What is 5/45 plus 4/21? (Answer: 19/63)

Exact Answer

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Problem: What is 5/45 plus 4/21?
Formula / Expression: 5/45 + 4/21
Final Answer: 19/63
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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 5/45 by 7, and multiply the numerator and denominator of 4/21 by 15 so both fractions share the common base 315.
Working: 5 × 7/45 × 7 = 35/315 and 4 × 15/21 × 15 = 60/315

Step 3: Add the Numerators
Now add the numerators (35 + 60 = 95) and keep the common denominator 315 unchanged.
Working: 35 + 60/315 = 95/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 95 and 315, which is 5. Divide both the numerator and denominator by 5.
Working: 95 ÷ 5/315 ÷ 5 = 19/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 63 produces a repeating decimal (approximately 0.301587, or 30.1587%).
Working: 19 ÷ 63 = 0.301587 (30.1587%)

Key Values:
- Simplified Fraction: 19/63
- Mixed Number Form: 19/63
- Decimal Value: 0.301587
- Percentage: 30.1587%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-45-plus-4-21/
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5/45 + 4/21 = 19/63

Simplified Fraction

19/63

Mixed Number

Proper (19/63)

Decimal Value

0.301587

Percentage

30.1587%

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Step-by-Step Solution: 5/45 + 4/21

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 5/45 by 7, and multiply the numerator and denominator of 4/21 by 15 so both fractions share the common base 315.

5 × 7/45 × 7 = 35/315 and 4 × 15/21 × 15 = 60/315

Step 3

Add the Numerators

Now add the numerators (35 + 60 = 95) and keep the common denominator 315 unchanged.

35 + 60/315 = 95/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 95 and 315, which is 5. Divide both the numerator and denominator by 5.

95 ÷ 5/315 ÷ 5 = 19/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 63 produces a repeating decimal (approximately 0.301587, or 30.1587%).

19 ÷ 63 = 0.301587 (30.1587%)

Visual Representation

The diagram below illustrates 5/45 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/63`
Mixed Number Form	`19/63`
Decimal Form	`0.301587`
Percentage	`30.1587%`

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Frequently Asked Questions

What is 5/45 plus 4/21 as a fraction?

5/45 + 4/21 in simplest fraction form is 19/63.

What is 5/45 plus 4/21 as a decimal?

5/45 + 4/21 converted to a decimal is 0.301587.

What is 5/45 plus 4/21 as a percentage?

5/45 + 4/21 expressed as a percentage is 30.1587%.

Does 5/45 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.301587...) because the denominator contains prime factors other than 2 and 5.