Question

1. are these ratios equivalent?

2 apples to 6 oranges
4 apples to 12 oranges
no
yes

1. are these ratios equivalent?

6 pencils to 8 pens
3 pencils to 5 pens

Explanation:

Question 3

Step1: Simplify first ratio

The ratio of apples to oranges is \( \frac{2}{6} \), simplify by dividing numerator and denominator by 2: \( \frac{2\div2}{6\div2}=\frac{1}{3} \)

Step2: Simplify second ratio

The ratio of apples to oranges is \( \frac{4}{12} \), simplify by dividing numerator and denominator by 4: \( \frac{4\div4}{12\div4}=\frac{1}{3} \)

Step3: Compare ratios

Both ratios simplify to \( \frac{1}{3} \), so they are equivalent.

Step1: Simplify first ratio

The ratio of pencils to pens is \( \frac{6}{8} \), simplify by dividing numerator and denominator by 2: \( \frac{6\div2}{8\div2}=\frac{3}{4} \)

Step2: Simplify second ratio

The ratio of pencils to pens is \( \frac{3}{5} \)

Step3: Compare ratios

\( \frac{3}{4} \) (or 0.75) is not equal to \( \frac{3}{5} \) (or 0.6), so the ratios are not equivalent.

Answer:

Yes

Question 4