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

To solve this worksheet, we need to find groups of three numbers in each grid that represent the same value. These numbers can be fractions, decimals, or percentages.

Here is the step-by-step logic for finding the matches in each grid:

Grid 1 (Top Left)
* Look for equivalents of $\frac{3}{4}$.
* $\frac{3}{4}$ as a decimal is $0.75$ ($3 \div 4 = 0.75$).
* $0.75$ as a percentage is $75\%$.
* Match: $\frac{3}{4}$, $0.75$, $75\%$

Grid 2 (Top Middle)
* Look for equivalents of $\frac{1}{5}$.
* $\frac{1}{5}$ as a decimal is $0.2$ ($1 \div 5 = 0.2$).
* $0.2$ as a percentage is $20\%$.
* Match: $0.2$, $\frac{1}{5}$, $20\%$

Grid 3 (Top Right)
* Look for equivalents of $\frac{1}{4}$.
* $\frac{1}{4}$ as a decimal is $0.25$.
* $0.25$ as a percentage is $25\%$.
* Note: $\frac{4}{10}$ is $0.4$, and $\frac{44}{100}$ is $0.44$, so they don't match.
* Match: $0.25$, $25\%$, $\frac{1}{4}$

Grid 4 (Second Row, Left)
* Look for equivalents of $\frac{7}{10}$.
* $\frac{7}{10}$ as a decimal is $0.7$.
* $0.7$ as a percentage is $70\%$.
* Match: $\frac{7}{10}$, $70\%$, $0.7$

Grid 5 (Second Row, Middle)
* Look for equivalents of $\frac{1}{2}$.
* $\frac{1}{2}$ as a decimal is $0.5$.
* $0.5$ as a percentage is $50\%$.
* Match: $\frac{1}{2}$, $50\%$, $0.5$

Grid 6 (Second Row, Right)
* Look for equivalents of $\frac{55}{100}$.
* $\frac{55}{100}$ simplifies to $\frac{11}{20}$, but let's look at the decimal. It is $0.55$.
* Wait, let's look closer. We have $\frac{55}{100}$, $55\%$, and... do we have $0.55? No.
* Let's check $\frac{5}{15}$. That simplifies to $\frac{1}{3}$. No match.
* Let's check $\frac{15}{100}$. That is $0.15$ and $15\%$.
* So, $\frac{15}{100} = 0.15 = 15\%$.
* Match: $\frac{15}{100}$, $0.15$, $15\%$

Grid 7 (Third Row, Left)
* Look for equivalents of $\frac{44}{100}$.
* $\frac{44}{100}$ as a decimal is $0.44$.
* $0.44$ as a percentage is $44\%$. Do we have $44\%$? No.
* Let's try $\frac{4}{100}$. That is $0.04$ and $4\%$. No match.
* Let's try $\frac{2}{5}$. $\frac{2}{5} = 0.4 = 40\%$.
* We have $0.4$, $\frac{2}{5}$, and $40\%$.
* Match: $0.4$, $\frac{2}{5}$, $40\%$

Grid 8 (Third Row, Middle)
* Look for equivalents of $\frac{6}{100}$? No, that's $0.06$.
* Look for $\frac{2}{3}$. $\frac{2}{3} \approx 0.66$ and $66\%$.
* We have $0.66$, $66\%$, and $\frac{2}{3}$.
* Match: $0.66$, $66\%$, $\frac{2}{3}$

Grid 9 (Third Row, Right)
* Look for equivalents of $\frac{1}{10}$.
* $\frac{1}{10}$ as a decimal is $0.1$. Do we have $0.1$? No, we have $0.01$ and $1.1$.
* Look for $\frac{11}{100}$. That is $0.11$ and $11\%$.
* We have $\frac{11}{100}$, $11\%$, and... do we have $0.11$? No.
* Let's re-examine.
* $\frac{1}{100} = 0.01 = 1\%$.
* We have $\frac{1}{100}$, $0.01$, and $1\%$.
* Match: $\frac{1}{100}$, $0.01$, $1\%$

Grid 10 (Bottom Left)
* Look for equivalents of $\frac{8}{10}$.
* $\frac{8}{10}$ as a decimal is $0.8$.
* $0.8$ as a percentage is $80\%$.
* Match: $\frac{8}{10}$, $0.8$, $80\%$

Grid 11 (Bottom Middle)
* Look for equivalents of $\frac{1}{3}$.
* $\frac{1}{3}$ as a decimal is $0.\dot{3}$ (repeating).
* $\frac{1}{3}$ as a percentage is $33\frac{1}{3}\%$.
* We have $0.\dot{3}$, $33\frac{1}{3}\%$, and $\frac{1}{3}$.
* Match: $0.\dot{3}$, $33\frac{1}{3}\%$, $\frac{1}{3}$

Grid 12 (Bottom Right)
* Look for equivalents of $\frac{1}{20}$.
* $\frac{1}{20}$ as a decimal is $0.05$ ($1 \div 20 = 0.05$).
* $0.05$ as a percentage is $5\%$.
* Match: $\frac{1}{20}$, $0.05$, $5\%$

Final Answer:
Here are the three equivalent values to color in for each grid:

1. Top Left: $\frac{3}{4}$, $0.75$, $75\%$
2. Top Middle: $0.2$, $\frac{1}{5}$, $20\%$
3. Top Right: $0.25$, $25\%$, $\frac{1}{4}$
4. 2nd Row Left: $\frac{7}{10}$, $0.7$, $70\%$
5. 2nd Row Middle: $\frac{1}{2}$, $0.5$, $50\%$
6. 2nd Row Right: $\frac{15}{100}$, $0.15$, $15\%$
7. 3rd Row Left: $0.4$, $\frac{2}{5}$, $40\%$
8. 3rd Row Middle: $0.66$, $66\%$, $\frac{2}{3}$
9. 3rd Row Right: $\frac{1}{100}$, $0.01$, $1\%$
10. Bottom Left: $\frac{8}{10}$, $0.8$, $80\%$
11. Bottom Middle: $0.\dot{3}$, $33\frac{1}{3}\%$, $\frac{1}{3}$
12. Bottom Right: $\frac{1}{20}$, $0.05$, $5\%$