What is 10/18 plus 15/21? (Answer: 80/63)

Exact Answer

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Problem: What is 10/18 plus 15/21?
Formula / Expression: 10/18 + 15/21
Final Answer: 1 17/63 (80/63)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).
Working: LCD(18, 21) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 10/18 by 7, and multiply the numerator and denominator of 15/21 by 6 so both fractions share the common base 126.
Working: 10 × 7/18 × 7 = 70/126 and 15 × 6/21 × 6 = 90/126

Step 3: Add the Numerators
Now add the numerators (70 + 90 = 160) and keep the common denominator 126 unchanged.
Working: 70 + 90/126 = 160/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 160 and 126, which is 2. Divide both the numerator and denominator by 2.
Working: 160 ÷ 2/126 ÷ 2 = 80/63

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (80) is greater than the denominator (63), divide 80 by 63: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/63.
Working: 80/63 = 1 17/63

Step 6: Decimal & Percentage Representation
Dividing the numerator 80 by denominator 63 produces a repeating decimal (approximately 1.269841, or 126.9841%).
Working: 80 ÷ 63 = 1.269841 (126.9841%)

Key Values:
- Simplified Fraction: 80/63
- Mixed Number Form: 1 17/63
- Decimal Value: 1.269841
- Percentage: 126.9841%

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10/18 + 15/21 = 80/63

Simplified Fraction

80/63

Mixed Number

1 17/63

Decimal Value

1.269841

Percentage

126.9841%

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Step-by-Step Solution: 10/18 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).

LCD(18, 21) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 10/18 by 7, and multiply the numerator and denominator of 15/21 by 6 so both fractions share the common base 126.

10 × 7/18 × 7 = 70/126 and 15 × 6/21 × 6 = 90/126

Step 3

Add the Numerators

Now add the numerators (70 + 90 = 160) and keep the common denominator 126 unchanged.

70 + 90/126 = 160/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 160 and 126, which is 2. Divide both the numerator and denominator by 2.

160 ÷ 2/126 ÷ 2 = 80/63

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (80) is greater than the denominator (63), divide 80 by 63: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/63.

80/63 = 117/63

Step 6

Decimal & Percentage Representation

Dividing the numerator 80 by denominator 63 produces a repeating decimal (approximately 1.269841, or 126.9841%).

80 ÷ 63 = 1.269841 (126.9841%)

Visual Representation

The diagram below illustrates 10/18 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`80/63`
Mixed Number Form	`1 17/63`
Decimal Form	`1.269841`
Percentage	`126.9841%`

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Frequently Asked Questions

What is 10/18 plus 15/21 as a fraction?

10/18 + 15/21 in simplest fraction form is 80/63 (or 1 17/63 as a mixed number).

What is 10/18 plus 15/21 as a decimal?

10/18 + 15/21 converted to a decimal is 1.269841.

What is 10/18 plus 15/21 as a percentage?

10/18 + 15/21 expressed as a percentage is 126.9841%.

How do you write 10/18 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 80/63 can be written as the mixed number 1 17/63.

Does 10/18 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.269841...) because the denominator contains prime factors other than 2 and 5.