Math Problem Statement

C) (8,94 + 9,39) : (7,57 - 1,4 · 2,05) Y) 46,08 : (1,5 - 1,116) · 0,4 + 44,8 X) 3,5 : 7 + 2,8 : 0,4 − 0,74 : 5 Ч) (0,57 : 1,9 · 4,4 − 0,68 : 1,7) : 0,4 Щ) 3,36 : 3,2 + (4 − (7 − 6,3) · 4,2) − 1,1

Solution

Let's solve the mathematical expressions in the uploaded image one by one.


C) (8.94 + 9.39) : (7.57 − 1.4 · 2.05)

  1. Solve the numerator:
    8.94+9.39=18.338.94 + 9.39 = 18.33

  2. Solve the denominator:
    1.42.05=2.871.4 \cdot 2.05 = 2.87
    7.572.87=4.77.57 - 2.87 = 4.7

  3. Final division:
    18.33:4.73.918.33 : 4.7 \approx 3.9


У) 46.08 : (1.5 − 1.116) · 0.4 + 44.8

  1. Solve the parenthesis:
    1.51.116=0.3841.5 - 1.116 = 0.384

  2. Division:
    46.08:0.38412046.08 : 0.384 \approx 120

  3. Multiply:
    1200.4=48120 \cdot 0.4 = 48

  4. Add:
    48+44.8=92.848 + 44.8 = 92.8


X) 3.5 : 7 + 2.8 : 0.4 − 0.74 : 5

  1. First term:
    3.5:7=0.53.5 : 7 = 0.5

  2. Second term:
    2.8:0.4=72.8 : 0.4 = 7

  3. Third term:
    0.74:5=0.1480.74 : 5 = 0.148

  4. Combine:
    0.5+70.148=7.3520.5 + 7 - 0.148 = 7.352


Ч) (0.57 : 1.9 · 4.4 − 0.68 : 1.7) : 0.4

  1. Solve the first division:
    0.57:1.90.30.57 : 1.9 \approx 0.3

  2. Multiply:
    0.34.4=1.320.3 \cdot 4.4 = 1.32

  3. Solve the second division:
    0.68:1.70.40.68 : 1.7 \approx 0.4

  4. Subtract:
    1.320.4=0.921.32 - 0.4 = 0.92

  5. Final division:
    0.92:0.4=2.30.92 : 0.4 = 2.3


Щ) 3.36 : 3.2 + (4 − (7 − 6.3) · 4.2) − 1.1

  1. First division:
    3.36:3.2=1.053.36 : 3.2 = 1.05

  2. Solve the parenthesis:
    76.3=0.77 - 6.3 = 0.7
    0.74.2=2.940.7 \cdot 4.2 = 2.94

  3. Subtract from 4:
    42.94=1.064 - 2.94 = 1.06

  4. Add and subtract:
    1.05+1.061.1=1.011.05 + 1.06 - 1.1 = 1.01


Final Results:

  1. C) 3.93.9
  2. У) 92.892.8
  3. X) 7.3527.352
  4. Ч) 2.32.3
  5. Щ) 1.011.01

Do you want detailed explanations for any specific step? Here are 5 related questions for practice:

  1. How would you simplify expressions with multiple parentheses like in example Щ?
  2. What is the order of operations (PEMDAS/BODMAS) and how does it apply here?
  3. Can you find other ways to organize calculations to reduce rounding errors?
  4. How would the answers change if some of the inputs had additional decimals?
  5. What tools can be used to verify these calculations?

Tip: Always double-check division operations involving decimals, as rounding can introduce small errors!

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Math Problem Analysis

Mathematical Concepts

Arithmetic Operations
Order of Operations (PEMDAS/BODMAS)
Decimals

Formulas

Basic arithmetic operations
Parentheses and multiplication/division rules

Theorems

Order of Operations

Suitable Grade Level

Grades 6-8