What is 13/60 plus 7/21? (Answer: 11/20)

Exact Answer

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Problem: What is 13/60 plus 7/21?
Formula / Expression: 13/60 + 7/21
Final Answer: 11/20
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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 13/60 by 7, and multiply the numerator and denominator of 7/21 by 20 so both fractions share the common base 420.
Working: 13 × 7/60 × 7 = 91/420 and 7 × 20/21 × 20 = 140/420

Step 3: Add the Numerators
Now add the numerators (91 + 140 = 231) and keep the common denominator 420 unchanged.
Working: 91 + 140/420 = 231/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 231 and 420, which is 21. Divide both the numerator and denominator by 21.
Working: 231 ÷ 21/420 ÷ 21 = 11/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 20 yields an exact terminating decimal of 0.55 (or 55%).
Working: 11 ÷ 20 = 0.55 (55%)

Key Values:
- Simplified Fraction: 11/20
- Mixed Number Form: 11/20
- Decimal Value: 0.55
- Percentage: 55%

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Solved with FractionsCalc:
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13/60 + 7/21 = 11/20

Simplified Fraction

11/20

Mixed Number

Proper (11/20)

Decimal Value

0.55

Percentage

55%

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Step-by-Step Solution: 13/60 + 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 13/60 by 7, and multiply the numerator and denominator of 7/21 by 20 so both fractions share the common base 420.

13 × 7/60 × 7 = 91/420 and 7 × 20/21 × 20 = 140/420

Step 3

Add the Numerators

Now add the numerators (91 + 140 = 231) and keep the common denominator 420 unchanged.

91 + 140/420 = 231/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 231 and 420, which is 21. Divide both the numerator and denominator by 21.

231 ÷ 21/420 ÷ 21 = 11/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 20 yields an exact terminating decimal of 0.55 (or 55%).

11 ÷ 20 = 0.55 (55%)

Visual Representation

The diagram below illustrates 13/60 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/20`
Mixed Number Form	`11/20`
Decimal Form	`0.55`
Percentage	`55%`

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Frequently Asked Questions

What is 13/60 plus 7/21 as a fraction?

13/60 + 7/21 in simplest fraction form is 11/20.

What is 13/60 plus 7/21 as a decimal?

13/60 + 7/21 converted to a decimal is 0.55.

What is 13/60 plus 7/21 as a percentage?

13/60 + 7/21 expressed as a percentage is 55%.

Does 13/60 plus 7/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.55) because the denominator in simplest terms contains only prime factors 2 and/or 5.