What is 14/60 plus 9/21? (Answer: 139/210)

Exact Answer

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Problem: What is 14/60 plus 9/21?
Formula / Expression: 14/60 + 9/21
Final Answer: 139/210
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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 14/60 by 7, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.
Working: 14 × 7/60 × 7 = 98/420 and 9 × 20/21 × 20 = 180/420

Step 3: Add the Numerators
Now add the numerators (98 + 180 = 278) and keep the common denominator 420 unchanged.
Working: 98 + 180/420 = 278/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 278 and 420, which is 2. Divide both the numerator and denominator by 2.
Working: 278 ÷ 2/420 ÷ 2 = 139/210

Step 5: Decimal & Percentage Representation
Dividing the numerator 139 by denominator 210 produces a repeating decimal (approximately 0.661905, or 66.1905%).
Working: 139 ÷ 210 = 0.661905 (66.1905%)

Key Values:
- Simplified Fraction: 139/210
- Mixed Number Form: 139/210
- Decimal Value: 0.661905
- Percentage: 66.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-14-60-plus-9-21/
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14/60 + 9/21 = 139/210

Simplified Fraction

139/210

Mixed Number

Proper (139/210)

Decimal Value

0.661905

Percentage

66.1905%

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Step-by-Step Solution: 14/60 + 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 14/60 by 7, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.

14 × 7/60 × 7 = 98/420 and 9 × 20/21 × 20 = 180/420

Step 3

Add the Numerators

Now add the numerators (98 + 180 = 278) and keep the common denominator 420 unchanged.

98 + 180/420 = 278/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 278 and 420, which is 2. Divide both the numerator and denominator by 2.

278 ÷ 2/420 ÷ 2 = 139/210

Step 5

Decimal & Percentage Representation

Dividing the numerator 139 by denominator 210 produces a repeating decimal (approximately 0.661905, or 66.1905%).

139 ÷ 210 = 0.661905 (66.1905%)

Visual Representation

The diagram below illustrates 14/60 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`139/210`
Mixed Number Form	`139/210`
Decimal Form	`0.661905`
Percentage	`66.1905%`

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Frequently Asked Questions

What is 14/60 plus 9/21 as a fraction?

14/60 + 9/21 in simplest fraction form is 139/210.

What is 14/60 plus 9/21 as a decimal?

14/60 + 9/21 converted to a decimal is 0.661905.

What is 14/60 plus 9/21 as a percentage?

14/60 + 9/21 expressed as a percentage is 66.1905%.

Does 14/60 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.661905...) because the denominator contains prime factors other than 2 and 5.