What is 8/45 plus 7/21? (Answer: 23/45)

Exact Answer

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Problem: What is 8/45 plus 7/21?
Formula / Expression: 8/45 + 7/21
Final Answer: 23/45
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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 8/45 by 7, and multiply the numerator and denominator of 7/21 by 15 so both fractions share the common base 315.
Working: 8 × 7/45 × 7 = 56/315 and 7 × 15/21 × 15 = 105/315

Step 3: Add the Numerators
Now add the numerators (56 + 105 = 161) and keep the common denominator 315 unchanged.
Working: 56 + 105/315 = 161/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 161 and 315, which is 7. Divide both the numerator and denominator by 7.
Working: 161 ÷ 7/315 ÷ 7 = 23/45

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 45 produces a repeating decimal (approximately 0.511111, or 51.1111%).
Working: 23 ÷ 45 = 0.511111 (51.1111%)

Key Values:
- Simplified Fraction: 23/45
- Mixed Number Form: 23/45
- Decimal Value: 0.511111
- Percentage: 51.1111%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-45-plus-7-21/
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8/45 + 7/21 = 23/45

Simplified Fraction

23/45

Mixed Number

Proper (23/45)

Decimal Value

0.511111

Percentage

51.1111%

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Step-by-Step Solution: 8/45 + 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 8/45 by 7, and multiply the numerator and denominator of 7/21 by 15 so both fractions share the common base 315.

8 × 7/45 × 7 = 56/315 and 7 × 15/21 × 15 = 105/315

Step 3

Add the Numerators

Now add the numerators (56 + 105 = 161) and keep the common denominator 315 unchanged.

56 + 105/315 = 161/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 161 and 315, which is 7. Divide both the numerator and denominator by 7.

161 ÷ 7/315 ÷ 7 = 23/45

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 45 produces a repeating decimal (approximately 0.511111, or 51.1111%).

23 ÷ 45 = 0.511111 (51.1111%)

Visual Representation

The diagram below illustrates 8/45 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/45`
Mixed Number Form	`23/45`
Decimal Form	`0.511111`
Percentage	`51.1111%`

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Frequently Asked Questions

What is 8/45 plus 7/21 as a fraction?

8/45 + 7/21 in simplest fraction form is 23/45.

What is 8/45 plus 7/21 as a decimal?

8/45 + 7/21 converted to a decimal is 0.511111.

What is 8/45 plus 7/21 as a percentage?

8/45 + 7/21 expressed as a percentage is 51.1111%.

Does 8/45 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.511111...) because the denominator contains prime factors other than 2 and 5.