What is 9/45 plus 10/21? (Answer: 71/105)

Exact Answer

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Problem: What is 9/45 plus 10/21?
Formula / Expression: 9/45 + 10/21
Final Answer: 71/105
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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 9/45 by 7, and multiply the numerator and denominator of 10/21 by 15 so both fractions share the common base 315.
Working: 9 × 7/45 × 7 = 63/315 and 10 × 15/21 × 15 = 150/315

Step 3: Add the Numerators
Now add the numerators (63 + 150 = 213) and keep the common denominator 315 unchanged.
Working: 63 + 150/315 = 213/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 213 and 315, which is 3. Divide both the numerator and denominator by 3.
Working: 213 ÷ 3/315 ÷ 3 = 71/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 105 produces a repeating decimal (approximately 0.67619, or 67.619%).
Working: 71 ÷ 105 = 0.67619 (67.619%)

Key Values:
- Simplified Fraction: 71/105
- Mixed Number Form: 71/105
- Decimal Value: 0.67619
- Percentage: 67.619%

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Solved with FractionsCalc:
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9/45 + 10/21 = 71/105

Simplified Fraction

71/105

Mixed Number

Proper (71/105)

Decimal Value

0.67619

Percentage

67.619%

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

9 × 7/45 × 7 = 63/315 and 10 × 15/21 × 15 = 150/315

Step 3

Add the Numerators

Now add the numerators (63 + 150 = 213) and keep the common denominator 315 unchanged.

63 + 150/315 = 213/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 213 and 315, which is 3. Divide both the numerator and denominator by 3.

213 ÷ 3/315 ÷ 3 = 71/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 105 produces a repeating decimal (approximately 0.67619, or 67.619%).

71 ÷ 105 = 0.67619 (67.619%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/105`
Mixed Number Form	`71/105`
Decimal Form	`0.67619`
Percentage	`67.619%`

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Frequently Asked Questions

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

9/45 + 10/21 in simplest fraction form is 71/105.

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

9/45 + 10/21 converted to a decimal is 0.67619.

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

9/45 + 10/21 expressed as a percentage is 67.619%.

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

It results in a repeating decimal (approximately 0.67619...) because the denominator contains prime factors other than 2 and 5.