What is 6/45 plus 10/21? (Answer: 64/105)

Exact Answer

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Problem: What is 6/45 plus 10/21?
Formula / Expression: 6/45 + 10/21
Final Answer: 64/105
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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 6/45 by 7, and multiply the numerator and denominator of 10/21 by 15 so both fractions share the common base 315.
Working: 6 × 7/45 × 7 = 42/315 and 10 × 15/21 × 15 = 150/315

Step 3: Add the Numerators
Now add the numerators (42 + 150 = 192) and keep the common denominator 315 unchanged.
Working: 42 + 150/315 = 192/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 192 and 315, which is 3. Divide both the numerator and denominator by 3.
Working: 192 ÷ 3/315 ÷ 3 = 64/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 64 by denominator 105 produces a repeating decimal (approximately 0.609524, or 60.9524%).
Working: 64 ÷ 105 = 0.609524 (60.9524%)

Key Values:
- Simplified Fraction: 64/105
- Mixed Number Form: 64/105
- Decimal Value: 0.609524
- Percentage: 60.9524%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-45-plus-10-21/
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6/45 + 10/21 = 64/105

Simplified Fraction

64/105

Mixed Number

Proper (64/105)

Decimal Value

0.609524

Percentage

60.9524%

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Step-by-Step Solution: 6/45 + 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 6/45 by 7, and multiply the numerator and denominator of 10/21 by 15 so both fractions share the common base 315.

6 × 7/45 × 7 = 42/315 and 10 × 15/21 × 15 = 150/315

Step 3

Add the Numerators

Now add the numerators (42 + 150 = 192) and keep the common denominator 315 unchanged.

42 + 150/315 = 192/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 192 and 315, which is 3. Divide both the numerator and denominator by 3.

192 ÷ 3/315 ÷ 3 = 64/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 64 by denominator 105 produces a repeating decimal (approximately 0.609524, or 60.9524%).

64 ÷ 105 = 0.609524 (60.9524%)

Visual Representation

The diagram below illustrates 6/45 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`64/105`
Mixed Number Form	`64/105`
Decimal Form	`0.609524`
Percentage	`60.9524%`

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Frequently Asked Questions

What is 6/45 plus 10/21 as a fraction?

6/45 + 10/21 in simplest fraction form is 64/105.

What is 6/45 plus 10/21 as a decimal?

6/45 + 10/21 converted to a decimal is 0.609524.

What is 6/45 plus 10/21 as a percentage?

6/45 + 10/21 expressed as a percentage is 60.9524%.

Does 6/45 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.609524...) because the denominator contains prime factors other than 2 and 5.