What is 18/28 plus 15/21? (Answer: 19/14)

Exact Answer

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Problem: What is 18/28 plus 15/21?
Formula / Expression: 18/28 + 15/21
Final Answer: 1 5/14 (19/14)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 28 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 28 × 21 = 588, keeping the calculation simpler).
Working: LCD(28, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 18/28 by 3, and multiply the numerator and denominator of 15/21 by 4 so both fractions share the common base 84.
Working: 18 × 3/28 × 3 = 54/84 and 15 × 4/21 × 4 = 60/84

Step 3: Add the Numerators
Now add the numerators (54 + 60 = 114) and keep the common denominator 84 unchanged.
Working: 54 + 60/84 = 114/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 84, which is 6. Divide both the numerator and denominator by 6.
Working: 114 ÷ 6/84 ÷ 6 = 19/14

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (19) is greater than the denominator (14), divide 19 by 14: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/14.
Working: 19/14 = 1 5/14

Step 6: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 14 produces a repeating decimal (approximately 1.357143, or 135.7143%).
Working: 19 ÷ 14 = 1.357143 (135.7143%)

Key Values:
- Simplified Fraction: 19/14
- Mixed Number Form: 1 5/14
- Decimal Value: 1.357143
- Percentage: 135.7143%

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18/28 + 15/21 = 19/14

Simplified Fraction

19/14

Mixed Number

1 5/14

Decimal Value

1.357143

Percentage

135.7143%

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Step-by-Step Solution: 18/28 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 28 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 28 × 21 = 588, keeping the calculation simpler).

LCD(28, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 18/28 by 3, and multiply the numerator and denominator of 15/21 by 4 so both fractions share the common base 84.

18 × 3/28 × 3 = 54/84 and 15 × 4/21 × 4 = 60/84

Step 3

Add the Numerators

Now add the numerators (54 + 60 = 114) and keep the common denominator 84 unchanged.

54 + 60/84 = 114/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 84, which is 6. Divide both the numerator and denominator by 6.

114 ÷ 6/84 ÷ 6 = 19/14

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (19) is greater than the denominator (14), divide 19 by 14: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/14.

19/14 = 15/14

Step 6

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 14 produces a repeating decimal (approximately 1.357143, or 135.7143%).

19 ÷ 14 = 1.357143 (135.7143%)

Visual Representation

The diagram below illustrates 18/28 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/14`
Mixed Number Form	`1 5/14`
Decimal Form	`1.357143`
Percentage	`135.7143%`

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Frequently Asked Questions

What is 18/28 plus 15/21 as a fraction?

18/28 + 15/21 in simplest fraction form is 19/14 (or 1 5/14 as a mixed number).

What is 18/28 plus 15/21 as a decimal?

18/28 + 15/21 converted to a decimal is 1.357143.

What is 18/28 plus 15/21 as a percentage?

18/28 + 15/21 expressed as a percentage is 135.7143%.

How do you write 18/28 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 19/14 can be written as the mixed number 1 5/14.

Does 18/28 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.357143...) because the denominator contains prime factors other than 2 and 5.