6th Grade Math Worksheets | Printable PDF Worksheets - Free Printable

Problem Overview:

The task is to identify and color three boxes in each grid that represent equivalent fractions, decimals, and percents. This requires converting between these forms to find matches.

Solution Approach:

1. Understand the Conversion Rules:
- Fraction to Decimal: Divide the numerator by the denominator.
- Fraction to Percent: Convert the fraction to a decimal, then multiply by 100.
- Decimal to Percent: Multiply the decimal by 100.
- Percent to Decimal: Divide the percent by 100.
- Percent to Fraction: Write the percent as a fraction over 100, then simplify.

2. Identify Equivalent Values:
- For each grid, convert all values to a common form (e.g., decimals) to compare them easily.
- Look for three values that are mathematically equivalent.

3. Color the Correct Boxes:
- Once the equivalents are identified, color the corresponding boxes.

Step-by-Step Solution for Each Grid:

#### Grid 1:
| $\frac{7}{10}$ | $25\%$ | $\frac{3}{4}$ |
| $0.75$ | $7\%$ | $73\%$ |
| $75\%$ | $0.25$ | $\frac{1}{7}$ |

- Convert to Decimals:
- $\frac{7}{10} = 0.7$
- $25\% = 0.25$
- $\frac{3}{4} = 0.75$
- $0.75 = 0.75$
- $7\% = 0.07$
- $73\% = 0.73$
- $75\% = 0.75$
- $0.25 = 0.25$
- $\frac{1}{7} \approx 0.1429$

- Identify Equivalents:
- $0.75$, $75\%$, and $\frac{3}{4}$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.75$, $75\%$, and $\frac{3}{4}$.

#### Grid 2:
| $0.2$ | $\frac{1}{2}$ | $2\%$ |
| $0.15$ | $\frac{1}{5}$ | $22\%$ |
| $5\%$ | $0.5$ | $20\%$ |

- Convert to Decimals:
- $0.2 = 0.2$
- $\frac{1}{2} = 0.5$
- $2\% = 0.02$
- $0.15 = 0.15$
- $\frac{1}{5} = 0.2$
- $22\% = 0.22$
- $5\% = 0.05$
- $0.5 = 0.5$
- $20\% = 0.2$

- Identify Equivalents:
- $0.2$, $\frac{1}{5}$, and $20\%$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.2$, $\frac{1}{5}$, and $20\%$.

#### Grid 3:
| $\frac{1}{7}$ | $40\%$ | $\frac{3}{4}$ |
| $0.25$ | $\frac{4}{10}$ | $25\%$ |
| $\frac{44}{100}$ | $0.52$ | $\frac{1}{4}$ |

- Convert to Decimals:
- $\frac{1}{7} \approx 0.1429$
- $40\% = 0.4$
- $\frac{3}{4} = 0.75$
- $0.25 = 0.25$
- $\frac{4}{10} = 0.4$
- $25\% = 0.25$
- $\frac{44}{100} = 0.44$
- $0.52 = 0.52$
- $\frac{1}{4} = 0.25$

- Identify Equivalents:
- $0.25$, $25\%$, and $\frac{1}{4}$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.25$, $25\%$, and $\frac{1}{4}$.

#### Grid 4:
| $\frac{7}{10}$ | $77\%$ | $\frac{7}{100}$ |
| $0.75$ | $7\%$ | $70\%$ |
| $75\%$ | $0.7$ | $\frac{1}{7}$ |

- Convert to Decimals:
- $\frac{7}{10} = 0.7$
- $77\% = 0.77$
- $\frac{7}{100} = 0.07$
- $0.75 = 0.75$
- $7\% = 0.07$
- $70\% = 0.7$
- $75\% = 0.75$
- $0.7 = 0.7$
- $\frac{1}{7} \approx 0.1429$

- Identify Equivalents:
- $0.7$, $70\%$, and $\frac{7}{10}$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.7$, $70\%$, and $\frac{7}{10}$.

#### Grid 5:
| $0.25$ | $0.025$ | $\frac{1}{2}\%$ |
| $0.15$ | $\frac{2}{5}$ | $50\%$ |
| $\frac{1}{2}$ | $0.5$ | $20\%$ |

- Convert to Decimals:
- $0.25 = 0.25$
- $0.025 = 0.025$
- $\frac{1}{2}\% = 0.005$
- $0.15 = 0.15$
- $\frac{2}{5} = 0.4$
- $50\% = 0.5$
- $\frac{1}{2} = 0.5$
- $0.5 = 0.5$
- $20\% = 0.2$

- Identify Equivalents:
- $0.5$, $\frac{1}{2}$, and $50\%$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.5$, $\frac{1}{2}$, and $50\%$.

#### Grid 6:
| $\frac{5}{15}$ | $15\%$ | $\frac{55}{100}$ |
| $0.15$ | $\frac{1}{15}$ | $55\%$ |
| $\frac{15}{100}$ | $0.51$ | $\frac{1}{5}$ |

- Convert to Decimals:
- $\frac{5}{15} \approx 0.3333$
- $15\% = 0.15$
- $\frac{55}{100} = 0.55$
- $0.15 = 0.15$
- $\frac{1}{15} \approx 0.0667$
- $55\% = 0.55$
- $\frac{15}{100} = 0.15$
- $0.51 = 0.51$
- $\frac{1}{5} = 0.2$

- Identify Equivalents:
- $0.15$, $\frac{15}{100}$, and $15\%$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.15$, $\frac{15}{100}$, and $15\%$.

#### Grid 7:
| $\frac{4}{100}$ | $25\%$ | $\frac{3}{4}$ |
| $0.4$ | $\frac{2}{5}$ | $40\%$ |
| $\frac{44}{100}$ | $0.44$ | $\frac{1}{4}$ |

- Convert to Decimals:
- $\frac{4}{100} = 0.04$
- $25\% = 0.25$
- $\frac{3}{4} = 0.75$
- $0.4 = 0.4$
- $\frac{2}{5} = 0.4$
- $40\% = 0.4$
- $\frac{44}{100} = 0.44$
- $0.44 = 0.44$
- $\frac{1}{4} = 0.25$

- Identify Equivalents:
- $0.4$, $\frac{2}{5}$, and $40\%$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.4$, $\frac{2}{5}$, and $40\%$.

#### Grid 8:
| $\frac{6}{100}$ | $16\%$ | $\frac{3}{5}$ |
| $0.66$ | $6\%$ | $66\%$ |
| $60\%$ | $0.6$ | $\frac{2}{3}$ |

- Convert to Decimals:
- $\frac{6}{100} = 0.06$
- $16\% = 0.16$
- $\frac{3}{5} = 0.6$
- $0.66 = 0.66$
- $6\% = 0.06$
- $66\% = 0.66$
- $60\% = 0.6$
- $0.6 = 0.6$
- $\frac{2}{3} \approx 0.6667$

- Identify Equivalents:
- $0.6$, $60\%$, and $\frac{3}{5}$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.6$, $60\%$, and $\frac{3}{5}$.

#### Grid 9:
| $\frac{1}{10}$ | $1\%$ | $\frac{11}{100}$ |
| $0.1\%$ | $0.01$ | $11\%$ |
| $\frac{1}{100}$ | $10\%$ | $1.1$ |

- Convert to Decimals:
- $\frac{1}{10} = 0.1$
- $1\% = 0.01$
- $\frac{11}{100} = 0.11$
- $0.1\% = 0.001$
- $0.01 = 0.01$
- $11\% = 0.11$
- $\frac{1}{100} = 0.01$
- $10\% = 0.1$
- $1.1 = 1.1$

- Identify Equivalents:
- $0.01$, $1\%$, and $\frac{1}{100}$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.01$, $1\%$, and $\frac{1}{100}$.

#### Grid 10:
| $\frac{8}{10}$ | $80\%$ | $\frac{3}{4}$ |
| $0.8$ | $\frac{4}{5}$ | $8.8\%$ |
| $\frac{8}{100}$ | $0.08$ | $\frac{1}{8}$ |

- Convert to Decimals:
- $\frac{8}{10} = 0.8$
- $80\% = 0.8$
- $\frac{3}{4} = 0.75$
- $0.8 = 0.8$
- $\frac{4}{5} = 0.8$
- $8.8\% = 0.088$
- $\frac{8}{100} = 0.08$
- $0.08 = 0.08$
- $\frac{1}{8} = 0.125$

- Identify Equivalents:
- $0.8$, $\frac{8}{10}$, and $80\%$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.8$, $\frac{8}{10}$, and $80\%$.

#### Grid 11:
| $0.\dot{3}$ | $33\frac{1}{3}\%$ | $\frac{33}{100}$ |
| $0.03$ | $0.3$ | $33\%$ |
| $\frac{30}{100}$ | $3\%$ | $\frac{1}{3}$ |

- Convert to Decimals:
- $0.\dot{3} = 0.3333$
- $33\frac{1}{3}\% = 0.3333$
- $\frac{33}{100} = 0.33$
- $0.03 = 0.03$
- $0.3 = 0.3$
- $33\% = 0.33$
- $\frac{30}{100} = 0.3$
- $3\% = 0.03$
- $\frac{1}{3} \approx 0.3333$

- Identify Equivalents:
- $0.\dot{3}$, $33\frac{1}{3}\%$, and $\frac{1}{3}$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.\dot{3}$, $33\frac{1}{3}\%$, and $\frac{1}{3}$.

#### Grid 12:
| $\frac{1}{20}$ | $0.05$ | $\frac{1}{5}$ |
| $0.02$ | $20\%$ | $0.2\%$ |
| $5\%$ | $0.5$ | $\frac{2}{100}$ |

- Convert to Decimals:
- $\frac{1}{20} = 0.05$
- $0.05 = 0.05$
- $\frac{1}{5} = 0.2$
- $0.02 = 0.02$
- $20\% = 0.2$
- $0.2\% = 0.002$
- $5\% = 0.05$
- $0.5 = 0.5$
- $\frac{2}{100} = 0.02$

- Identify Equivalents:
- $0.05$, $\frac{1}{20}$, and $5\%$ are equivalent.

- Color the Boxes:
- Color the boxes containing $0.05$, $\frac{1}{20}$, and $5\%$.

Final Answer:

The final answer involves coloring the correct boxes in each grid based on the equivalences identified above. The boxed answers are summarized as follows:

- Grid 1: $0.75$, $75\%$, $\frac{3}{4}$
- Grid 2: $0.2$, $\frac{1}{5}$, $20\%$
- Grid 3: $0.25$, $25\%$, $\frac{1}{4}$
- Grid 4: $0.7$, $70\%$, $\frac{7}{10}$
- Grid 5: $0.5$, $\frac{1}{2}$, $50\%$
- Grid 6: $0.15$, $\frac{15}{100}$, $15\%$
- Grid 7: $0.4$, $\frac{2}{5}$, $40\%$
- Grid 8: $0.6$, $60\%$, $\frac{3}{5}$
- Grid 9: $0.01$, $1\%$, $\frac{1}{100}$
- Grid 10: $0.8$, $\frac{8}{10}$, $80\%$
- Grid 11: $0.\dot{3}$, $33\frac{1}{3}\%$, $\frac{1}{3}$
- Grid 12: $0.05$, $\frac{1}{20}$, $5\%$

$$
\boxed{\text{See detailed steps above for coloring instructions.}}
$$