What is 11/30 plus 10/21? (Answer: 59/70)

Exact Answer

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Problem: What is 11/30 plus 10/21?
Formula / Expression: 11/30 + 10/21
Final Answer: 59/70
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).
Working: LCD(30, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 11/30 by 7, and multiply the numerator and denominator of 10/21 by 10 so both fractions share the common base 210.
Working: 11 × 7/30 × 7 = 77/210 and 10 × 10/21 × 10 = 100/210

Step 3: Add the Numerators
Now add the numerators (77 + 100 = 177) and keep the common denominator 210 unchanged.
Working: 77 + 100/210 = 177/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 177 and 210, which is 3. Divide both the numerator and denominator by 3.
Working: 177 ÷ 3/210 ÷ 3 = 59/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 70 produces a repeating decimal (approximately 0.842857, or 84.2857%).
Working: 59 ÷ 70 = 0.842857 (84.2857%)

Key Values:
- Simplified Fraction: 59/70
- Mixed Number Form: 59/70
- Decimal Value: 0.842857
- Percentage: 84.2857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-11-30-plus-10-21/
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11/30 + 10/21 = 59/70

Simplified Fraction

59/70

Mixed Number

Proper (59/70)

Decimal Value

0.842857

Percentage

84.2857%

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Step-by-Step Solution: 11/30 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 11/30 by 7, and multiply the numerator and denominator of 10/21 by 10 so both fractions share the common base 210.

11 × 7/30 × 7 = 77/210 and 10 × 10/21 × 10 = 100/210

Step 3

Add the Numerators

Now add the numerators (77 + 100 = 177) and keep the common denominator 210 unchanged.

77 + 100/210 = 177/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 177 and 210, which is 3. Divide both the numerator and denominator by 3.

177 ÷ 3/210 ÷ 3 = 59/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 70 produces a repeating decimal (approximately 0.842857, or 84.2857%).

59 ÷ 70 = 0.842857 (84.2857%)

Visual Representation

The diagram below illustrates 11/30 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/70`
Mixed Number Form	`59/70`
Decimal Form	`0.842857`
Percentage	`84.2857%`

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Frequently Asked Questions

What is 11/30 plus 10/21 as a fraction?

11/30 + 10/21 in simplest fraction form is 59/70.

What is 11/30 plus 10/21 as a decimal?

11/30 + 10/21 converted to a decimal is 0.842857.

What is 11/30 plus 10/21 as a percentage?

11/30 + 10/21 expressed as a percentage is 84.2857%.

Does 11/30 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.842857...) because the denominator contains prime factors other than 2 and 5.