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Mathematics

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Here are the solutions to the addition problems:

1a)

109+21130\begin{align*} 109 \\ + \quad 21 \\ \hline 130 \end{align*}

The sum is 130\boxed{\text{130}}.

1b)

87+108195\begin{align*} 87 \\ + \quad 108 \\ \hline 195 \end{align*}

The sum is 195\boxed{\text{195}}.

1c)

480+179659\begin{align*} 480 \\ + \quad 179 \\ \hline 659 \end{align*}

The sum is 659\boxed{\text{659}}.

1d)

216+29245\begin{align*} 216 \\ + \quad 29 \\ \hline 245 \end{align*}

The sum is 245\boxed{\text{245}}.

2a)

  1. Add the hundredths column

    2+9=112 + 9 = 11. Write down 1, carry over 1.

  2. Add the tenths column

    9+1+1(carry-over)=119 + 1 + 1 (\text{carry-over}) = 11. Write down 1, carry over 1. Place the decimal point.

  3. Add the ones column

    0+6+1(carry-over)=70 + 6 + 1 (\text{carry-over}) = 7.

  4. Add the tens column

    5+1=65 + 1 = 6.

  5. Add the hundreds column

    6+0=66 + 0 = 6.

    650.92+16.19667.11\begin{align*} 650.92 \\ + \quad 16.19 \\ \hline 667.11 \end{align*}

    The sum is 667.11\boxed{\text{667.11}}.

    2b)

  6. Add the hundredths column

    5+5=105 + 5 = 10. Write down 0, carry over 1.

  7. Add the tenths column

    3+3+1(carry-over)=73 + 3 + 1 (\text{carry-over}) = 7. Place the decimal point.

  8. Add the ones column

    2+7=92 + 7 = 9.

  9. Add the tens column

    9+6=159 + 6 = 15. Write down 5, carry over 1.

  10. Add the hundreds column

    4+2+1(carry-over)=74 + 2 + 1 (\text{carry-over}) = 7.

    492.35+267.35759.70\begin{align*} 492.35 \\ + \quad 267.35 \\ \hline 759.70 \end{align*}

    The sum is 759.70\boxed{\text{759.70}}.

    2c)

  11. Add the hundredths column

    6+5=116 + 5 = 11. Write down 1, carry over 1.

  12. Add the tenths column

    2+8+1(carry-over)=112 + 8 + 1 (\text{carry-over}) = 11. Write down 1, carry over 1. Place the decimal point.

  13. Add the ones column

    1+9+1(carry-over)=111 + 9 + 1 (\text{carry-over}) = 11. Write down 1, carry over 1.

  14. Add the tens column

    1+4+1(carry-over)=61 + 4 + 1 (\text{carry-over}) = 6.

  15. Add the hundreds column

    7+0=77 + 0 = 7.

    711.26+49.85761.11\begin{align*} 711.26 \\ + \quad 49.85 \\ \hline 761.11 \end{align*}

    The sum is 761.11\boxed{\text{761.11}}.

    2d)

  16. Add the hundredths column

    9+7=169 + 7 = 16. Write down 6, carry over 1.

  17. Add the tenths column

    6+8+1(carry-over)=156 + 8 + 1 (\text{carry-over}) = 15. Write down 5, carry over 1. Place the decimal point.

  18. Add the ones column

    9+4+1(carry-over)=149 + 4 + 1 (\text{carry-over}) = 14. Write down 4, carry over 1.

  19. Add the tens column

    1+1+1(carry-over)=31 + 1 + 1 (\text{carry-over}) = 3.

  20. Add the hundreds column

    0+2=20 + 2 = 2.

    19.69+214.87234.56\begin{align*} 19.69 \\ + \quad 214.87 \\ \hline 234.56 \end{align*}

    The sum is 234.56\boxed{\text{234.56}}.

    3a)

  21. Add the hundredths column

    5+4+5=145 + 4 + 5 = 14. Write down 4, carry over 1.

  22. Add the tenths column

    3+1+4+1(carry-over)=93 + 1 + 4 + 1 (\text{carry-over}) = 9. Place the decimal point.

  23. Add the ones column

    2+3+4=92 + 3 + 4 = 9.

  24. Add the tens column

    4+1+2=74 + 1 + 2 = 7.

  25. Add the hundreds column

    2+4+0=62 + 4 + 0 = 6.

    242.35413.14+24.45679.94\begin{align*} 242.35 \\ 413.14 \\ + \quad 24.45 \\ \hline 679.94 \end{align*}

    The sum is 679.94\boxed{\text{679.94}}.

    3b)

  26. Add the hundredths column

    2+5+7=142 + 5 + 7 = 14. Write down 4, carry over 1.

  27. Add the tenths column

    4+1+1+1(carry-over)=74 + 1 + 1 + 1 (\text{carry-over}) = 7. Place the decimal point.

  28. Add the ones column

    7+2+3=127 + 2 + 3 = 12. Write down 2, carry over 1.

  29. Add the tens column

    3+3+9+1(carry-over)=163 + 3 + 9 + 1 (\text{carry-over}) = 16. Write down 6, carry over 1.

  30. Add the hundreds column

    0+1+0+1(carry-over)=20 + 1 + 0 + 1 (\text{carry-over}) = 2.

    37.42132.15+93.17262.74\begin{align*} 37.42 \\ 132.15 \\ + \quad 93.17 \\ \hline 262.74 \end{align*}

    The sum is 262.74\boxed{\text{262.74}}.

    3c)

  31. Add the hundredths column

    3+9+2=143 + 9 + 2 = 14. Write down 4, carry over 1.

  32. Add the tenths column

    1+2+8+1(carry-over)=121 + 2 + 8 + 1 (\text{carry-over}) = 12. Write down 2, carry over 1. Place the decimal point.

  33. Add the ones column

    2+8+6+1(carry-over)=172 + 8 + 6 + 1 (\text{carry-over}) = 17. Write down 7, carry over 1.

  34. Add the tens column

    4+4+5+1(carry-over)=144 + 4 + 5 + 1 (\text{carry-over}) = 14. Write down 4, carry over 1.

  35. Add the hundreds column

    7+2+0+1(carry-over)=107 + 2 + 0 + 1 (\text{carry-over}) = 10.

    742.13248.29+56.821047.24\begin{align*} 742.13 \\ 248.29 \\ + \quad 56.82 \\ \hline 1047.24 \end{align*}

    The sum is 1047.24\boxed{\text{1047.24}}.

    3d)

  36. Add the hundredths column

    7+1+5=137 + 1 + 5 = 13. Write down 3, carry over 1.

  37. Add the tenths column

    2+8+0+1(carry-over)=112 + 8 + 0 + 1 (\text{carry-over}) = 11. Write down 1, carry over 1. Place the decimal point.

  38. Add the ones column

    5+0+4+1(carry-over)=105 + 0 + 4 + 1 (\text{carry-over}) = 10. Write down 0, carry over 1.

  39. Add the tens column

    1+1+9+1(carry-over)=121 + 1 + 9 + 1 (\text{carry-over}) = 12. Write down 2, carry over 1.

  40. Add the hundreds column

    1+3+1+1(carry-over)=61 + 3 + 1 + 1 (\text{carry-over}) = 6.

    115.27310.81+194.05620.13\begin{align*} 115.27 \\ 310.81 \\ + \quad 194.05 \\ \hline 620.13 \end{align*}

    The sum is 620.13\boxed{\text{620.13}}.

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