Let’s solve this step by step.
We are given a table with 5 amino acids and their counts in a protein:
- alanine (ala): 13
- glycine (gly): 20
- serine (ser): 7
- proline (pro): 9
- valine (val): 18
Total number of amino acids = 13 + 20 + 7 + 9 + 18
Let’s add them:
13 + 20 = 33
33 + 7 = 40
40 + 9 = 49
49 + 18 =
67
So, total amino acids =
67
Now, we need to find the mole fraction for each.
Mole fraction = (number of that amino acid) / (total number of amino acids)
So:
- ala: 13 / 67 ≈ ?
- gly: 20 / 67 ≈ ?
- ser: 7 / 67 ≈ ?
- pro: 9 / 67 ≈ ?
- val: 18 / 67 ≈ ?
Let’s calculate each one carefully.
First, 13 ÷ 67:
67 × 0.19 = 12.73 → close to 13
13 - 12.73 = 0.27 → so about 0.194
Actually, let’s do proper division:
13 ÷ 67 = 0.194029... ≈
0.194
20 ÷ 67:
67 × 0.2985 ≈ 20? Let’s compute:
67 × 0.3 = 20.1 → too big
67 × 0.298 = 67×0.3 - 67×0.002 = 20.1 - 0.134 = 19.966 → very close to 20
So 20 ÷ 67 ≈
0.2985 → round to
0.299? Wait, let's be precise.
Better to use calculator-style steps:
20 ÷ 67 = 0.298507... → typically rounded to 3 decimal places:
0.299
But wait — let’s check if we should keep more precision or follow standard rounding.
Actually, since the problem says “mole fraction”, and doesn’t specify decimal places, but in chemistry usually 3 or 4 decimals are used. But looking at the answer format expected, probably 3 decimal places is fine.
Wait — let me recalculate all with consistent precision.
Use exact fractions first, then convert to decimal.
Total = 67
ala: 13/67 = ?
Do long division:
67 into 130 → 1 time → 67, remainder 63 → bring down 0 → 630
67 into 630 → 9 times → 603, remainder 27 → bring down 0 → 270
67 into 270 → 4 times → 268, remainder 2 → so 0.194...
So 13/67 ≈ 0.1940 →
0.194
gly: 20/67
67 into 200 → 2 times → 134, rem 66 → 660
67 into 660 → 9 times → 603, rem 57 → 570
67 into 570 → 8 times → 536, rem 34 → 340
67 into 340 → 5 times → 335, rem 5 → so 0.2985... →
0.299 (rounded to 3 decimals)
Wait — 0.2985 rounds to 0.299? Yes, because 5 or above rounds
Parent Tip: Review the logic above to help your child master the concept of genetics basics worksheet.
