What is 11/60 plus 5/21? (Answer: 59/140)

Exact Answer

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Problem: What is 11/60 plus 5/21?
Formula / Expression: 11/60 + 5/21
Final Answer: 59/140
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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 5/21 by 20 so both fractions share the common base 420.
Working: 11 × 7/60 × 7 = 77/420 and 5 × 20/21 × 20 = 100/420

Step 3: Add the Numerators
Now add the numerators (77 + 100 = 177) and keep the common denominator 420 unchanged.
Working: 77 + 100/420 = 177/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 177 and 420, which is 3. Divide both the numerator and denominator by 3.
Working: 177 ÷ 3/420 ÷ 3 = 59/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 140 produces a repeating decimal (approximately 0.421429, or 42.1429%).
Working: 59 ÷ 140 = 0.421429 (42.1429%)

Key Values:
- Simplified Fraction: 59/140
- Mixed Number Form: 59/140
- Decimal Value: 0.421429
- Percentage: 42.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-60-plus-5-21/
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11/60 + 5/21 = 59/140

Simplified Fraction

59/140

Mixed Number

Proper (59/140)

Decimal Value

0.421429

Percentage

42.1429%

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Step-by-Step Solution: 11/60 + 5/21

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 5/21 by 20 so both fractions share the common base 420.

11 × 7/60 × 7 = 77/420 and 5 × 20/21 × 20 = 100/420

Step 3

Add the Numerators

Now add the numerators (77 + 100 = 177) and keep the common denominator 420 unchanged.

77 + 100/420 = 177/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 177 and 420, which is 3. Divide both the numerator and denominator by 3.

177 ÷ 3/420 ÷ 3 = 59/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 140 produces a repeating decimal (approximately 0.421429, or 42.1429%).

59 ÷ 140 = 0.421429 (42.1429%)

Visual Representation

The diagram below illustrates 11/60 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/140`
Mixed Number Form	`59/140`
Decimal Form	`0.421429`
Percentage	`42.1429%`

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Frequently Asked Questions

What is 11/60 plus 5/21 as a fraction?

11/60 + 5/21 in simplest fraction form is 59/140.

What is 11/60 plus 5/21 as a decimal?

11/60 + 5/21 converted to a decimal is 0.421429.

What is 11/60 plus 5/21 as a percentage?

11/60 + 5/21 expressed as a percentage is 42.1429%.

Does 11/60 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.421429...) because the denominator contains prime factors other than 2 and 5.