Ten thousands

Thousands

Hundreds

tens

ones

4

8

5

7

3

Six hundreds twentyfives

One hundred twentyfives

twentyfives

fives

ones

1

3

4

1

2

8 6 4 × 3 6 _______________ 
3 4 3_{5} × 2 4_{5} ______________ 
5 3 2 8 6 4 × 3 6 _______________ 5 1 8 4 
3 3 2 3 4 3_{5} × 2 4_{5} ______________ 3 0 3 2_{5} 
Step 1: 6 × 4 = 24. 24 = 10 + 10 + 4 You have 2 tens to carry. Write 4 down in the ones place. Carry 2 tens by putting 2 in the tens place (Shown in red) 
Step 1: 4 × 3 = 12. 12 = 5 + 5 + 2 You have 2 fives to carry. Write 2 down in the ones place. Carry 2 fives by putting 2 in the fives place (Shown in red) 
Step 2: 6 × 6 = 36. 36 + 2 = 38 tens 38 tens = 10 tens + 10 tens + 10 tens + 8 tens = 100 + 100 + 100 + 80 = 100 + 100 + 100 + 8 tens You have 3 hundreds to carry. Write 8 down in the tens place and carry 3 hundreds by putting 3 in the hundreds place (Shown in green) 
Step 2: 4 × 4 = 16. 16 + 2 = 18 fives 18 fives = 5 fives + 5 fives + 5 fives + 3 fives = 25 + 25 + 25 + 15 = 25 + 25 + 25 + 3 fives You have 3 twentyfives to carry. Write 3 down in the fives place and carry 3 twentyfives by putting 3 in the twentyfives place (Shown in green) 
Step 3: 6 × 8 = 48. 48 + 3 = 51 hundreds 51 hundreds = 10 hundreds + 10 hundreds + 10 hundreds + 10 hundreds + 10 hundreds + 1 hundred = 1000 + 1000 + 1000 + 1000 + 1000 + 100 = 1000 + 1000 + 1000 + 1000 + 1000 + 1 hundred You have 5 thousands to carry. Write 1 down in the hundreds place and carry 5 thousands by putting 5 in the thousands place (Shown in black) Bring down the 5 in the thousands place 
Step 3: 4 × 3 = 12. 12 + 3 = 15 twentyfives 15 twentyfives = 5 twentyfives + 5 twentyfives + 5 twentyfives + 0 twentyfive = 125 + 125 + 125 + 0 = 125 + 125 + 125 + 0 twentyfive You have 3 one hundred twentyfives to carry. Write 0 down in the twenty fives place and carry 3 one hundred twentyfives by putting 3 in the one hundred twentyfive place (Shown in black) Bring down the 3 in the one hundred twentyfives place. Notice again the 0 in the twentyfives place. 
2 1 1 8 6 4 × 3 0 ______________________ 2 5 9 2 0 
1 1 1 3 4 3_{5} × 2 0_{5} _____________________ 1 2 4 1 0_{5} 
Step 6: 3 × 4 = 12 tens. 12 tens = 10 tens + 2 tens = 100 + 2 tens Carry 1 hundred by putting 1 in the hundreds place (Shown in red) Write 2 down in the tens place. Since there is nothing in the ones place, just put a 0. 
Step 6: 2 × 3 = 6 fives. 6 fives = 5 fives + 1 five = 25 + 1 five Carry 1 twenty five by putting 1 in the twentyfives place (Shown in red) Write 1 down in the fives place. Since there is nothing in the ones place, just put a 0. 
Step 7: 3 × 6 = 18 hundreds. 18 hundreds + 1 hundred = 19 hundreds 19 hundreds = 10 hundreds + 9 hundreds = 1000 + 9 hundreds Write 9 down in the hundreds place and carry 1 thousand by putting 1 in the thousand place (Shown in green) 
Step 7: 2 × 4 = 8 twentyfives. 8 twentyfives + 1 twentyfive = 9 twentyfives 9 twentyfives = 5 twentyfives + 4 twentyfives = 125 + 4 twentyfives Write 4 down in the twentyfives place and carry 1 one hundred twentyfive by putting 1 in the one hundred twentyfive place (Shown in green) 
Step 8: 3 × 8 = 24 thousands. 24 thousands + 1 thousand = 25 thousands 25 thousands = 10 thousands + 10 thousands + 5 thousands = 10000 + 10000 + 5 thousands Write 5 down in the thousands place and carry 2 ten thousands by putting 2 in the ten thousands place (Shown in black) Bring the 2 down in the ten thousands place 
Step 8: 2 × 3 = 6 one hundred twentyfives. 6 one hundred twentyfives + 1 one hundred twenty five = 7 one hundred twentyfives 7 one hundred twentyfives = 5 one hundred twentyfives + 2 one hundred twentyfive = 625 + 2 one hundred twentyfive Write 2 down in the one hundred twentyfives place and carry 1 six hundred twentyfive by putting 1 in the six hundred twentyfive place (Shown in black) 
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Oct 24, 16 06:10 PM
Straightforward proof of the law of sines. Easy to follow and understand