What is 4/30 plus 2/3? (Answer: 4/5)

Exact Answer

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Problem: What is 4/30 plus 2/3?
Formula / Expression: 4/30 + 2/3
Final Answer: 4/5
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 30 is an exact multiple of 3 (3 × 10 = 30). The Least Common Denominator (LCD) is simply 30, meaning we only need to scale one fraction.
Working: LCD(30, 3) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 4/30 by 1, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.
Working: 4 × 1/30 × 1 = 4/30 and 2 × 10/3 × 10 = 20/30

Step 3: Add the Numerators
Now add the numerators (4 + 20 = 24) and keep the common denominator 30 unchanged.
Working: 4 + 20/30 = 24/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 24 and 30, which is 6. Divide both the numerator and denominator by 6.
Working: 24 ÷ 6/30 ÷ 6 = 4/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 5 yields an exact terminating decimal of 0.8 (or 80%).
Working: 4 ÷ 5 = 0.8 (80%)

Key Values:
- Simplified Fraction: 4/5
- Mixed Number Form: 4/5
- Decimal Value: 0.8
- Percentage: 80%

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Solved with FractionsCalc:
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4/30 + 2/3 = 4/5

Simplified Fraction

4/5

Mixed Number

Proper (4/5)

Decimal Value

0.8

Percentage

80%

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Step-by-Step Solution: 4/30 + 2/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 30 is an exact multiple of 3 (3 × 10 = 30). The Least Common Denominator (LCD) is simply 30, meaning we only need to scale one fraction.

LCD(30, 3) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 4/30 by 1, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.

4 × 1/30 × 1 = 4/30 and 2 × 10/3 × 10 = 20/30

Step 3

Add the Numerators

Now add the numerators (4 + 20 = 24) and keep the common denominator 30 unchanged.

4 + 20/30 = 24/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 24 and 30, which is 6. Divide both the numerator and denominator by 6.

24 ÷ 6/30 ÷ 6 = 4/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 5 yields an exact terminating decimal of 0.8 (or 80%).

4 ÷ 5 = 0.8 (80%)

Visual Representation

The diagram below illustrates 4/30 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/5`
Mixed Number Form	`4/5`
Decimal Form	`0.8`
Percentage	`80%`

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Frequently Asked Questions

What is 4/30 plus 2/3 as a fraction?

4/30 + 2/3 in simplest fraction form is 4/5.

What is 4/30 plus 2/3 as a decimal?

4/30 + 2/3 converted to a decimal is 0.8.

What is 4/30 plus 2/3 as a percentage?

4/30 + 2/3 expressed as a percentage is 80%.

Does 4/30 plus 2/3 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.8) because the denominator in simplest terms contains only prime factors 2 and/or 5.