What is 5/45 plus 7/21? (Answer: 4/9)

Exact Answer

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Problem: What is 5/45 plus 7/21?
Formula / Expression: 5/45 + 7/21
Final Answer: 4/9
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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 7/21 by 15 so both fractions share the common base 315.
Working: 5 × 7/45 × 7 = 35/315 and 7 × 15/21 × 15 = 105/315

Step 3: Add the Numerators
Now add the numerators (35 + 105 = 140) and keep the common denominator 315 unchanged.
Working: 35 + 105/315 = 140/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 140 and 315, which is 35. Divide both the numerator and denominator by 35.
Working: 140 ÷ 35/315 ÷ 35 = 4/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 9 produces a repeating decimal (approximately 0.444444, or 44.4444%).
Working: 4 ÷ 9 = 0.444444 (44.4444%)

Key Values:
- Simplified Fraction: 4/9
- Mixed Number Form: 4/9
- Decimal Value: 0.444444
- Percentage: 44.4444%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-45-plus-7-21/
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5/45 + 7/21 = 4/9

Simplified Fraction

4/9

Mixed Number

Proper (4/9)

Decimal Value

0.444444

Percentage

44.4444%

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Step-by-Step Solution: 5/45 + 7/21

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 7/21 by 15 so both fractions share the common base 315.

5 × 7/45 × 7 = 35/315 and 7 × 15/21 × 15 = 105/315

Step 3

Add the Numerators

Now add the numerators (35 + 105 = 140) and keep the common denominator 315 unchanged.

35 + 105/315 = 140/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 140 and 315, which is 35. Divide both the numerator and denominator by 35.

140 ÷ 35/315 ÷ 35 = 4/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 9 produces a repeating decimal (approximately 0.444444, or 44.4444%).

4 ÷ 9 = 0.444444 (44.4444%)

Visual Representation

The diagram below illustrates 5/45 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/9`
Mixed Number Form	`4/9`
Decimal Form	`0.444444`
Percentage	`44.4444%`

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Frequently Asked Questions

What is 5/45 plus 7/21 as a fraction?

5/45 + 7/21 in simplest fraction form is 4/9.

What is 5/45 plus 7/21 as a decimal?

5/45 + 7/21 converted to a decimal is 0.444444.

What is 5/45 plus 7/21 as a percentage?

5/45 + 7/21 expressed as a percentage is 44.4444%.

Does 5/45 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.444444...) because the denominator contains prime factors other than 2 and 5.