What is 10/45 plus 9/21? (Answer: 41/63)

Exact Answer

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Problem: What is 10/45 plus 9/21?
Formula / Expression: 10/45 + 9/21
Final Answer: 41/63
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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 10/45 by 7, and multiply the numerator and denominator of 9/21 by 15 so both fractions share the common base 315.
Working: 10 × 7/45 × 7 = 70/315 and 9 × 15/21 × 15 = 135/315

Step 3: Add the Numerators
Now add the numerators (70 + 135 = 205) and keep the common denominator 315 unchanged.
Working: 70 + 135/315 = 205/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 205 and 315, which is 5. Divide both the numerator and denominator by 5.
Working: 205 ÷ 5/315 ÷ 5 = 41/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).
Working: 41 ÷ 63 = 0.650794 (65.0794%)

Key Values:
- Simplified Fraction: 41/63
- Mixed Number Form: 41/63
- Decimal Value: 0.650794
- Percentage: 65.0794%

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Solved with FractionsCalc:
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10/45 + 9/21 = 41/63

Simplified Fraction

41/63

Mixed Number

Proper (41/63)

Decimal Value

0.650794

Percentage

65.0794%

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Step-by-Step Solution: 10/45 + 9/21

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 10/45 by 7, and multiply the numerator and denominator of 9/21 by 15 so both fractions share the common base 315.

10 × 7/45 × 7 = 70/315 and 9 × 15/21 × 15 = 135/315

Step 3

Add the Numerators

Now add the numerators (70 + 135 = 205) and keep the common denominator 315 unchanged.

70 + 135/315 = 205/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 205 and 315, which is 5. Divide both the numerator and denominator by 5.

205 ÷ 5/315 ÷ 5 = 41/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).

41 ÷ 63 = 0.650794 (65.0794%)

Visual Representation

The diagram below illustrates 10/45 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/63`
Mixed Number Form	`41/63`
Decimal Form	`0.650794`
Percentage	`65.0794%`

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Frequently Asked Questions

What is 10/45 plus 9/21 as a fraction?

10/45 + 9/21 in simplest fraction form is 41/63.

What is 10/45 plus 9/21 as a decimal?

10/45 + 9/21 converted to a decimal is 0.650794.

What is 10/45 plus 9/21 as a percentage?

10/45 + 9/21 expressed as a percentage is 65.0794%.

Does 10/45 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.650794...) because the denominator contains prime factors other than 2 and 5.