What is 19/60 plus 7/21? (Answer: 13/20)

Exact Answer

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Problem: What is 19/60 plus 7/21?
Formula / Expression: 19/60 + 7/21
Final Answer: 13/20
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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 19/60 by 7, and multiply the numerator and denominator of 7/21 by 20 so both fractions share the common base 420.
Working: 19 × 7/60 × 7 = 133/420 and 7 × 20/21 × 20 = 140/420

Step 3: Add the Numerators
Now add the numerators (133 + 140 = 273) and keep the common denominator 420 unchanged.
Working: 133 + 140/420 = 273/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 273 and 420, which is 21. Divide both the numerator and denominator by 21.
Working: 273 ÷ 21/420 ÷ 21 = 13/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 20 yields an exact terminating decimal of 0.65 (or 65%).
Working: 13 ÷ 20 = 0.65 (65%)

Key Values:
- Simplified Fraction: 13/20
- Mixed Number Form: 13/20
- Decimal Value: 0.65
- Percentage: 65%

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Solved with FractionsCalc:
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19/60 + 7/21 = 13/20

Simplified Fraction

13/20

Mixed Number

Proper (13/20)

Decimal Value

0.65

Percentage

65%

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Step-by-Step Solution: 19/60 + 7/21

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 19/60 by 7, and multiply the numerator and denominator of 7/21 by 20 so both fractions share the common base 420.

19 × 7/60 × 7 = 133/420 and 7 × 20/21 × 20 = 140/420

Step 3

Add the Numerators

Now add the numerators (133 + 140 = 273) and keep the common denominator 420 unchanged.

133 + 140/420 = 273/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 273 and 420, which is 21. Divide both the numerator and denominator by 21.

273 ÷ 21/420 ÷ 21 = 13/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 20 yields an exact terminating decimal of 0.65 (or 65%).

13 ÷ 20 = 0.65 (65%)

Visual Representation

The diagram below illustrates 19/60 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/20`
Mixed Number Form	`13/20`
Decimal Form	`0.65`
Percentage	`65%`

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Frequently Asked Questions

What is 19/60 plus 7/21 as a fraction?

19/60 + 7/21 in simplest fraction form is 13/20.

What is 19/60 plus 7/21 as a decimal?

19/60 + 7/21 converted to a decimal is 0.65.

What is 19/60 plus 7/21 as a percentage?

19/60 + 7/21 expressed as a percentage is 65%.

Does 19/60 plus 7/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.65) because the denominator in simplest terms contains only prime factors 2 and/or 5.