What is 8/60 plus 4/21? (Answer: 34/105)

Exact Answer

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Problem: What is 8/60 plus 4/21?
Formula / Expression: 8/60 + 4/21
Final Answer: 34/105
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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 4/21 by 20 so both fractions share the common base 420.
Working: 8 × 7/60 × 7 = 56/420 and 4 × 20/21 × 20 = 80/420

Step 3: Add the Numerators
Now add the numerators (56 + 80 = 136) and keep the common denominator 420 unchanged.
Working: 56 + 80/420 = 136/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 136 and 420, which is 4. Divide both the numerator and denominator by 4.
Working: 136 ÷ 4/420 ÷ 4 = 34/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 34 by denominator 105 produces a repeating decimal (approximately 0.32381, or 32.381%).
Working: 34 ÷ 105 = 0.32381 (32.381%)

Key Values:
- Simplified Fraction: 34/105
- Mixed Number Form: 34/105
- Decimal Value: 0.32381
- Percentage: 32.381%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-60-plus-4-21/
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8/60 + 4/21 = 34/105

Simplified Fraction

34/105

Mixed Number

Proper (34/105)

Decimal Value

0.32381

Percentage

32.381%

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Step-by-Step Solution: 8/60 + 4/21

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 4/21 by 20 so both fractions share the common base 420.

8 × 7/60 × 7 = 56/420 and 4 × 20/21 × 20 = 80/420

Step 3

Add the Numerators

Now add the numerators (56 + 80 = 136) and keep the common denominator 420 unchanged.

56 + 80/420 = 136/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 136 and 420, which is 4. Divide both the numerator and denominator by 4.

136 ÷ 4/420 ÷ 4 = 34/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 34 by denominator 105 produces a repeating decimal (approximately 0.32381, or 32.381%).

34 ÷ 105 = 0.32381 (32.381%)

Visual Representation

The diagram below illustrates 8/60 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`34/105`
Mixed Number Form	`34/105`
Decimal Form	`0.32381`
Percentage	`32.381%`

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Frequently Asked Questions

What is 8/60 plus 4/21 as a fraction?

8/60 + 4/21 in simplest fraction form is 34/105.

What is 8/60 plus 4/21 as a decimal?

8/60 + 4/21 converted to a decimal is 0.32381.

What is 8/60 plus 4/21 as a percentage?

8/60 + 4/21 expressed as a percentage is 32.381%.

Does 8/60 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.32381...) because the denominator contains prime factors other than 2 and 5.