Select all fractions equivalent to 312

Question

. Use the model to help you.

A large rectangle is divided into 12 equal-sized pieces. These pieces are arranged into 3 rows and 4 columns. The second column is colored yellow.

(1 point)
Responses

12

1 2

612

6 12

624

6 24

14

1 4

48

Answer 1

To find all fractions equivalent to \( \frac{3}{12} \), we can simplify \( \frac{3}{12} \) and also find other fractions that yield the same value.

1. First, simplify \( \frac{3}{12} \):

   • Divide both the numerator and the denominator by 3: \[ \frac{3 \div 3}{12 \div 3} = \frac{1}{4} \]
   • Thus, \( \frac{3}{12} = \frac{1}{4} \).

2. Now let’s determine other fractions from the response choices that are equivalent to \( \frac{3}{12} \) or \( \frac{1}{4} \):

   • \( \frac{6}{12} \) (Numerator and denominator both multiplied by 2): \[ \frac{6 \div 6}{12 \div 6} = \frac{1}{2} \]
   • \( \frac{6}{24} \) (Numerator multiplied by 2 and denominator by 2): \[ \frac{6 \div 6}{24 \div 6} = \frac{1}{4} \]
   • \( \frac{3}{12} \) is already considered.
   • \( \frac{1}{2} \) is not equivalent.
   • \( 12 \) isn't a fraction and doesn’t apply.
   • Similarly, \( 4 \) doesn’t apply.
   • \( \frac{48}{?} \) does not correspond to equivalent fractions either.

3. From the options you provided, the equivalent fractions are:

   • \( \frac{6}{24} \)
   • \( \frac{1}{4} \)

Thus, based on these calculations, the equivalent fractions to \( \frac{3}{12} \) from the provided options are:

• \( \frac{6}{12} \)
• \( \frac{6}{24} \)
• \( \frac{1}{4} \)

If some of the options contained other fractions that could reduce to \( \frac{1}{4} \), let me know!