What is 11/60 plus 7/21? (Answer: 31/60)

Exact Answer

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Problem: What is 11/60 plus 7/21?
Formula / Expression: 11/60 + 7/21
Final Answer: 31/60
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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 11/60 by 7, and multiply the numerator and denominator of 7/21 by 20 so both fractions share the common base 420.
Working: 11 × 7/60 × 7 = 77/420 and 7 × 20/21 × 20 = 140/420

Step 3: Add the Numerators
Now add the numerators (77 + 140 = 217) and keep the common denominator 420 unchanged.
Working: 77 + 140/420 = 217/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 217 and 420, which is 7. Divide both the numerator and denominator by 7.
Working: 217 ÷ 7/420 ÷ 7 = 31/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 60 produces a repeating decimal (approximately 0.516667, or 51.6667%).
Working: 31 ÷ 60 = 0.516667 (51.6667%)

Key Values:
- Simplified Fraction: 31/60
- Mixed Number Form: 31/60
- Decimal Value: 0.516667
- Percentage: 51.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-60-plus-7-21/
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11/60 + 7/21 = 31/60

Simplified Fraction

31/60

Mixed Number

Proper (31/60)

Decimal Value

0.516667

Percentage

51.6667%

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Step-by-Step Solution: 11/60 + 7/21

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 11/60 by 7, and multiply the numerator and denominator of 7/21 by 20 so both fractions share the common base 420.

11 × 7/60 × 7 = 77/420 and 7 × 20/21 × 20 = 140/420

Step 3

Add the Numerators

Now add the numerators (77 + 140 = 217) and keep the common denominator 420 unchanged.

77 + 140/420 = 217/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 217 and 420, which is 7. Divide both the numerator and denominator by 7.

217 ÷ 7/420 ÷ 7 = 31/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 60 produces a repeating decimal (approximately 0.516667, or 51.6667%).

31 ÷ 60 = 0.516667 (51.6667%)

Visual Representation

The diagram below illustrates 11/60 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/60`
Mixed Number Form	`31/60`
Decimal Form	`0.516667`
Percentage	`51.6667%`

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Frequently Asked Questions

What is 11/60 plus 7/21 as a fraction?

11/60 + 7/21 in simplest fraction form is 31/60.

What is 11/60 plus 7/21 as a decimal?

11/60 + 7/21 converted to a decimal is 0.516667.

What is 11/60 plus 7/21 as a percentage?

11/60 + 7/21 expressed as a percentage is 51.6667%.

Does 11/60 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.516667...) because the denominator contains prime factors other than 2 and 5.