What is 18/30 plus 15/21? (Answer: 46/35)

Exact Answer

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Problem: What is 18/30 plus 15/21?
Formula / Expression: 18/30 + 15/21
Final Answer: 1 11/35 (46/35)
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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 18/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.
Working: 18 × 7/30 × 7 = 126/210 and 15 × 10/21 × 10 = 150/210

Step 3: Add the Numerators
Now add the numerators (126 + 150 = 276) and keep the common denominator 210 unchanged.
Working: 126 + 150/210 = 276/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 276 and 210, which is 6. Divide both the numerator and denominator by 6.
Working: 276 ÷ 6/210 ÷ 6 = 46/35

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (46) is greater than the denominator (35), divide 46 by 35: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/35.
Working: 46/35 = 1 11/35

Step 6: Decimal & Percentage Representation
Dividing the numerator 46 by denominator 35 produces a repeating decimal (approximately 1.314286, or 131.4286%).
Working: 46 ÷ 35 = 1.314286 (131.4286%)

Key Values:
- Simplified Fraction: 46/35
- Mixed Number Form: 1 11/35
- Decimal Value: 1.314286
- Percentage: 131.4286%

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18/30 + 15/21 = 46/35

Simplified Fraction

46/35

Mixed Number

1 11/35

Decimal Value

1.314286

Percentage

131.4286%

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Step-by-Step Solution: 18/30 + 15/21

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 18/30 by 7, and multiply the numerator and denominator of 15/21 by 10 so both fractions share the common base 210.

18 × 7/30 × 7 = 126/210 and 15 × 10/21 × 10 = 150/210

Step 3

Add the Numerators

Now add the numerators (126 + 150 = 276) and keep the common denominator 210 unchanged.

126 + 150/210 = 276/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 276 and 210, which is 6. Divide both the numerator and denominator by 6.

276 ÷ 6/210 ÷ 6 = 46/35

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (46) is greater than the denominator (35), divide 46 by 35: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/35.

46/35 = 111/35

Step 6

Decimal & Percentage Representation

Dividing the numerator 46 by denominator 35 produces a repeating decimal (approximately 1.314286, or 131.4286%).

46 ÷ 35 = 1.314286 (131.4286%)

Visual Representation

The diagram below illustrates 18/30 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`46/35`
Mixed Number Form	`1 11/35`
Decimal Form	`1.314286`
Percentage	`131.4286%`

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Frequently Asked Questions

What is 18/30 plus 15/21 as a fraction?

18/30 + 15/21 in simplest fraction form is 46/35 (or 1 11/35 as a mixed number).

What is 18/30 plus 15/21 as a decimal?

18/30 + 15/21 converted to a decimal is 1.314286.

What is 18/30 plus 15/21 as a percentage?

18/30 + 15/21 expressed as a percentage is 131.4286%.

How do you write 18/30 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 46/35 can be written as the mixed number 1 11/35.

Does 18/30 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.314286...) because the denominator contains prime factors other than 2 and 5.