Math Problem Statement

Berechnen

Berechnen

Solution

The image contains math exercises focused on fractions and decimal numbers. Let’s tackle Exercise 4 together, where you convert fractions to decimal numbers for easier comparison.

Conversion to Decimal Numbers:

Part (a):

  1. 47\frac{4}{7}:
    4÷7=0.571428...4 \div 7 = 0.571428... (approx. 0.570.57)
  2. 58\frac{5}{8}:
    5÷8=0.6255 \div 8 = 0.625
  3. 710\frac{7}{10}:
    7÷10=0.77 \div 10 = 0.7
  4. 1115\frac{11}{15}:
    11÷15=0.733...11 \div 15 = 0.733... (approx. 0.730.73)

Part (b):

  1. 1150\frac{11}{50}:
    11÷50=0.2211 \div 50 = 0.22
  2. 1770\frac{17}{70}:
    17÷70=0.242857...17 \div 70 = 0.242857... (approx. 0.240.24)
  3. 1980\frac{19}{80}:
    19÷80=0.237519 \div 80 = 0.2375 (approx. 0.240.24)
  4. 2190\frac{21}{90}:
    21÷90=0.233...21 \div 90 = 0.233... (approx. 0.230.23)

Now you can easily compare these decimals to determine their relative sizes or order them if needed. Let me know if you’d like me to go further with sorting!


Questions for Deeper Exploration:

  1. How can you simplify these fractions before converting them to decimals?
  2. What is the benefit of converting fractions into decimals for comparison?
  3. Can you identify patterns in recurring decimal fractions like 47\frac{4}{7}?
  4. How do you determine the number of decimal places needed for accuracy?
  5. Can you reverse the process, converting decimals back into fractions?

Tip:

When comparing fractions, finding a common denominator can also be helpful, especially when working manually.

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Math Problem Analysis

Mathematical Concepts

Fractions
Decimal Numbers
Comparison of Fractions

Formulas

Division of Numerator by Denominator for Decimal Conversion

Theorems

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Suitable Grade Level

Grades 5-7