1. **Problem 1a: Add the numbers 356490 and 267316** Formula: Addition of multi-digit numbers is done digit by digit from right to left, carrying over when sum exceeds 9. Step 1: Write numbers aligned by place value: $$\begin{array}{r} 356490 \\ +267316 \\ \hline \end{array}$$ Step 2: Add units: $0+6=6$ Step 3: Add tens: $9+1=10$, write 0 carry 1 Step 4: Add hundreds: $4+3=7$ plus carry 1 = 8 Step 5: Add thousands: $6+7=13$, write 3 carry 1 Step 6: Add ten-thousands: $5+6=11$ plus carry 1 = 12, write 2 carry 1 Step 7: Add hundred-thousands: $3+2=5$ plus carry 1 = 6 Result: $$\begin{array}{r} 356490 \\ +267316 \\ \hline 623806 \\ \end{array}$$ 2. **Problem 1b: Add the numbers 5386484 and 3277366** Step 1: Align numbers: $$\begin{array}{r} 5386484 \\ +3277366 \\ \hline \end{array}$$ Step 2: Add units: $4+6=10$, write 0 carry 1 Step 3: Add tens: $8+6=14$ plus carry 1 = 15, write 5 carry 1 Step 4: Add hundreds: $4+3=7$ plus carry 1 = 8 Step 5: Add thousands: $6+7=13$, write 3 carry 1 Step 6: Add ten-thousands: $8+7=15$ plus carry 1 = 16, write 6 carry 1 Step 7: Add hundred-thousands: $3+2=5$ plus carry 1 = 6 Step 8: Add millions: $5+3=8$ Result: $$\begin{array}{r} 5386484 \\ +3277366 \\ \hline 8663850 \\ \end{array}$$ 3. **Problem 1v: Add the numbers 588635906 and 271647384** Step 1: Align numbers: $$\begin{array}{r} 588635906 \\ +271647384 \\ \hline \end{array}$$ Step 2: Add units: $6+4=10$, write 0 carry 1 Step 3: Add tens: $0+8=8$ plus carry 1 = 9 Step 4: Add hundreds: $9+3=12$, write 2 carry 1 Step 5: Add thousands: $5+7=12$ plus carry 1 = 13, write 3 carry 1 Step 6: Add ten-thousands: $3+4=7$ plus carry 1 = 8 Step 7: Add hundred-thousands: $6+6=12$, write 2 carry 1 Step 8: Add millions: $8+1=9$ plus carry 1 = 10, write 0 carry 1 Step 9: Add ten-millions: $8+7=15$ plus carry 1 = 16, write 6 carry 1 Step 10: Add hundred-millions: $5+2=7$ plus carry 1 = 8 Result: $$\begin{array}{r} 588635906 \\ +271647384 \\ \hline 860283290 \\ \end{array}$$ 4. **Problem 2a: Subtract 247356 from 356290** Step 1: Align numbers: $$\begin{array}{r} 356290 \\ -247356 \\ \hline \end{array}$$ Step 2: Subtract units: $0-6$ cannot, borrow 1 from tens Step 3: After borrowing, units: $10-6=4$ Step 4: Tens: $8-5=3$ Step 5: Hundreds: $1-3$ cannot, borrow 1 from thousands Step 6: After borrowing, hundreds: $11-3=8$ Step 7: Thousands: $5-7$ cannot, borrow 1 from ten-thousands Step 8: After borrowing, thousands: $15-7=8$ Step 9: Ten-thousands: $4-4=0$ Step 10: Hundred-thousands: $2-2=1$ Result: $$\begin{array}{r} 356290 \\ -247356 \\ \hline 108934 \\ \end{array}$$ 5. **Problem 2b: Subtract 1267388 from 1453459** Step 1: Align numbers: $$\begin{array}{r} 1453459 \\ -1267388 \\ \hline \end{array}$$ Step 2: Units: $9-8=1$ Step 3: Tens: $5-8$ cannot, borrow 1 from hundreds Step 4: After borrowing, tens: $15-8=7$ Step 5: Hundreds: $2-3$ cannot, borrow 1 from thousands Step 6: After borrowing, hundreds: $12-3=9$ Step 7: Thousands: $3-7$ cannot, borrow 1 from ten-thousands Step 8: After borrowing, thousands: $13-7=6$ Step 9: Ten-thousands: $3-6$ cannot, borrow 1 from hundred-thousands Step 10: After borrowing, ten-thousands: $13-6=7$ Step 11: Hundred-thousands: $3-2=1$ Step 12: Millions: $1-1=0$ Result: $$\begin{array}{r} 1453459 \\ -1267388 \\ \hline 185071 \\ \end{array}$$ 6. **Problem 2v: Subtract 76674584 from 88265008** Step 1: Align numbers: $$\begin{array}{r} 88265008 \\ -76674584 \\ \hline \end{array}$$ Step 2: Units: $8-4=4$ Step 3: Tens: $0-8$ cannot, borrow 1 from hundreds Step 4: After borrowing, tens: $10-8=2$ Step 5: Hundreds: $4-5$ cannot, borrow 1 from thousands Step 6: After borrowing, hundreds: $14-5=9$ Step 7: Thousands: $9-4=5$ Step 8: Ten-thousands: $5-7$ cannot, borrow 1 from hundred-thousands Step 9: After borrowing, ten-thousands: $15-7=8$ Step 10: Hundred-thousands: $7-6=1$ Step 11: Millions: $8-6=2$ Step 12: Ten-millions: $8-7=1$ Result: $$\begin{array}{r} 88265008 \\ -76674584 \\ \hline 11590424 \\ \end{array}$$ 7. **Problem 3a: Add 15643567 and 1954644** Step 1: Align numbers: $$\begin{array}{r} 15643567 \\ +1954644 \\ \hline \end{array}$$ Step 2: Add units to millions with carry as needed: $7+4=11$, write 1 carry 1 $6+4=10$ plus carry 1 = 11, write 1 carry 1 $5+6=11$ plus carry 1 = 12, write 2 carry 1 $3+5=8$ plus carry 1 = 9 $4+4=8$ $6+9=15$, write 5 carry 1 $5+1=6$ plus carry 1 = 7 $1+0=1$ Result: $$\begin{array}{r} 15643567 \\ +1954644 \\ \hline 17698211 \\ \end{array}$$ 8. **Problem 3b: Add 41358890 and 3179757** Step 1: Align numbers: $$\begin{array}{r} 41358890 \\ +3179757 \\ \hline \end{array}$$ Step 2: Add units to ten-millions with carry: $0+7=7$ $9+5=14$, write 4 carry 1 $8+7=15$ plus carry 1 = 16, write 6 carry 1 $8+9=17$ plus carry 1 = 18, write 8 carry 1 $5+7=12$ plus carry 1 = 13, write 3 carry 1 $3+1=4$ plus carry 1 = 5 $1+3=4$ $4+0=4$ Result: $$\begin{array}{r} 41358890 \\ +3179757 \\ \hline 44538647 \\ \end{array}$$ 9. **Problem 3v: Add 347834356 and 25756810** Step 1: Align numbers: $$\begin{array}{r} 347834356 \\ +25756810 \\ \hline \end{array}$$ Step 2: Add units to hundred-millions with carry: $6+0=6$ $5+1=6$ $3+8=11$, write 1 carry 1 $4+6=10$ plus carry 1 = 11, write 1 carry 1 $8+5=13$ plus carry 1 = 14, write 4 carry 1 $7+7=14$ plus carry 1 = 15, write 5 carry 1 $4+5=9$ plus carry 1 = 10, write 0 carry 1 $3+2=5$ plus carry 1 = 6 $3+0=3$ Result: $$\begin{array}{r} 347834356 \\ +25756810 \\ \hline 373591166 \\ \end{array}$$ 10. **Problem 3g: Add 489764296 and 187597643** Step 1: Align numbers: $$\begin{array}{r} 489764296 \\ +187597643 \\ \hline \end{array}$$ Step 2: Add units to hundred-millions with carry: $6+3=9$ $9+4=13$, write 3 carry 1 $2+6=8$ plus carry 1 = 9 $4+7=11$, write 1 carry 1 $6+9=15$ plus carry 1 = 16, write 6 carry 1 $7+5=12$ plus carry 1 = 13, write 3 carry 1 $9+7=16$ plus carry 1 = 17, write 7 carry 1 $8+8=16$ plus carry 1 = 17, write 7 carry 1 $4+1=5$ plus carry 1 = 6 Result: $$\begin{array}{r} 489764296 \\ +187597643 \\ \hline 677361939 \\ \end{array}$$ 11. **Problem 4a: Subtract 7785451 from 54138365** Step 1: Align numbers: $$\begin{array}{r} 54138365 \\ -7785451 \\ \hline \end{array}$$ Step 2: Subtract units to ten-millions with borrowing as needed: $5-1=4$ $6-5=1$ $3-4$ borrow 1: $13-4=9$ $7-5=2$ $8-8=0$ $1-7$ borrow 1: $11-7=4$ $3-7$ borrow 1: $13-7=6$ $4-0=4$ Result: $$\begin{array}{r} 54138365 \\ -7785451 \\ \hline 46352914 \\ \end{array}$$ 12. **Problem 4b: Subtract 5642325 from 64317904** Step 1: Align numbers: $$\begin{array}{r} 64317904 \\ -5642325 \\ \hline \end{array}$$ Step 2: Subtract units to ten-millions with borrowing: $4-5$ borrow 1: $14-5=9$ $9-2=7$ $0-3$ borrow 1: $10-3=7$ $8-2=6$ $1-4$ borrow 1: $11-4=7$ $3-6$ borrow 1: $13-6=7$ $4-5$ borrow 1: $14-5=9$ $6-0=6$ Result: $$\begin{array}{r} 64317904 \\ -5642325 \\ \hline 58675579 \\ \end{array}$$ 13. **Problem 4v: Subtract 45342530 from 835487217** Step 1: Align numbers: $$\begin{array}{r} 835487217 \\ -45342530 \\ \hline \end{array}$$ Step 2: Subtract units to hundred-millions with borrowing: $7-0=7$ $1-3$ borrow 1: $11-3=8$ $2-5$ borrow 1: $12-5=7$ $7-2=5$ $8-4=4$ $4-3=1$ $5-5=0$ $3-4$ borrow 1: $13-4=9$ $8-0=8$ Result: $$\begin{array}{r} 835487217 \\ -45342530 \\ \hline 790144687 \\ \end{array}$$ 14. **Problem 4g: Subtract 287187643 from 568100452** Step 1: Align numbers: $$\begin{array}{r} 568100452 \\ -287187643 \\ \hline \end{array}$$ Step 2: Subtract units to hundred-millions with borrowing: $2-3$ borrow 1: $12-3=9$ $5-4=1$ $4-6$ borrow 1: $14-6=8$ $0-7$ borrow 1: $10-7=3$ $0-8$ borrow 1: $10-8=2$ $1-1=0$ $8-7=1$ $6-8$ borrow 1: $16-8=8$ $5-2=3$ Result: $$\begin{array}{r} 568100452 \\ -287187643 \\ \hline 280912809 \\ \end{array}$$ 15. **Problem 5a: Check if 2413890 + 1700 equals 2415590** Calculate sum: $$2413890 + 1700 = 2415590$$ Matches given answer: 2415590 16. **Problem 5b: Check if 2413980 + 1700 equals 2415680** Calculate sum: $$2413980 + 1700 = 2415680$$ Matches given answer: 2415680 17. **Problem 5v: Check if 3617628 - 1500 equals 3616128** Calculate difference: $$3617628 - 1500 = 3616128$$ Matches given answer: 3616128 18. **Problem 5g: Check if 3616728 - 1500 equals 3615228** Calculate difference: $$3616728 - 1500 = 3615228$$ Matches given answer: 3615228 **Final answers:** 1a) 623806 1b) 8663850 1v) 860283290 2a) 108934 2b) 185071 2v) 11590424 3a) 17698211 3b) 44538647 3v) 373591166 3g) 677361939 4a) 46352914 4b) 58675579 4v) 790144687 4g) 280912809 5a) Correct 5b) Correct 5v) Correct 5g) Correct