Math Problem Statement

Convert given fractions to decimals and decimals to fractions, and simplify them where necessary.

Solution

Let me analyze the image and solve the problems.The worksheet asks to either convert fractions to decimals or decimals to fractions. Below are the solutions:

Fractions to Decimals

  1. 7/9:
    Divide 7÷9=0.777...7 \div 9 = 0.777... (repeating).
    Decimal: 0.70.\overline{7}.

  2. 5/8:
    Divide 5÷8=0.6255 \div 8 = 0.625.
    Decimal: 0.6250.625.

  3. 9/10:
    Divide 9÷10=0.99 \div 10 = 0.9.
    Decimal: 0.90.9.

  4. 3/4:
    Divide 3÷4=0.753 \div 4 = 0.75.
    Decimal: 0.750.75.

  5. 11/20:
    Divide 11÷20=0.5511 \div 20 = 0.55.
    Decimal: 0.550.55.

Decimals to Fractions

  1. 0.62:
    Rewrite as 62/10062/100, simplify to 31/5031/50.
    Fraction: 31/5031/50.

  2. 0.725:
    Rewrite as 725/1000725/1000, simplify to 29/4029/40.
    Fraction: 29/4029/40.

  3. 0.925:
    Rewrite as 925/1000925/1000, simplify to 37/4037/40.
    Fraction: 37/4037/40.

  4. 0.05:
    Rewrite as 5/1005/100, simplify to 1/201/20.
    Fraction: 1/201/20.

  5. 0.104:
    Rewrite as 104/1000104/1000, simplify to 13/12513/125.
    Fraction: 13/12513/125.

  6. 0.276:
    Rewrite as 276/1000276/1000, simplify to 69/25069/250.
    Fraction: 69/25069/250.

Let me know if you need additional clarifications or details!


Additional Practice Questions:

  1. Convert 7/87/8 to a decimal.
  2. Rewrite 0.8750.875 as a fraction in simplest form.
  3. Simplify the fraction 48/6448/64.
  4. Write 0.30.\overline{3} as a fraction.
  5. Find the decimal equivalent of 1/31/3.

Tip:

To convert a fraction to a decimal, divide the numerator by the denominator. Simplify fractions when converting decimals to fractions to their lowest terms.

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Math Problem Analysis

Mathematical Concepts

Fraction to Decimal Conversion
Decimal to Fraction Conversion
Simplification of Fractions

Formulas

Decimal = Numerator ÷ Denominator
Fraction = Decimal × 10^n, where n is the number of decimal places

Theorems

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Suitable Grade Level

Grades 5-7