To divide 96 in the ratio 5:7, find the two parts by splitting 96 according to the fractional share of each part. The answer is 40 and 56. The sum of the ratio terms is 5 + 7 = 12. The first part is (5/12) × 96 = 40, and the second part is (7/12) × 96 = 56.
To divide 96 in ratio 5:7: sum = 12, one part = 96/12 = 8.
First part (5 shares) = 5 × 8 = 40.
Second part (7 shares) = 7 × 8 = 56.
Check: 40 + 56 = 96 and 40:56 = 5:7. ✓
Formula: First part = a/(a+b) × N; Second part = b/(a+b) × N.
Step 1: Add the ratio terms. 5 + 7 = 12
Step 2: Find the value of one part. 96 ÷ 12 = 8
Step 3: Multiply each ratio term by 8. First part = 5 × 8 = 40 Second part = 7 × 8 = 56
Answer: The two parts are 40 and 56.
Verification: 40 + 56 = 96 ✓ 40 : 56 = 5 : 7 ✓ (divide both by 8)
To divide a number N in the ratio a : b:
Formula: First part = (a / (a+b)) × N Second part = (b / (a+b)) × N
For N = 96, a = 5, b = 7: First part = (5/12) × 96 = 40 Second part = (7/12) × 96 = 56
More examples: • Divide 120 in ratio 3:5: Parts: (3/8)×120 = 45 and (5/8)×120 = 75
• Divide 180 in ratio 4:5: Parts: (4/9)×180 = 80 and (5/9)×180 = 100
• Divide 72 in ratio 1:2: Parts: (1/3)×72 = 24 and (2/3)×72 = 48
Step 1: Sum of ratio = 5+7 = 12. Step 2: Value of one unit = 96/12 = 8. Step 3: First part = 5×8 = 40; Second part = 7×8 = 56. The two parts are 40 and 56. Check: 40+56=96 ✓.
To divide N in ratio a:b — First part = (a/(a+b)) × N; Second part = (b/(a+b)) × N.
The two parts are 40 (for ratio 5) and 56 (for ratio 7).
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