Write each of the following ratios in simplest form.
1. The ratio of 5 3/5 to 2 1/10
A~8 TO 3?
2. The ratio of 7 dimes to 3 quarters
A~ 14 TO 15?
#1 correct
#2 if you are talking 'value', correct
To write each of the given ratios in simplest form, we need to simplify the fractions involved.
1. The ratio of 5 3/5 to 2 1/10:
To find the ratio of 5 3/5 to 2 1/10, we need to first convert the mixed numbers to improper fractions.
5 3/5 can be converted to an improper fraction by multiplying the whole number (5) by the denominator and adding the numerator, then putting that sum over the denominator:
5 3/5 = (5 * 5 + 3) / 5 = 28/5
2 1/10 can be converted to an improper fraction in the same way:
2 1/10 = (2 * 10 + 1) / 10 = 21/10
Now we can write the ratio as a fraction:
The ratio of 5 3/5 to 2 1/10 is 28/5 : 21/10.
To simplify a ratio, we need to simplify the fractions separately.
First, simplify 28/5:
There are no common factors between the numerator and denominator, so the fraction is already in simplified form.
Next, simplify 21/10:
Both 21 and 10 can be divided by 7, resulting in a simplified fraction:
21/10 = (21 ÷ 7) / (10 ÷ 7) = 3/2
Now we can write the ratio in simplest form:
28/5 : 21/10 simplifies to 28/5 : 3/2.
To compare or express these fractions using the same denominator, we can convert them to a common denominator. In this case, the least common denominator is 10:
28/5 can be converted to the equivalent fraction with a denominator of 10 by multiplying both the numerator and denominator by 2:
28/5 = (28 * 2) / (5 * 2) = 56/10
Now our ratio becomes:
56/10 : 3/2
Finally, we simplify the ratio one more time by dividing both fractions by their greatest common factor, which is 2:
56/10 = (56 ÷ 2) / (10 ÷ 2) = 28/5
3/2 remains the same.
So, the ratio in simplest form is:
28/5 : 3/2
2. The ratio of 7 dimes to 3 quarters:
To write the ratio of 7 dimes to 3 quarters, we simply express it as a fraction:
The ratio of 7 dimes to 3 quarters is 7/3.
Since both 7 and 3 have no common factors, the ratio 7/3 is already in simplest form.
So, the ratio in simplest form for the second question is:
7/3