What is 10/21 plus 9/18? (Answer: 41/42)

Exact Answer

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Problem: What is 10/21 plus 9/18?
Formula / Expression: 10/21 + 9/18
Final Answer: 41/42
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 10/21 by 6, and multiply the numerator and denominator of 9/18 by 7 so both fractions share the common base 126.
Working: 10 × 6/21 × 6 = 60/126 and 9 × 7/18 × 7 = 63/126

Step 3: Add the Numerators
Now add the numerators (60 + 63 = 123) and keep the common denominator 126 unchanged.
Working: 60 + 63/126 = 123/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 123 and 126, which is 3. Divide both the numerator and denominator by 3.
Working: 123 ÷ 3/126 ÷ 3 = 41/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 42 produces a repeating decimal (approximately 0.97619, or 97.619%).
Working: 41 ÷ 42 = 0.97619 (97.619%)

Key Values:
- Simplified Fraction: 41/42
- Mixed Number Form: 41/42
- Decimal Value: 0.97619
- Percentage: 97.619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-21-plus-9-18/
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10/21 + 9/18 = 41/42

Simplified Fraction

41/42

Mixed Number

Proper (41/42)

Decimal Value

0.97619

Percentage

97.619%

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Step-by-Step Solution: 10/21 + 9/18

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 18) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 10/21 by 6, and multiply the numerator and denominator of 9/18 by 7 so both fractions share the common base 126.

10 × 6/21 × 6 = 60/126 and 9 × 7/18 × 7 = 63/126

Step 3

Add the Numerators

Now add the numerators (60 + 63 = 123) and keep the common denominator 126 unchanged.

60 + 63/126 = 123/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 123 and 126, which is 3. Divide both the numerator and denominator by 3.

123 ÷ 3/126 ÷ 3 = 41/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 42 produces a repeating decimal (approximately 0.97619, or 97.619%).

41 ÷ 42 = 0.97619 (97.619%)

Visual Representation

The diagram below illustrates 10/21 plus 9/18 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/42`
Mixed Number Form	`41/42`
Decimal Form	`0.97619`
Percentage	`97.619%`

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Frequently Asked Questions

What is 10/21 plus 9/18 as a fraction?

10/21 + 9/18 in simplest fraction form is 41/42.

What is 10/21 plus 9/18 as a decimal?

10/21 + 9/18 converted to a decimal is 0.97619.

What is 10/21 plus 9/18 as a percentage?

10/21 + 9/18 expressed as a percentage is 97.619%.

Does 10/21 plus 9/18 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.97619...) because the denominator contains prime factors other than 2 and 5.