4 \times 3 + 4 \times 5
4 + \left( 3 \times 5\right) = 4 \times 3 + 4 \times 5
\left( 4 \times 3\right) + 5 = 4 \times 5 + 3 \times 5
\left(4 + 3\right) \times 5 = 4 \times 5 + 3 \times 5
Fill in the boxes to complete the working out using the associative law.
35 + 29 + 11 = 35 + ( ⬚ + ⬚ )
28 + 46 - 16 = 28 + ( ⬚ - ⬚ )
Consider 27 + 48 + 13.
Which pair of numbers will be easiest to add together first?
Fill in the boxes to complete the working out.
27 + 48 + 13 = 27 + ( ⬚ + ⬚ )
Fill in the boxes to complete the working out using the associative law.
13 \times 4 \times 5 = ⬚ \times ( 4 \times ⬚ )
Evaluate 17 + 39 + 23 using reordering.
Consider 52 - 24 - 12.
Is 52 - 12 - 24 equal to the above expression?
Which of the arithmetic rules can we apply to the expression to transform it into \\ 52 - 12 - 24?
Derek is evaluating the subtraction below. He noticed that it would be easier to subtract 27 from 47 first and rearranged the numbers using reordering.
Complete the following statement and then evaluate it:
47 - 18 - 27 = ⬚ - 27 - ⬚
Consider 56 - 18 - 26.
Which of the two numbers will be easier to subtract from 56 first?
Complete the following statement and then evaluate it:
56 - 18 - 26 = 56 - ⬚ - ⬚
Evaluate 57 - 29 - 17 using reordering.
Consider 48 \div 8 \div 2.
Is 48 \div 2 \div 8 equal to the above expression?
Which of the arithmetic rules can we apply to the expression to transform it into \\ 48 \div 2 \div 8?
Consider 4 \times 13 \times 5.
Which pair of numbers will be easiest to multiply together first?
Complete the following statement and then evaluate it:
4 \times 13 \times 5 = ⬚ \times ⬚ \times 13
Evaluate 4 \times 17 \times 5 using regrouping.
Consider 35 \times 23.
Complete the following statement:
35 \times 23 is the same as 35 \times ( 20 + ⬚ ).
Complete the following statement:
35 \times \left(20 + 3\right) is the same as 35 \times ⬚ + 35 \times 3.Which arithmetic rule explains the equality between 35 \times 23 and 35 \times 20 + 35 \times 3?
Evaluate the expression.
Consider 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 ⬚.
Which arithmetic rule explains the equality between 26 \times 29 and 26 \times 30 - 26 \times 1?
Evaluate the expression.
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 rectangle below:
Find the total area of the rectangle.
Find the non-shaded area of the rectangle.
Find the shaded area of the rectangle.
Evaluate the following using the distributive law.
Dave is evaluating 132 \div 11 \div 4. He noticed that it would be easier to divide 132 by 4 first and rearranged the numbers using reordering.
Fill in the boxes to complete his working out.
132 \div 11 \div 4 = 132 \div ⬚ \div 11
Consider 168 \div 7.
Fill in the box to complete the sentence.
168 \div 7 = ( 140 + ⬚ )\div 7.
Fill in the box to complete the sentence.
\left(140 + 28\right) \div 7 is the same as 140 \div 7 + ⬚ \div 7.
Which arithmetic rule explains the equality between 168 \div 7 and 140 \div 7 + 28 \div 7?
Evaluate the expression.
Consider 119 \div 7.
Fill in the box to complete the sentence.
119 \div 7 is the same as ( 140 - ⬚ )\div 7.
Fill in the box to complete the sentence.
\left(140 - 21\right) \div 7 is the same as 140 \div ⬚ - 21 \div ⬚.
Which arithmetic rule explains the equality between 119 \div 7 and 140 \div 7 - 21 \div 7?
Evaluate the expression.
Evaluate the following using the distributive law.