What is 18/42 plus 15/21? (Answer: 8/7)

Exact Answer

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Problem: What is 18/42 plus 15/21?
Formula / Expression: 18/42 + 15/21
Final Answer: 1 1/7 (8/7)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.
Working: LCD(42, 21) = 42

Step 2: Convert to Equivalent Fractions with Common Denominator 42
Multiply the numerator and denominator of 18/42 by 1, and multiply the numerator and denominator of 15/21 by 2 so both fractions share the common base 42.
Working: 18 × 1/42 × 1 = 18/42 and 15 × 2/21 × 2 = 30/42

Step 3: Add the Numerators
Now add the numerators (18 + 30 = 48) and keep the common denominator 42 unchanged.
Working: 18 + 30/42 = 48/42

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 48 and 42, which is 6. Divide both the numerator and denominator by 6.
Working: 48 ÷ 6/42 ÷ 6 = 8/7

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (8) is greater than the denominator (7), divide 8 by 7: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/7.
Working: 8/7 = 1 1/7

Step 6: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 7 produces a repeating decimal (approximately 1.142857, or 114.2857%).
Working: 8 ÷ 7 = 1.142857 (114.2857%)

Key Values:
- Simplified Fraction: 8/7
- Mixed Number Form: 1 1/7
- Decimal Value: 1.142857
- Percentage: 114.2857%

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Solved with FractionsCalc:
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18/42 + 15/21 = 8/7

Simplified Fraction

8/7

Mixed Number

1 1/7

Decimal Value

1.142857

Percentage

114.2857%

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Step-by-Step Solution: 18/42 + 15/21

Step 1

Find the Least Common Denominator (LCD)

Notice that 42 is an exact multiple of 21 (21 × 2 = 42). The Least Common Denominator (LCD) is simply 42, meaning we only need to scale one fraction.

LCD(42, 21) = 42

Step 2

Convert to Equivalent Fractions with Common Denominator 42

Multiply the numerator and denominator of 18/42 by 1, and multiply the numerator and denominator of 15/21 by 2 so both fractions share the common base 42.

18 × 1/42 × 1 = 18/42 and 15 × 2/21 × 2 = 30/42

Step 3

Add the Numerators

Now add the numerators (18 + 30 = 48) and keep the common denominator 42 unchanged.

18 + 30/42 = 48/42

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 48 and 42, which is 6. Divide both the numerator and denominator by 6.

48 ÷ 6/42 ÷ 6 = 8/7

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (8) is greater than the denominator (7), divide 8 by 7: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/7.

8/7 = 11/7

Step 6

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 7 produces a repeating decimal (approximately 1.142857, or 114.2857%).

8 ÷ 7 = 1.142857 (114.2857%)

Visual Representation

The diagram below illustrates 18/42 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/7`
Mixed Number Form	`1 1/7`
Decimal Form	`1.142857`
Percentage	`114.2857%`

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Frequently Asked Questions

What is 18/42 plus 15/21 as a fraction?

18/42 + 15/21 in simplest fraction form is 8/7 (or 1 1/7 as a mixed number).

What is 18/42 plus 15/21 as a decimal?

18/42 + 15/21 converted to a decimal is 1.142857.

What is 18/42 plus 15/21 as a percentage?

18/42 + 15/21 expressed as a percentage is 114.2857%.

How do you write 18/42 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 8/7 can be written as the mixed number 1 1/7.

Does 18/42 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.142857...) because the denominator contains prime factors other than 2 and 5.