Math Problem Statement

The image uploaded contains a table with missing values related to fractions, decimals, and percentages.

Solution

The image you uploaded contains a table with mathematical values. I'll help you fill in the missing numbers based on the data provided. Here's what I see:

Table Data Interpretation:

  1. First Row:

    • Left Column: Blank
    • Middle Column: 0.32
    • Right Column: 32%
  2. Second Row:

    • Left Column: 12\frac{1}{2}
    • Middle Column: Blank
    • Right Column: 5%
  3. Third Row:

    • Left Column: 105.3125\frac{105.3}{125}
    • Middle Column: 0.843
    • Right Column: 84.4%

Solving the Table:

The relationship between the columns seems to be based on converting between fractions/decimals and percentages.

  1. First Row:
    We have the middle column as 0.32 and the right column as 32%. The missing left column should be the fraction equivalent of 0.32.

    Left Column=32100=825\text{Left Column} = \frac{32}{100} = \frac{8}{25}

  2. Second Row:
    The left column is given as 12\frac{1}{2}, and the right column is 5%. We need to find the middle column, which should be the decimal equivalent of 12\frac{1}{2}.

    12=0.5\frac{1}{2} = 0.5

    Since 5% is much smaller than 50%, the 5% might correspond to something other than 12\frac{1}{2}. But generally, for 12\frac{1}{2}, the middle value would be 0.5. This suggests a potential mismatch or error in the original data.

  3. Third Row:
    The left column is 105.3125\frac{105.3}{125}, which simplifies to approximately 0.8424. The middle column is given as 0.843, which is consistent, and the right column is 84.4%, also consistent.

Final Table:

Let's fill in the missing numbers based on the above analysis:

Fraction/RatioDecimalPercentage
825\frac{8}{25}0.3232%
12\frac{1}{2}0.5(possibly incorrect)
105.3125\frac{105.3}{125}0.84384.4%

There seems to be a discrepancy with the second row, so if this is a copied table, double-check that value.

Would you like further details or clarification?

Questions:

  1. What is the correct decimal equivalent for 12\frac{1}{2}?
  2. How do you convert a fraction to a percentage?
  3. What might cause a mismatch between fraction, decimal, and percentage columns?
  4. How would you interpret a discrepancy between given data in similar tables?
  5. Can percentages ever exceed 100% in standard problems?

Tip:

Always cross-verify percentages and decimals for consistency, especially when dealing with fractions.

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Math Problem Analysis

Mathematical Concepts

Fractions
Decimals
Percentages
Conversion between formats

Formulas

Fraction to Decimal: a/b = a ÷ b
Decimal to Percentage: Decimal × 100 = Percentage
Fraction to Percentage: (a/b) × 100 = Percentage

Theorems

Relationship between fractions, decimals, and percentages
Proportionality in conversions between mathematical forms

Suitable Grade Level

Grades 5-7