120 divided by 7 equals 17 with a remainder of 1. As a decimal, 120 ÷ 7 = 17.142857142857... (a repeating decimal). As a mixed fraction, it is 17 1/7. This division cannot be done exactly because 7 does not divide into 120 evenly — it leaves a remainder of 1.
120 ÷ 7 = 17 remainder 1.
As a decimal: 17.142857... (repeating decimal, block: 142857).
As a mixed fraction: 17 1/7.
As an improper fraction: 120/7.
Verification: 7 × 17 + 1 = 119 + 1 = 120 ✓
7 × 17 = 119 (closest multiple of 7 below 120).
The decimal 0.142857... is the repeating decimal for 1/7.
Setting up: 120 ÷ 7
Step 1: How many times does 7 go into 12? 7 × 1 = 7 7 × 2 = 14 (too large) So 7 goes into 12 once (1 time). Write 1 in the quotient. 12 − 7 = 5 (remainder)
Step 2: Bring down the next digit (0). New number = 50. How many times does 7 go into 50? 7 × 7 = 49 7 × 8 = 56 (too large) So 7 goes into 50 seven times (7 times). Write 7 in the quotient. 50 − 49 = 1 (remainder)
Result: Quotient = 17, Remainder = 1
Verification: 7 × 17 + 1 = 119 + 1 = 120 ✓
As a decimal: 120 ÷ 7 = 17.142857142857... This is a recurring (repeating) decimal. The repeating block is 142857 — it repeats infinitely: 17.142857̄
As a mixed fraction: 120 ÷ 7 = 17 remainder 1 Mixed fraction = 17 1/7
As an improper fraction: 120/7 (already in simplest form — HCF of 120 and 7 is 1)
Approximate decimal value: 120 ÷ 7 ≈ 17.14 (rounded to 2 decimal places) 120 ÷ 7 ≈ 17.143 (rounded to 3 decimal places)
Note on 142857 — the cyclic number: 1/7 = 0.142857142857... This repeating block (142857) is a special cyclic number with interesting mathematical properties.
Multiples of 7 near 120: 7 × 15 = 105 7 × 16 = 112 7 × 17 = 119 ← closest without exceeding 120 7 × 18 = 126 ← exceeds 120
So 7 × 17 = 119 → 120 − 119 = 1 (remainder)
Comparison: • 119 ÷ 7 = 17 exactly (no remainder) • 120 ÷ 7 = 17 remainder 1 • 126 ÷ 7 = 18 exactly (no remainder)
Other divisions of 120: • 120 ÷ 2 = 60 • 120 ÷ 3 = 40 • 120 ÷ 4 = 30 • 120 ÷ 5 = 24 • 120 ÷ 6 = 20 • 120 ÷ 7 = 17.14... • 120 ÷ 8 = 15 • 120 ÷ 10 = 12
120 divided by 7 = 17 remainder 1. As a decimal: 17.142857... (repeating). As a mixed fraction: 17 1/7. Since 7 × 17 = 119 and 120 − 119 = 1, the quotient is 17 with remainder 1.
120 ÷ 7 = 17.142857142857... This is a recurring decimal — the block 142857 repeats infinitely. Rounded to 2 decimal places: 17.14.
120 ÷ 7 = 120/7 as an improper fraction, or 17 1/7 as a mixed number. The fraction 120/7 is already in its simplest form since HCF(120, 7) = 1.
The remainder when 120 is divided by 7 is 1. Since 7 × 17 = 119 and 120 − 119 = 1, the quotient is 17 and the remainder is 1.
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