What is 11/60 plus 8/21? (Answer: 79/140)

Exact Answer

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Problem: What is 11/60 plus 8/21?
Formula / Expression: 11/60 + 8/21
Final Answer: 79/140
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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 8/21 by 20 so both fractions share the common base 420.
Working: 11 × 7/60 × 7 = 77/420 and 8 × 20/21 × 20 = 160/420

Step 3: Add the Numerators
Now add the numerators (77 + 160 = 237) and keep the common denominator 420 unchanged.
Working: 77 + 160/420 = 237/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 237 and 420, which is 3. Divide both the numerator and denominator by 3.
Working: 237 ÷ 3/420 ÷ 3 = 79/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 140 produces a repeating decimal (approximately 0.564286, or 56.4286%).
Working: 79 ÷ 140 = 0.564286 (56.4286%)

Key Values:
- Simplified Fraction: 79/140
- Mixed Number Form: 79/140
- Decimal Value: 0.564286
- Percentage: 56.4286%

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Solved with FractionsCalc:
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11/60 + 8/21 = 79/140

Simplified Fraction

79/140

Mixed Number

Proper (79/140)

Decimal Value

0.564286

Percentage

56.4286%

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Step-by-Step Solution: 11/60 + 8/21

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 8/21 by 20 so both fractions share the common base 420.

11 × 7/60 × 7 = 77/420 and 8 × 20/21 × 20 = 160/420

Step 3

Add the Numerators

Now add the numerators (77 + 160 = 237) and keep the common denominator 420 unchanged.

77 + 160/420 = 237/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 237 and 420, which is 3. Divide both the numerator and denominator by 3.

237 ÷ 3/420 ÷ 3 = 79/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 140 produces a repeating decimal (approximately 0.564286, or 56.4286%).

79 ÷ 140 = 0.564286 (56.4286%)

Visual Representation

The diagram below illustrates 11/60 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/140`
Mixed Number Form	`79/140`
Decimal Form	`0.564286`
Percentage	`56.4286%`

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Frequently Asked Questions

What is 11/60 plus 8/21 as a fraction?

11/60 + 8/21 in simplest fraction form is 79/140.

What is 11/60 plus 8/21 as a decimal?

11/60 + 8/21 converted to a decimal is 0.564286.

What is 11/60 plus 8/21 as a percentage?

11/60 + 8/21 expressed as a percentage is 56.4286%.

Does 11/60 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.564286...) because the denominator contains prime factors other than 2 and 5.