Question

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{0.5cm}} tens $\times$ \underline{\hspace{0.5cm}} hundreds = 993 \underline{\hspace{1cm}}
$3,310 \times 300 =$ \underline{\hspace{1cm}}

f. $500 \times 600$
\underline{\hspace{0.5cm}} hundreds $\times$ \underline{\hspace{0.5cm}} 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:

1a

• Step1: Calculate 23×2 = 46 → 46 tens
• Step2: 46 tens = 46×10 = 460

1b

• Step1: 23×2 = 46 → 46 hundreds
• Step2: 46 hundreds = 46×100 = 4600

1c

• Step1: 41×4 ones = 164 ones
• Step2: 164 ones = 164

1d

• Step1: 41×4 = 164; tens×hundreds = ten-thousands → 164 ten-thousands
• Step2: 164×10000 = 164000

1e

• Step1: 3310=331 tens, 300=3 hundreds; 331×3=993 → 993 ten-thousands
• Step2: 993×10000 = 993000

1f

• Step1: 500=5 hundreds, 600=6 hundreds; 5×6=30 → 30 ten-thousands
• Step2: 30×10000 = 300000

2a

• Step1: Right side: 2×3=6 tens×tens=6 hundreds
• Step2: 6 tens≠6 hundreds → False

2b

• Step1: Left: 44×20×10=8800; Right:440×2=880
• Step2: 8800≠880 → False

2c

• Step1: 90 hundreds=90×100=9000; 900 tens=900×10=9000
• Step2: Both sides equal → True

2d

• Step1: Left:64×8×100=51200; Right:640×8×10=51200
• Step2: Both sides equal → True

Answer:

a. 46 tens; 460
b. 46 hundreds; 4600
c. ones; 164
d. ten-thousands; 164000
e. 331 tens × 3 hundreds = 993 ten-thousands; 993000
f. 5 hundreds × 6 hundreds = 30 ten-thousands; 300000
2a. False
2b. False
2c. True
2d. True