Fill in the boxes and complete the equivalent fractions:
`2/(3)=square/(9)=10/(square)=square/(21)`

Answer

To solve the problem of finding equivalent fractions for the given fractions, we will fill in the boxes step by step.

### Step 1: Understanding Equivalent Fractions
Equivalent fractions are fractions that represent the same value or proportion, even though they may have different numerators and denominators.

### Step 2: Finding the First Equivalent Fraction
We start with the fraction \( \frac{2}{3} \) and need to find an equivalent fraction with a denominator of 9.

To find this, we can set up the equation:
\[ \frac{2}{3} = \frac{x}{9} \]
To find \( x \), we can cross-multiply:
\[ 2 \times 9 = 3 \times x \implies 18 = 3x \implies x = \frac{18}{3} = 6 \]
So, the first equivalent fraction is \( \frac{6}{9} \).

### Step 3: Finding the Second Equivalent Fraction
Next, we need to find the equivalent fraction for \( \frac{10}{?} \) that is equal to \( \frac{2}{3} \).

We set up the equation:
\[ \frac{2}{3} = \frac{10}{y} \]
Cross-multiplying gives us:
\[ 2y = 3 \times 10 \implies 2y = 30 \implies y = \frac{30}{2} = 15 \]
Thus, the second equivalent fraction is \( \frac{10}{15} \).

### Step 4: Finding the Third Equivalent Fraction
Now, we need to find the equivalent fraction for \( \frac{?}{21} \) that is equal to \( \frac{2}{3} \).

Setting up the equation:
\[ \frac{2}{3} = \frac{z}{21} \]
Cross-multiplying gives us:
\[ 2 \times 21 = 3z \implies 42 = 3z \implies z = \frac{42}{3} = 14 \]
So, the third equivalent fraction is \( \frac{14}{21} \).

### Final Answer
Now we can fill in the boxes:
\[ \frac{2}{3} = \frac{6}{9} = \frac{10}{15} = \frac{14}{21} \]

### Summary of Equivalent Fractions
- \( \frac{2}{3} \)
- \( \frac{6}{9} \)
- \( \frac{10}{15} \)
- \( \frac{14}{21} \)