Finding Equivalent Fractions, Decimals, and Percents (A) Worksheet ... - Free Printable

Problem Overview:

The task is to identify and color three boxes in each grid that represent equivalent fractions, decimals, and percents. The goal is to find numbers that are mathematically equivalent to each other across the different formats.

Solution Approach:

1. Understand the Equivalence:
- Fractions: Represent parts of a whole.
- Decimals: Decimal representations of fractions.
- Percents: Fractions expressed as parts per 100.

2. Convert Between Formats:
- To convert a fraction to a decimal: Divide the numerator by the denominator.
- To convert a fraction to a percent: Multiply the fraction by 100.
- To convert a decimal to a percent: Multiply the decimal by 100.
- To convert a percent to a decimal: Divide the percent by 100.

3. Identify Equivalent Values:
- Compare each number in the grid to find three values (one fraction, one decimal, and one percent) that are equivalent.

Step-by-Step Solution:

#### Grid 1:
| $\frac{25}{10}$ | $25\%$ | $\frac{1}{4}$ |
|------------------|--------|---------------|
| $0.25$ | $2\%$ | $20\%$ |

- $\frac{25}{10} = 2.5$ (not equivalent to any other value in this grid).
- $25\% = 0.25$ (equivalent to $0.25$).
- $\frac{1}{4} = 0.25 = 25\%$ (equivalent to $0.25$ and $25\%$).

Equivalent Set: $25\%, \frac{1}{4}, 0.25$

#### Grid 2:
| $0.5$ | $\frac{1}{2}$ | $2\%$ |
|------------------|----------------|-------------|
| $50\%$ | $\frac{1}{5}$ | $22\%$ |

- $0.5 = 50\% = \frac{1}{2}$ (all three are equivalent).
- $\frac{1}{2} = 0.5 = 50\%$ (already identified).
- $2\% = 0.02$ (not equivalent to any other value in this grid).

Equivalent Set: $0.5, \frac{1}{2}, 50\%$

#### Grid 3:
| $\frac{1}{4}$ | $75\%$ | $\frac{3}{4}$ |
|------------------|-----------------|----------------|
| $0.75$ | $\frac{5}{7}$ | $0.57$ |

- $\frac{1}{4} = 0.25 = 25\%$ (not equivalent to any other value in this grid).
- $75\% = 0.75 = \frac{3}{4}$ (all three are equivalent).
- $\frac{3}{4} = 0.75 = 75\%$ (already identified).

Equivalent Set: $75\%, \frac{3}{4}, 0.75$

#### Grid 4:
| $\frac{1}{10}$ | $0.1$ | $\frac{1}{100}$ |
|------------------|-----------------|-----------------|
| $1.1$ | $11\%$ | $10\%$ |

- $\frac{1}{10} = 0.1 = 10\%$ (all three are equivalent).
- $0.1 = \frac{1}{10} = 10\%$ (already identified).
- $\frac{1}{100} = 0.01 = 1\%$ (not equivalent to any other value in this grid).

Equivalent Set: $\frac{1}{10}, 0.1, 10\%$

#### Grid 5:
| $0.3$ | $0.13$ | $30\%$ |
|------------------|-----------------|---------------|
| $\frac{1}{30}$ | $\frac{3}{10}$ | $33\%$ |

- $0.3 = 30\% = \frac{3}{10}$ (all three are equivalent).
- $0.13 = 13\% = \frac{13}{100}$ (not equivalent to any other value in this grid).
- $\frac{1}{30} = 0.033\overline{3} = 3.\overline{3}\%$ (not equivalent to any other value in this grid).

Equivalent Set: $0.3, \frac{3}{10}, 30\%$

#### Grid 6:
| $\frac{7}{10}$ | $70\%$ | $0.07$ |
|------------------|-----------------|---------------|
| $0.7$ | $\frac{7}{15}$ | $57\%$ |

- $\frac{7}{10} = 0.7 = 70\%$ (all three are equivalent).
- $70\% = 0.7 = \frac{7}{10}$ (already identified).
- $0.07 = 7\% = \frac{7}{100}$ (not equivalent to any other value in this grid).

Equivalent Set: $\frac{7}{10}, 0.7, 70\%$

#### Grid 7:
| $\frac{9}{10}$ | $90\%$ | $9\%$ |
|------------------|-----------------|---------------|
| $0.9$ | $\frac{99}{100}$ | $0.19$ |

- $\frac{9}{10} = 0.9 = 90\%$ (all three are equivalent).
- $90\% = 0.9 = \frac{9}{10}$ (already identified).
- $9\% = 0.09 = \frac{9}{100}$ (not equivalent to any other value in this grid).

Equivalent Set: $\frac{9}{10}, 0.9, 90\%$

#### Grid 8:
| $\frac{1}{100}$ | $1\%$ | $\frac{1}{10}$ |
|------------------|-----------------|----------------|
| $0.01$ | $1.1$ | $11\%$ |

- $\frac{1}{100} = 0.01 = 1\%$ (all three are equivalent).
- $1\% = 0.01 = \frac{1}{100}$ (already identified).
- $\frac{1}{10} = 0.1 = 10\%$ (not equivalent to any other value in this grid).

Equivalent Set: $\frac{1}{100}, 0.01, 1\%$

#### Grid 9:
| $\frac{4}{10}$ | $4\%$ | $\frac{44}{100}$ |
|------------------|-----------------|------------------|
| $\frac{4}{100}$ | $0.04$ | $0.4$ |

- $\frac{4}{10} = 0.4 = 40\%$ (not equivalent to any other value in this grid).
- $4\% = 0.04 = \frac{4}{100}$ (all three are equivalent).
- $\frac{44}{100} = 0.44 = 44\%$ (not equivalent to any other value in this grid).

Equivalent Set: $\frac{4}{100}, 0.04, 4\%$

#### Grid 10:
| $\frac{1}{5}$ | $20\%$ | $\frac{2}{100}$ |
|------------------|-----------------|-----------------|
| $0.02$ | $\frac{2}{5}$ | $0.2$ |

- $\frac{1}{5} = 0.2 = 20\%$ (all three are equivalent).
- $20\% = 0.2 = \frac{1}{5}$ (already identified).
- $\frac{2}{100} = 0.02 = 2\%$ (not equivalent to any other value in this grid).

Equivalent Set: $\frac{1}{5}, 0.2, 20\%$

#### Grid 11:
| $40\%$ | $44\%$ | $\frac{2}{5}$ |
|------------------|-----------------|----------------|
| $0.4$ | $0.04$ | $\frac{1}{40}$ |

- $40\% = 0.4 = \frac{2}{5}$ (all three are equivalent).
- $44\% = 0.44 = \frac{44}{100}$ (not equivalent to any other value in this grid).
- $\frac{2}{5} = 0.4 = 40\%$ (already identified).

Equivalent Set: $40\%, 0.4, \frac{2}{5}$

#### Grid 12:
| $\frac{3}{5}$ | $0.6$ | $\frac{1}{6}$ |
|------------------|-----------------|----------------|
| $0.06$ | $60\%$ | $16\%$ |

- $\frac{3}{5} = 0.6 = 60\%$ (all three are equivalent).
- $0.6 = \frac{3}{5} = 60\%$ (already identified).
- $\frac{1}{6} = 0.166\overline{6} = 16.\overline{6}\%$ (not equivalent to any other value in this grid).

Equivalent Set: $\frac{3}{5}, 0.6, 60\%$

Final Answer:

The equivalent sets for each grid are:

1. $25\%, \frac{1}{4}, 0.25$
2. $0.5, \frac{1}{2}, 50\%$
3. $75\%, \frac{3}{4}, 0.75$
4. $\frac{1}{10}, 0.1, 10\%$
5. $0.3, \frac{3}{10}, 30\%$
6. $\frac{7}{10}, 0.7, 70\%$
7. $\frac{9}{10}, 0.9, 90\%$
8. $\frac{1}{100}, 0.01, 1\%$
9. $\frac{4}{100}, 0.04, 4\%$
10. $\frac{1}{5}, 0.2, 20\%$
11. $40\%, 0.4, \frac{2}{5}$
12. $\frac{3}{5}, 0.6, 60\%$

$$
\boxed{
\begin{array}{ccc}
25\%, \frac{1}{4}, 0.25 & 0.5, \frac{1}{2}, 50\% & 75\%, \frac{3}{4}, 0.75 \\
\frac{1}{10}, 0.1, 10\% & 0.3, \frac{3}{10}, 30\% & \frac{7}{10}, 0.7, 70\% \\
\frac{9}{10}, 0.9, 90\% & \frac{1}{100}, 0.01, 1\% & \frac{4}{100}, 0.04, 4\% \\
\frac{1}{5}, 0.2, 20\% & 40\%, 0.4, \frac{2}{5} & \frac{3}{5}, 0.6, 60\% \\
\end{array}
}
$$