What is 1/30 plus 11/21? (Answer: 39/70)

Exact Answer

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Problem: What is 1/30 plus 11/21?
Formula / Expression: 1/30 + 11/21
Final Answer: 39/70
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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 1/30 by 7, and multiply the numerator and denominator of 11/21 by 10 so both fractions share the common base 210.
Working: 1 × 7/30 × 7 = 7/210 and 11 × 10/21 × 10 = 110/210

Step 3: Add the Numerators
Now add the numerators (7 + 110 = 117) and keep the common denominator 210 unchanged.
Working: 7 + 110/210 = 117/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 117 and 210, which is 3. Divide both the numerator and denominator by 3.
Working: 117 ÷ 3/210 ÷ 3 = 39/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 70 produces a repeating decimal (approximately 0.557143, or 55.7143%).
Working: 39 ÷ 70 = 0.557143 (55.7143%)

Key Values:
- Simplified Fraction: 39/70
- Mixed Number Form: 39/70
- Decimal Value: 0.557143
- Percentage: 55.7143%

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Solved with FractionsCalc:
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1/30 + 11/21 = 39/70

Simplified Fraction

39/70

Mixed Number

Proper (39/70)

Decimal Value

0.557143

Percentage

55.7143%

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Step-by-Step Solution: 1/30 + 11/21

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 1/30 by 7, and multiply the numerator and denominator of 11/21 by 10 so both fractions share the common base 210.

1 × 7/30 × 7 = 7/210 and 11 × 10/21 × 10 = 110/210

Step 3

Add the Numerators

Now add the numerators (7 + 110 = 117) and keep the common denominator 210 unchanged.

7 + 110/210 = 117/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 117 and 210, which is 3. Divide both the numerator and denominator by 3.

117 ÷ 3/210 ÷ 3 = 39/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 70 produces a repeating decimal (approximately 0.557143, or 55.7143%).

39 ÷ 70 = 0.557143 (55.7143%)

Visual Representation

The diagram below illustrates 1/30 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/70`
Mixed Number Form	`39/70`
Decimal Form	`0.557143`
Percentage	`55.7143%`

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Frequently Asked Questions

What is 1/30 plus 11/21 as a fraction?

1/30 + 11/21 in simplest fraction form is 39/70.

What is 1/30 plus 11/21 as a decimal?

1/30 + 11/21 converted to a decimal is 0.557143.

What is 1/30 plus 11/21 as a percentage?

1/30 + 11/21 expressed as a percentage is 55.7143%.

Does 1/30 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.557143...) because the denominator contains prime factors other than 2 and 5.