Question

name
date

1. fill in the blanks using your knowledge of place value units and basic facts.

a. $23 \times 20$
think: 23 ones $\times$ 2 tens = \underline{\hspace{1cm}} tens
$23 \times 20 =$ \underline{\hspace{1cm}}
b. $230 \times 20$
think: 23 tens $\times$ 2 tens = \underline{\hspace{1cm}}
$230 \times 20 =$ \underline{\hspace{1cm}}
c. $41 \times 4$
41 ones $\times$ 4 ones = 164 \underline{\hspace{1cm}}
$41 \times 4 =$ \underline{\hspace{1cm}}
d. $410 \times 400$
41 tens $\times$ 4 hundreds = 164 \underline{\hspace{1cm}}
$410 \times 400 =$ \underline{\hspace{1cm}}
e. $3,310 \times 300$
\underline{\hspace{1cm}} tens $\times$ \underline{\hspace{1cm}} hundreds = 993 \underline{\hspace{1cm}}
$3,310 \times 300 =$ \underline{\hspace{1cm}}
f. $500 \times 600$
\underline{\hspace{1cm}} hundreds $\times$ \underline{\hspace{1cm}} hundreds = 30 \underline{\hspace{1cm}}
$500 \times 600 =$ \underline{\hspace{1cm}}

1. determine if these equations are true or false. defend your answer using your knowledge of place value and the commutative, associative, and/or distributive properties.

a. 6 tens $= 2$ tens $\times 3$ tens
b. $44 \times 20 \times 10 = 440 \times 2$
c. 86 ones $\times 90$ hundreds $= 86$ ones $\times 900$ tens
d. $64 \times 8 \times 100 = 640 \times 8 \times 10$

Explanation:

Problem 1a

Step1: Calculate 23 ones × 2 tens

23 ones × 2 tens = 23 × 2 tens = 46 tens

Step2: Calculate 23 × 20

Since 46 tens = 46 × 10 = 460, so 23 × 20 = 460

Step1: Analyze 23 tens × 2 tens

23 tens × 2 tens = 23 × 2 × (tens × tens) = 46 × 100 = 4600 (because tens × tens = hundreds)

Step2: Calculate 230 × 20

230 is 23 tens, 20 is 2 tens, so 23 tens × 2 tens = 46 hundreds = 4600, so 230 × 20 = 4600

Step1: Determine the unit for 41 ones × 4 ones

41 ones × 4 ones = 164 ones (because ones × ones = ones)

Step2: Calculate 41 × 4

41 × 4 = 164

Answer:

46; 460

Problem 1b