What is 7/30 plus 2/8? (Answer: 29/60)

Exact Answer

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Problem: What is 7/30 plus 2/8?
Formula / Expression: 7/30 + 2/8
Final Answer: 29/60
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 30 × 8 = 240, keeping the calculation simpler).
Working: LCD(30, 8) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 7/30 by 4, and multiply the numerator and denominator of 2/8 by 15 so both fractions share the common base 120.
Working: 7 × 4/30 × 4 = 28/120 and 2 × 15/8 × 15 = 30/120

Step 3: Add the Numerators
Now add the numerators (28 + 30 = 58) and keep the common denominator 120 unchanged.
Working: 28 + 30/120 = 58/120

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 120, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/120 ÷ 2 = 29/60

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 60 produces a repeating decimal (approximately 0.483333, or 48.3333%).
Working: 29 ÷ 60 = 0.483333 (48.3333%)

Key Values:
- Simplified Fraction: 29/60
- Mixed Number Form: 29/60
- Decimal Value: 0.483333
- Percentage: 48.3333%

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Solved with FractionsCalc:
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7/30 + 2/8 = 29/60

Simplified Fraction

29/60

Mixed Number

Proper (29/60)

Decimal Value

0.483333

Percentage

48.3333%

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Step-by-Step Solution: 7/30 + 2/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 120 (which is smaller than their product 30 × 8 = 240, keeping the calculation simpler).

LCD(30, 8) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 7/30 by 4, and multiply the numerator and denominator of 2/8 by 15 so both fractions share the common base 120.

7 × 4/30 × 4 = 28/120 and 2 × 15/8 × 15 = 30/120

Step 3

Add the Numerators

Now add the numerators (28 + 30 = 58) and keep the common denominator 120 unchanged.

28 + 30/120 = 58/120

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 120, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/120 ÷ 2 = 29/60

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 60 produces a repeating decimal (approximately 0.483333, or 48.3333%).

29 ÷ 60 = 0.483333 (48.3333%)

Visual Representation

The diagram below illustrates 7/30 plus 2/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/60`
Mixed Number Form	`29/60`
Decimal Form	`0.483333`
Percentage	`48.3333%`

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Frequently Asked Questions

What is 7/30 plus 2/8 as a fraction?

7/30 + 2/8 in simplest fraction form is 29/60.

What is 7/30 plus 2/8 as a decimal?

7/30 + 2/8 converted to a decimal is 0.483333.

What is 7/30 plus 2/8 as a percentage?

7/30 + 2/8 expressed as a percentage is 48.3333%.

Does 7/30 plus 2/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.483333...) because the denominator contains prime factors other than 2 and 5.