Math Problem Statement

Solve various arithmetic, algebraic, percentage, and geometry problems as provided in the worksheet.

Solution

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Solutions to the Problems:

  1. 57,834 + 9,057
    57,834+9,057=66,89157,834 + 9,057 = 66,891

  2. 386 × 49
    386×49=18,914386 \times 49 = 18,914

  3. 7026 − 2947
    70262947=4,0797026 - 2947 = 4,079

  4. 7496 ÷ 8
    7496÷8=9377496 \div 8 = 937

  5. 13h14h=112h\frac{1}{3}h − \frac{1}{4}h = \frac{1}{12}h
    1314=412312=112\frac{1}{3} − \frac{1}{4} = \frac{4}{12} − \frac{3}{12} = \frac{1}{12}

  6. 4% of 60,000
    4%×60,000=0.04×60,000=2,4004\% \times 60,000 = 0.04 \times 60,000 = 2,400

  7. 1036210^3 − 6^2
    103=1,00010^3 = 1,000, 62=366^2 = 36. So, 1,00036=9641,000 − 36 = 964.

  8. 720=7207=7137^{20} = 7^{20 − 7} = 7^{13}
    Simplifies to: 7137^{13}.

  9. 20 + 0.4
    20+0.4=20.420 + 0.4 = 20.4

  10. 110×38\frac{1}{10} × \frac{3}{8}
    110×38=380\frac{1}{10} × \frac{3}{8} = \frac{3}{80}

  11. Speed of 16 km/h for 10 min
    16 km/h=1660 km/min.16 \text{ km/h} = \frac{16}{60} \text{ km/min}.
    In 10 min: 1660×10=16060=2.67km.\frac{16}{60} × 10 = \frac{160}{60} = 2.67 \, \text{km}.

  12. Cost of 3.5kg at 14p per 12kg3.5 \, \text{kg at 14p per } \frac{1}{2} \, \text{kg}
    3.5÷0.5=7 (halves).3.5 \div 0.5 = 7 \text{ (halves)}.
    Total cost: 7×14=98p=£0.98.7 × 14 = 98 \, \text{p} = £0.98.


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Tip: Always double-check arithmetic in non-calculator exams by reverse calculating.

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Math Problem Analysis

Mathematical Concepts

Arithmetic operations
Percentage calculations
Basic algebra
Fractional arithmetic
Speed and distance
Geometry (area, perimeter, and angles)

Formulas

Percentage formula: (part/whole) × 100
Area of a rectangle: length × width
Circumference of a circle: 2πr
Speed = Distance ÷ Time

Theorems

Basic principles of fractions
Geometric properties of circles and isosceles triangles

Suitable Grade Level

Grades 6-8