Write each ratio as a fraction in simplest form : 11 1/3 out of 50 2/3, 5 1/4 out of 20 3/4, 28 1/2 : 30 1/4
11 1/3 out of 50 2/3
= (34/3)/(62/3)
= 17/31
now you do the other two in the same way, let me know what you got.
To convert each ratio into a fraction in simplest form, we need to find a common denominator for the fractions.
1) 11 1/3 out of 50 2/3:
To find a common denominator, we multiply the two denominators: 3 * 3 = 9.
Then, convert the mixed numbers into improper fractions:
11 1/3 = 34/3
50 2/3 = 152/3
The ratio is 34/3 : 152/3
2) 5 1/4 out of 20 3/4:
Again, we need to find a common denominator for the fractions, which is 4.
Convert the mixed numbers into improper fractions:
5 1/4 = 21/4
20 3/4 = 83/4
The ratio is 21/4 : 83/4
3) 28 1/2 : 30 1/4:
Finding a common denominator, we multiply the two denominators: 2 * 4 = 8.
Convert the mixed numbers into improper fractions:
28 1/2 = 57/2
30 1/4 = 121/4
The ratio is 57/2 : 121/4
Now, let's simplify each fraction in the ratios:
1) 34/3 : 152/3:
Since the denominators are the same, we can compare the numerators:
34 : 152
To simplify the ratio, we divide both numbers by their greatest common divisor, which is 2:
34 ÷ 2 : 152 ÷ 2
17 : 76
2) 21/4 : 83/4:
Again, since the denominators are the same, we can compare the numerators:
21 : 83
We simplify the ratio by dividing both numbers by their greatest common divisor, which is 1:
21 ÷ 1 : 83 ÷ 1
21 : 83
3) 57/2 : 121/4:
Since the denominators are different, we need to find a common denominator, which is 4.
Multiplying the first ratio by 2/2 and the second ratio by 1/1, we get:
(57/2) * (2/2) : (121/4) * (1/1)
114/4 : 121/4
The denominators are the same, so we can compare the numerators:
114 : 121
To simplify the ratio, we divide both numbers by their greatest common divisor, which is 1:
114 ÷ 1 : 121 ÷ 1
114 : 121
To write each ratio as a fraction in simplest form, we need to convert the mixed numbers into improper fractions and then divide the two fractions to get the ratio.
1. First, let's convert the mixed numbers 11 1/3 and 50 2/3 into improper fractions:
- 11 1/3 = (11 * 3 + 1) / 3 = 34/3
- 50 2/3 = (50 * 3 + 2) / 3 = 152/3
2. Divide the two improper fractions to get the ratio:
- (34/3) / (152/3) = 34/3 * 3/152 = 34/152 = 17/76
Therefore, the ratio 11 1/3 out of 50 2/3 can be written as 17/76.
Let's do the same for the other ratios:
3. Convert the mixed numbers 5 1/4 and 20 3/4 into improper fractions:
- 5 1/4 = (5 * 4 + 1) / 4 = 21/4
- 20 3/4 = (20 * 4 + 3) / 4 = 83/4
4. Divide the two improper fractions to get the ratio:
- (21/4) / (83/4) = 21/4 * 4/83 = 21/83
Therefore, the ratio 5 1/4 out of 20 3/4 can be written as 21/83.
5. Convert the mixed numbers 28 1/2 and 30 1/4 into improper fractions:
- 28 1/2 = (28 * 2 + 1) / 2 = 57/2
- 30 1/4 = (30 * 4 + 1) / 4 = 121/4
6. Divide the two improper fractions to get the ratio:
- (57/2) / (121/4) = 57/2 * 4/121 = 57/121
Therefore, the ratio 28 1/2 : 30 1/4 can be written as 57/121.
To summarize:
- 11 1/3 out of 50 2/3 = 17/76
- 5 1/4 out of 20 3/4 = 21/83
- 28 1/2 : 30 1/4 = 57/121