Math Problem Statement

1.14(5) + 1.19(5) + 3.46(2) + .82(4) + 2.04 + 3.63 + 2.19(2) + .59(14) × 1.24(4) + 1.94(4) × 1.50 + 2.88 + 2.19 + 2.52 + 1.90 + 4.84 + 1.29(2) + .66(6) + 3.52(3) + 3.04 + 1.15 + .79(10) + 1.16 + 2.09(2) + .79(12) + .21(4) + 1.60 + .29(3)=?

Solution

To solve this expression, I’ll break it down step-by-step, starting with calculations involving multiplication (such as .59(14).59(14) or .79(10).79(10)) and then summing all parts.

Step-by-Step Solution

Breaking down the terms with multiplications:

  1. 1.14×5=5.701.14 \times 5 = 5.70
  2. 1.19×5=5.951.19 \times 5 = 5.95
  3. 3.46×2=6.923.46 \times 2 = 6.92
  4. 0.82×4=3.280.82 \times 4 = 3.28
  5. 2.042.04
  6. 3.633.63
  7. 2.19×2=4.382.19 \times 2 = 4.38
  8. 0.59×14=8.260.59 \times 14 = 8.26
  9. 1.24×4=4.961.24 \times 4 = 4.96
  10. 1.94×4=7.761.94 \times 4 = 7.76
  11. 1.501.50
  12. 2.882.88
  13. 2.192.19
  14. 2.522.52
  15. 1.901.90
  16. 4.844.84
  17. 1.29×2=2.581.29 \times 2 = 2.58
  18. 0.66×6=3.960.66 \times 6 = 3.96
  19. 3.52×3=10.563.52 \times 3 = 10.56
  20. 3.043.04
  21. 1.151.15
  22. 0.79×10=7.900.79 \times 10 = 7.90
  23. 1.161.16
  24. 2.09×2=4.182.09 \times 2 = 4.18
  25. 0.79×12=9.480.79 \times 12 = 9.48
  26. 0.21×4=0.840.21 \times 4 = 0.84
  27. 1.601.60
  28. 0.29×3=0.870.29 \times 3 = 0.87

Now summing all the terms:

5.70+5.95+6.92+3.28+2.04+3.63+4.38+8.26+4.96+7.76+1.50+2.88+2.19+2.52+1.90+4.84+2.58+3.96+10.56+3.04+1.15+7.90+1.16+4.18+9.48+0.84+1.60+0.875.70 + 5.95 + 6.92 + 3.28 + 2.04 + 3.63 + 4.38 + 8.26 + 4.96 + 7.76 + 1.50 + 2.88 + 2.19 + 2.52 + 1.90 + 4.84 + 2.58 + 3.96 + 10.56 + 3.04 + 1.15 + 7.90 + 1.16 + 4.18 + 9.48 + 0.84 + 1.60 + 0.87

Calculating this sum gives: Total=116.19\text{Total} = 116.19

Final Answer

116.19\boxed{116.19}

Would you like a breakdown of any specific steps, or have any questions about this solution?


Related Questions:

  1. How would the solution change if the values inside each multiplication were increased by 1?
  2. How can we automate this kind of calculation in a calculator or software?
  3. What if we had to round each result to the nearest whole number before summing?
  4. How would using scientific notation for each number affect the accuracy of the solution?
  5. Can you explain why the order of operations matters in such a calculation?

Tip:

When handling large calculations with repeated values, it's often helpful to organize calculations in segments (like all multiplications first) before performing the final sum. This reduces the chance of missing terms.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Multiplication
Addition

Formulas

a × b for multiplication
a + b for addition

Theorems

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Suitable Grade Level

Grades 6-8