What is 18/60 plus 9/21? (Answer: 51/70)

Exact Answer

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Problem: What is 18/60 plus 9/21?
Formula / Expression: 18/60 + 9/21
Final Answer: 51/70
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 60 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 420 (which is smaller than their product 60 × 21 = 1260, keeping the calculation simpler).
Working: LCD(60, 21) = 420

Step 2: Convert to Equivalent Fractions with Common Denominator 420
Multiply the numerator and denominator of 18/60 by 7, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.
Working: 18 × 7/60 × 7 = 126/420 and 9 × 20/21 × 20 = 180/420

Step 3: Add the Numerators
Now add the numerators (126 + 180 = 306) and keep the common denominator 420 unchanged.
Working: 126 + 180/420 = 306/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 306 and 420, which is 6. Divide both the numerator and denominator by 6.
Working: 306 ÷ 6/420 ÷ 6 = 51/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 70 produces a repeating decimal (approximately 0.728571, or 72.8571%).
Working: 51 ÷ 70 = 0.728571 (72.8571%)

Key Values:
- Simplified Fraction: 51/70
- Mixed Number Form: 51/70
- Decimal Value: 0.728571
- Percentage: 72.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-18-60-plus-9-21/
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18/60 + 9/21 = 51/70

Simplified Fraction

51/70

Mixed Number

Proper (51/70)

Decimal Value

0.728571

Percentage

72.8571%

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Step-by-Step Solution: 18/60 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 60 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 420 (which is smaller than their product 60 × 21 = 1260, keeping the calculation simpler).

LCD(60, 21) = 420

Step 2

Convert to Equivalent Fractions with Common Denominator 420

Multiply the numerator and denominator of 18/60 by 7, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.

18 × 7/60 × 7 = 126/420 and 9 × 20/21 × 20 = 180/420

Step 3

Add the Numerators

Now add the numerators (126 + 180 = 306) and keep the common denominator 420 unchanged.

126 + 180/420 = 306/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 306 and 420, which is 6. Divide both the numerator and denominator by 6.

306 ÷ 6/420 ÷ 6 = 51/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 70 produces a repeating decimal (approximately 0.728571, or 72.8571%).

51 ÷ 70 = 0.728571 (72.8571%)

Visual Representation

The diagram below illustrates 18/60 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/70`
Mixed Number Form	`51/70`
Decimal Form	`0.728571`
Percentage	`72.8571%`

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Frequently Asked Questions

What is 18/60 plus 9/21 as a fraction?

18/60 + 9/21 in simplest fraction form is 51/70.

What is 18/60 plus 9/21 as a decimal?

18/60 + 9/21 converted to a decimal is 0.728571.

What is 18/60 plus 9/21 as a percentage?

18/60 + 9/21 expressed as a percentage is 72.8571%.

Does 18/60 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.728571...) because the denominator contains prime factors other than 2 and 5.