Using division, select all the fractions that are equivalent to 30/40

Question

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(1 point)
Responses

5/10

5/10

5/8

5/8

3/4

3/4

12/15

12/15

6/8

Answer 1

To find fractions that are equivalent to \( \frac{30}{40} \), we can simplify \( \frac{30}{40} \) to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 30 and 40 is 10.

So we divide both the numerator and the denominator by 10:

\[ \frac{30 \div 10}{40 \div 10} = \frac{3}{4} \]

Now, we check the given options to see which fractions are equivalent to \( \frac{3}{4} \):

1. \( \frac{5}{10} \): Simplifies to \( \frac{1}{2} \) (not equivalent).
2. \( \frac{5}{8} \): Does not simplify to \( \frac{3}{4} \) (not equivalent).
3. \( \frac{3}{4} \): Is equivalent (correct).
4. \( \frac{12}{15} \): Simplifies to \( \frac{4}{5} \) (not equivalent).
5. \( \frac{6}{8} \): Simplifies to \( \frac{3}{4} \) (correct).

So the fractions that are equivalent to \( \frac{30}{40} \) are:

• \( \frac{3}{4} \)
• \( \frac{6}{8} \)

Final answers: \( \frac{3}{4} \) and \( \frac{6}{8} \).