Final answer:
The ratios 1:6 and 7:42 are proportional because when written as fractions and simplified, 1/6 is equivalent to 7/42. Both ratios simplify to the same fractional value, proving they are proportional.
Step-by-step explanation:
Are the ratios 1:6 and 7:42 proportional to each other? To determine if ratios are proportional, we can compare them by converting them into fractions and then checking if they are equivalent.
First, we convert the ratio 1:6 into a fraction: 1/6. We do the same for the ratio 7:42, which simplifies to 7/42. Notice that 7 divded by 6 is actually the fraction 1/6, which means these fractions are equivalent. Since 7 is 6 times 7, and 42 is 6 times 6, the two ratios are in fact the same when simplified, but represented with different numbers. Hence, they form a proportion.
Therefore, we can say that the ratios 1:6 and 7:42 are proportional because 1/6 is equal to 7/42 after simplification.