What is 5/30 plus 7/21? (Answer: 1/2)

Exact Answer

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Problem: What is 5/30 plus 7/21?
Formula / Expression: 5/30 + 7/21
Final Answer: 1/2
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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 7/21 by 10 so both fractions share the common base 210.
Working: 5 × 7/30 × 7 = 35/210 and 7 × 10/21 × 10 = 70/210

Step 3: Add the Numerators
Now add the numerators (35 + 70 = 105) and keep the common denominator 210 unchanged.
Working: 35 + 70/210 = 105/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 105 and 210, which is 105. Divide both the numerator and denominator by 105.
Working: 105 ÷ 105/210 ÷ 105 = 1/2

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).
Working: 1 ÷ 2 = 0.5 (50%)

Key Values:
- Simplified Fraction: 1/2
- Mixed Number Form: 1/2
- Decimal Value: 0.5
- Percentage: 50%

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Solved with FractionsCalc:
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5/30 + 7/21 = 1/2

Simplified Fraction

1/2

Mixed Number

Proper (1/2)

Decimal Value

0.5

Percentage

50%

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Step-by-Step Solution: 5/30 + 7/21

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 7/21 by 10 so both fractions share the common base 210.

5 × 7/30 × 7 = 35/210 and 7 × 10/21 × 10 = 70/210

Step 3

Add the Numerators

Now add the numerators (35 + 70 = 105) and keep the common denominator 210 unchanged.

35 + 70/210 = 105/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 105 and 210, which is 105. Divide both the numerator and denominator by 105.

105 ÷ 105/210 ÷ 105 = 1/2

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 2 yields an exact terminating decimal of 0.5 (or 50%).

1 ÷ 2 = 0.5 (50%)

Visual Representation

The diagram below illustrates 5/30 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/2`
Mixed Number Form	`1/2`
Decimal Form	`0.5`
Percentage	`50%`

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Frequently Asked Questions

What is 5/30 plus 7/21 as a fraction?

5/30 + 7/21 in simplest fraction form is 1/2.

What is 5/30 plus 7/21 as a decimal?

5/30 + 7/21 converted to a decimal is 0.5.

What is 5/30 plus 7/21 as a percentage?

5/30 + 7/21 expressed as a percentage is 50%.

Does 5/30 plus 7/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.5) because the denominator in simplest terms contains only prime factors 2 and/or 5.