2/3 = ?/6 = 6/? = ?/12 = 10/?

Answer 1

To solve the given set of equivalent fractions, we need to find the unknown values. Let's solve each unknown step by step:

1. \( \frac{2}{3} = \frac{?}{6} \)

To find the unknown numerator, set up the equation:
\[ \frac{2}{3} = \frac{x}{6} \]

Cross-multiply to solve for \( x \):
\[ 2 \times 6 = 3 \times x \]
\[ 12 = 3x \]
\[ x = \frac{12}{3} \]
\[ x = 4 \]

So, \( \frac{2}{3} = \frac{4}{6} \).

2. \( \frac{2}{3} = 6/? \)

To find the unknown denominator, set up the equation:
\[ \frac{2}{3} = \frac{6}{y} \]

Cross-multiply to solve for \( y \):
\[ 2y = 3 \times 6 \]
\[ 2y = 18 \]
\[ y = \frac{18}{2} \]
\[ y = 9 \]

So, \( \frac{2}{3} = \frac{6}{9} \).

3. \( \frac{2}{3} = ?/12 \)

To find the unknown numerator, set up the equation:
\[ \frac{2}{3} = \frac{z}{12} \]

Cross-multiply to solve for \( z \):
\[ 2 \times 12 = 3 \times z \]
\[ 24 = 3z \]
\[ z = \frac{24}{3} \]
\[ z = 8 \]

So, \( \frac{2}{3} = \frac{8}{12} \).

4. \( \frac{2}{3} = 10/? \)

To find the unknown denominator, set up the equation:
\[ \frac{2}{3} = \frac{10}{w} \]

Cross-multiply to solve for \( w \):
\[ 2w = 3 \times 10 \]
\[ 2w = 30 \]
\[ w = \frac{30}{2} \]
\[ w = 15 \]

So, \( \frac{2}{3} = \frac{10}{15} \).

Summarizing all the equivalent fractions:
\[ \frac{2}{3} = \frac{4}{6} = \frac{6}{9} = \frac{8}{12} = \frac{10}{15} \]

Thus, the answers to the unknowns are:
- \( \frac{2}{3} = \frac{4}{6} \)
- \( \frac{2}{3} = \frac{6}{9} \)
- \( \frac{2}{3} = \frac{8}{12} \)
- \( \frac{2}{3} = \frac{10}{15} \)