What is 1/30 plus 2/3? (Answer: 7/10)

Exact Answer

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Problem: What is 1/30 plus 2/3?
Formula / Expression: 1/30 + 2/3
Final Answer: 7/10
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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 1/30 by 1, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.
Working: 1 × 1/30 × 1 = 1/30 and 2 × 10/3 × 10 = 20/30

Step 3: Add the Numerators
Now add the numerators (1 + 20 = 21) and keep the common denominator 30 unchanged.
Working: 1 + 20/30 = 21/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 21 and 30, which is 3. Divide both the numerator and denominator by 3.
Working: 21 ÷ 3/30 ÷ 3 = 7/10

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 10 yields an exact terminating decimal of 0.7 (or 70%).
Working: 7 ÷ 10 = 0.7 (70%)

Key Values:
- Simplified Fraction: 7/10
- Mixed Number Form: 7/10
- Decimal Value: 0.7
- Percentage: 70%

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Solved with FractionsCalc:
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1/30 + 2/3 = 7/10

Simplified Fraction

7/10

Mixed Number

Proper (7/10)

Decimal Value

0.7

Percentage

70%

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Step-by-Step Solution: 1/30 + 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 1/30 by 1, and multiply the numerator and denominator of 2/3 by 10 so both fractions share the common base 30.

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

Step 3

Add the Numerators

Now add the numerators (1 + 20 = 21) and keep the common denominator 30 unchanged.

1 + 20/30 = 21/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 21 and 30, which is 3. Divide both the numerator and denominator by 3.

21 ÷ 3/30 ÷ 3 = 7/10

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 10 yields an exact terminating decimal of 0.7 (or 70%).

7 ÷ 10 = 0.7 (70%)

Visual Representation

The diagram below illustrates 1/30 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/10`
Mixed Number Form	`7/10`
Decimal Form	`0.7`
Percentage	`70%`

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Frequently Asked Questions

What is 1/30 plus 2/3 as a fraction?

1/30 + 2/3 in simplest fraction form is 7/10.

What is 1/30 plus 2/3 as a decimal?

1/30 + 2/3 converted to a decimal is 0.7.

What is 1/30 plus 2/3 as a percentage?

1/30 + 2/3 expressed as a percentage is 70%.

Does 1/30 plus 2/3 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.7) because the denominator in simplest terms contains only prime factors 2 and/or 5.