What is 5/30 plus 12/21? (Answer: 31/42)

Exact Answer

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Problem: What is 5/30 plus 12/21?
Formula / Expression: 5/30 + 12/21
Final Answer: 31/42
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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 5/30 by 7, and multiply the numerator and denominator of 12/21 by 10 so both fractions share the common base 210.
Working: 5 × 7/30 × 7 = 35/210 and 12 × 10/21 × 10 = 120/210

Step 3: Add the Numerators
Now add the numerators (35 + 120 = 155) and keep the common denominator 210 unchanged.
Working: 35 + 120/210 = 155/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 155 and 210, which is 5. Divide both the numerator and denominator by 5.
Working: 155 ÷ 5/210 ÷ 5 = 31/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 42 produces a repeating decimal (approximately 0.738095, or 73.8095%).
Working: 31 ÷ 42 = 0.738095 (73.8095%)

Key Values:
- Simplified Fraction: 31/42
- Mixed Number Form: 31/42
- Decimal Value: 0.738095
- Percentage: 73.8095%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-30-plus-12-21/
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5/30 + 12/21 = 31/42

Simplified Fraction

31/42

Mixed Number

Proper (31/42)

Decimal Value

0.738095

Percentage

73.8095%

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Step-by-Step Solution: 5/30 + 12/21

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 5/30 by 7, and multiply the numerator and denominator of 12/21 by 10 so both fractions share the common base 210.

5 × 7/30 × 7 = 35/210 and 12 × 10/21 × 10 = 120/210

Step 3

Add the Numerators

Now add the numerators (35 + 120 = 155) and keep the common denominator 210 unchanged.

35 + 120/210 = 155/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 155 and 210, which is 5. Divide both the numerator and denominator by 5.

155 ÷ 5/210 ÷ 5 = 31/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 42 produces a repeating decimal (approximately 0.738095, or 73.8095%).

31 ÷ 42 = 0.738095 (73.8095%)

Visual Representation

The diagram below illustrates 5/30 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/42`
Mixed Number Form	`31/42`
Decimal Form	`0.738095`
Percentage	`73.8095%`

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Frequently Asked Questions

What is 5/30 plus 12/21 as a fraction?

5/30 + 12/21 in simplest fraction form is 31/42.

What is 5/30 plus 12/21 as a decimal?

5/30 + 12/21 converted to a decimal is 0.738095.

What is 5/30 plus 12/21 as a percentage?

5/30 + 12/21 expressed as a percentage is 73.8095%.

Does 5/30 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.738095...) because the denominator contains prime factors other than 2 and 5.