What is 8/60 plus 3/21? (Answer: 29/105)

Exact Answer

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Problem: What is 8/60 plus 3/21?
Formula / Expression: 8/60 + 3/21
Final Answer: 29/105
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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 8/60 by 7, and multiply the numerator and denominator of 3/21 by 20 so both fractions share the common base 420.
Working: 8 × 7/60 × 7 = 56/420 and 3 × 20/21 × 20 = 60/420

Step 3: Add the Numerators
Now add the numerators (56 + 60 = 116) and keep the common denominator 420 unchanged.
Working: 56 + 60/420 = 116/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 116 and 420, which is 4. Divide both the numerator and denominator by 4.
Working: 116 ÷ 4/420 ÷ 4 = 29/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 105 produces a repeating decimal (approximately 0.27619, or 27.619%).
Working: 29 ÷ 105 = 0.27619 (27.619%)

Key Values:
- Simplified Fraction: 29/105
- Mixed Number Form: 29/105
- Decimal Value: 0.27619
- Percentage: 27.619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-60-plus-3-21/
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8/60 + 3/21 = 29/105

Simplified Fraction

29/105

Mixed Number

Proper (29/105)

Decimal Value

0.27619

Percentage

27.619%

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Step-by-Step Solution: 8/60 + 3/21

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 8/60 by 7, and multiply the numerator and denominator of 3/21 by 20 so both fractions share the common base 420.

8 × 7/60 × 7 = 56/420 and 3 × 20/21 × 20 = 60/420

Step 3

Add the Numerators

Now add the numerators (56 + 60 = 116) and keep the common denominator 420 unchanged.

56 + 60/420 = 116/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 116 and 420, which is 4. Divide both the numerator and denominator by 4.

116 ÷ 4/420 ÷ 4 = 29/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 105 produces a repeating decimal (approximately 0.27619, or 27.619%).

29 ÷ 105 = 0.27619 (27.619%)

Visual Representation

The diagram below illustrates 8/60 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/105`
Mixed Number Form	`29/105`
Decimal Form	`0.27619`
Percentage	`27.619%`

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Frequently Asked Questions

What is 8/60 plus 3/21 as a fraction?

8/60 + 3/21 in simplest fraction form is 29/105.

What is 8/60 plus 3/21 as a decimal?

8/60 + 3/21 converted to a decimal is 0.27619.

What is 8/60 plus 3/21 as a percentage?

8/60 + 3/21 expressed as a percentage is 27.619%.

Does 8/60 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.27619...) because the denominator contains prime factors other than 2 and 5.