What is 7/60 plus 3/21? (Answer: 109/420)

Exact Answer

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Problem: What is 7/60 plus 3/21?
Formula / Expression: 7/60 + 3/21
Final Answer: 109/420
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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 7/60 by 7, and multiply the numerator and denominator of 3/21 by 20 so both fractions share the common base 420.
Working: 7 × 7/60 × 7 = 49/420 and 3 × 20/21 × 20 = 60/420

Step 3: Add the Numerators
Now add the numerators (49 + 60 = 109) and keep the common denominator 420 unchanged.
Working: 49 + 60/420 = 109/420

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 420 is 1, confirming that 109/420 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/420

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 420 produces a repeating decimal (approximately 0.259524, or 25.9524%).
Working: 109 ÷ 420 = 0.259524 (25.9524%)

Key Values:
- Simplified Fraction: 109/420
- Mixed Number Form: 109/420
- Decimal Value: 0.259524
- Percentage: 25.9524%

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Solved with FractionsCalc:
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7/60 + 3/21 = 109/420

Simplified Fraction

109/420

Mixed Number

Proper (109/420)

Decimal Value

0.259524

Percentage

25.9524%

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Step-by-Step Solution: 7/60 + 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 7/60 by 7, and multiply the numerator and denominator of 3/21 by 20 so both fractions share the common base 420.

7 × 7/60 × 7 = 49/420 and 3 × 20/21 × 20 = 60/420

Step 3

Add the Numerators

Now add the numerators (49 + 60 = 109) and keep the common denominator 420 unchanged.

49 + 60/420 = 109/420

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 420 is 1, confirming that 109/420 cannot be reduced further—it is already in its simplest irreducible form.

109/420

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 420 produces a repeating decimal (approximately 0.259524, or 25.9524%).

109 ÷ 420 = 0.259524 (25.9524%)

Visual Representation

The diagram below illustrates 7/60 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/420`
Mixed Number Form	`109/420`
Decimal Form	`0.259524`
Percentage	`25.9524%`

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Frequently Asked Questions

What is 7/60 plus 3/21 as a fraction?

7/60 + 3/21 in simplest fraction form is 109/420.

What is 7/60 plus 3/21 as a decimal?

7/60 + 3/21 converted to a decimal is 0.259524.

What is 7/60 plus 3/21 as a percentage?

7/60 + 3/21 expressed as a percentage is 25.9524%.

Does 7/60 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.259524...) because the denominator contains prime factors other than 2 and 5.