What is 20/45 plus 10/21? (Answer: 58/63)

Exact Answer

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Problem: What is 20/45 plus 10/21?
Formula / Expression: 20/45 + 10/21
Final Answer: 58/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 20/45 by 7, and multiply the numerator and denominator of 10/21 by 15 so both fractions share the common base 315.
Working: 20 × 7/45 × 7 = 140/315 and 10 × 15/21 × 15 = 150/315

Step 3: Add the Numerators
Now add the numerators (140 + 150 = 290) and keep the common denominator 315 unchanged.
Working: 140 + 150/315 = 290/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 290 and 315, which is 5. Divide both the numerator and denominator by 5.
Working: 290 ÷ 5/315 ÷ 5 = 58/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 58 by denominator 63 produces a repeating decimal (approximately 0.920635, or 92.0635%).
Working: 58 ÷ 63 = 0.920635 (92.0635%)

Key Values:
- Simplified Fraction: 58/63
- Mixed Number Form: 58/63
- Decimal Value: 0.920635
- Percentage: 92.0635%

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Solved with FractionsCalc:
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20/45 + 10/21 = 58/63

Simplified Fraction

58/63

Mixed Number

Proper (58/63)

Decimal Value

0.920635

Percentage

92.0635%

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Step-by-Step Solution: 20/45 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 20/45 by 7, and multiply the numerator and denominator of 10/21 by 15 so both fractions share the common base 315.

20 × 7/45 × 7 = 140/315 and 10 × 15/21 × 15 = 150/315

Step 3

Add the Numerators

Now add the numerators (140 + 150 = 290) and keep the common denominator 315 unchanged.

140 + 150/315 = 290/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 290 and 315, which is 5. Divide both the numerator and denominator by 5.

290 ÷ 5/315 ÷ 5 = 58/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 58 by denominator 63 produces a repeating decimal (approximately 0.920635, or 92.0635%).

58 ÷ 63 = 0.920635 (92.0635%)

Visual Representation

The diagram below illustrates 20/45 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`58/63`
Mixed Number Form	`58/63`
Decimal Form	`0.920635`
Percentage	`92.0635%`

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Frequently Asked Questions

What is 20/45 plus 10/21 as a fraction?

20/45 + 10/21 in simplest fraction form is 58/63.

What is 20/45 plus 10/21 as a decimal?

20/45 + 10/21 converted to a decimal is 0.920635.

What is 20/45 plus 10/21 as a percentage?

20/45 + 10/21 expressed as a percentage is 92.0635%.

Does 20/45 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.920635...) because the denominator contains prime factors other than 2 and 5.