What is 3/45 plus 10/21? (Answer: 19/35)

Exact Answer

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Problem: What is 3/45 plus 10/21?
Formula / Expression: 3/45 + 10/21
Final Answer: 19/35
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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 3/45 by 7, and multiply the numerator and denominator of 10/21 by 15 so both fractions share the common base 315.
Working: 3 × 7/45 × 7 = 21/315 and 10 × 15/21 × 15 = 150/315

Step 3: Add the Numerators
Now add the numerators (21 + 150 = 171) and keep the common denominator 315 unchanged.
Working: 21 + 150/315 = 171/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 171 and 315, which is 9. Divide both the numerator and denominator by 9.
Working: 171 ÷ 9/315 ÷ 9 = 19/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 35 produces a repeating decimal (approximately 0.542857, or 54.2857%).
Working: 19 ÷ 35 = 0.542857 (54.2857%)

Key Values:
- Simplified Fraction: 19/35
- Mixed Number Form: 19/35
- Decimal Value: 0.542857
- Percentage: 54.2857%

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Solved with FractionsCalc:
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3/45 + 10/21 = 19/35

Simplified Fraction

19/35

Mixed Number

Proper (19/35)

Decimal Value

0.542857

Percentage

54.2857%

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Step-by-Step Solution: 3/45 + 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 3/45 by 7, and multiply the numerator and denominator of 10/21 by 15 so both fractions share the common base 315.

3 × 7/45 × 7 = 21/315 and 10 × 15/21 × 15 = 150/315

Step 3

Add the Numerators

Now add the numerators (21 + 150 = 171) and keep the common denominator 315 unchanged.

21 + 150/315 = 171/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 171 and 315, which is 9. Divide both the numerator and denominator by 9.

171 ÷ 9/315 ÷ 9 = 19/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 35 produces a repeating decimal (approximately 0.542857, or 54.2857%).

19 ÷ 35 = 0.542857 (54.2857%)

Visual Representation

The diagram below illustrates 3/45 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/35`
Mixed Number Form	`19/35`
Decimal Form	`0.542857`
Percentage	`54.2857%`

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Frequently Asked Questions

What is 3/45 plus 10/21 as a fraction?

3/45 + 10/21 in simplest fraction form is 19/35.

What is 3/45 plus 10/21 as a decimal?

3/45 + 10/21 converted to a decimal is 0.542857.

What is 3/45 plus 10/21 as a percentage?

3/45 + 10/21 expressed as a percentage is 54.2857%.

Does 3/45 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.542857...) because the denominator contains prime factors other than 2 and 5.