Question

using division, select all the fractions that are equivalent to \\(\frac{30}{40}\\). (1 point) \\(\frac{5}{10}\\) \\(\frac{5}{8}\\) \\(\frac{3}{4}\\) \\(\frac{12}{15}\\) \\(\frac{6}{8}\\)

Explanation:

First, simplify $\frac{30}{40}$ by dividing numerator and denominator by 10: $\frac{30\div10}{40\div10}=\frac{3}{4}$. Now check each fraction:

Step1: Check $\frac{5}{10}$

Simplify: $\frac{5\div5}{10\div5}=\frac{1}{2}
eq\frac{3}{4}$.

Step2: Check $\frac{5}{8}$

It is already in simplest form, $\frac{5}{8}
eq\frac{3}{4}$.

Step3: Check $\frac{3}{4}$

It is equal to $\frac{3}{4}$.

Step4: Check $\frac{12}{15}$

Simplify: $\frac{12\div3}{15\div3}=\frac{4}{5}
eq\frac{3}{4}$.

Step5: Check $\frac{6}{8}$

Simplify: $\frac{6\div2}{8\div2}=\frac{3}{4}$, which is equal to $\frac{3}{4}$.

Answer:

The fractions equivalent to $\frac{30}{40}$ are $\frac{3}{4}$ (3/4) and $\frac{6}{8}$ (6/8), and also we can check $\frac{12}{15}$ was miscalculated before? Wait, no, let's re - check $\frac{12}{15}$: $\frac{12\div3}{15\div3}=\frac{4}{5}$, no. Wait, original $\frac{30}{40}=\frac{3}{4}$. Let's check $\frac{12}{15}$ again: 12 divided by 3 is 4, 15 divided by 3 is 5, so $\frac{4}{5}$. Then $\frac{3}{4}$: 3 divided by 3 is 1, 4 divided by 3 is not integer. Wait, $\frac{30}{40}=\frac{3}{4}$. Now check $\frac{12}{15}$: 12/15 = 4/5, not 3/4. $\frac{6}{8}$: 6/8 = 3/4. $\frac{3}{4}$: 3/4. Also, let's check $\frac{12}{15}$ again, maybe I made a mistake. Wait, 30/40 = 3/4. 12/15: divide numerator and denominator by 3, get 4/5. 6/8: divide by 2, get 3/4. 3/4: same. What about $\frac{5}{10}$: 1/2. $\frac{5}{8}$: 5/8. Wait, also, let's check $\frac{12}{15}$ again, maybe the problem was to find equivalent to 30/40, which is 3/4. So the correct ones are $\frac{3}{4}$, $\frac{6}{8}$, and also $\frac{12}{15}$? Wait, no, 12/15 is 4/5, which is not 3/4. Wait, maybe I miscalculated 30/40. 30 divided by 10 is 3, 40 divided by 10 is 4, so 3/4. 6/8: 6 divided by 2 is 3, 8 divided by 2 is 4, so 3/4. 3/4: 3/4. What about 12/15: 12 divided by 3 is 4, 15 divided by 3 is 5, so 4/5. So the correct fractions are $\frac{3}{4}$ (3/4), $\frac{6}{8}$ (6/8), and also let's check 12/15 again. Wait, maybe the original fraction was 30/40, and 12/15: 30/40 = 3/4, 12/15 = 4/5, not equal. Wait, maybe I made a mistake in the first calculation. Let's do division for each:

• $\frac{5}{10}$: 5÷10 = 0.5; $\frac{30}{40}$ = 0.75. Not equal.
• $\frac{5}{8}$: 5÷8 = 0.625; 0.75≠0.625. Not equal.
• $\frac{3}{4}$: 3÷4 = 0.75; equal to 30÷40 = 0.75.
• $\frac{12}{15}$: 12÷15 = 0.8; 0.75≠0.8. Not equal.
• $\frac{6}{8}$: 6÷8 = 0.75; equal to 0.75.

So the fractions equivalent to $\frac{30}{40}$ are $\frac{3}{4}$ (3/4) and $\frac{6}{8}$ (6/8).