What is 4/18 plus 7/21? (Answer: 5/9)

Exact Answer

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Problem: What is 4/18 plus 7/21?
Formula / Expression: 4/18 + 7/21
Final Answer: 5/9
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).
Working: LCD(18, 21) = 126

Step 2: Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 4/18 by 7, and multiply the numerator and denominator of 7/21 by 6 so both fractions share the common base 126.
Working: 4 × 7/18 × 7 = 28/126 and 7 × 6/21 × 6 = 42/126

Step 3: Add the Numerators
Now add the numerators (28 + 42 = 70) and keep the common denominator 126 unchanged.
Working: 28 + 42/126 = 70/126

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 70 and 126, which is 14. Divide both the numerator and denominator by 14.
Working: 70 ÷ 14/126 ÷ 14 = 5/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).
Working: 5 ÷ 9 = 0.555556 (55.5556%)

Key Values:
- Simplified Fraction: 5/9
- Mixed Number Form: 5/9
- Decimal Value: 0.555556
- Percentage: 55.5556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-18-plus-7-21/
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4/18 + 7/21 = 5/9

Simplified Fraction

5/9

Mixed Number

Proper (5/9)

Decimal Value

0.555556

Percentage

55.5556%

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Step-by-Step Solution: 4/18 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 126 (which is smaller than their product 18 × 21 = 378, keeping the calculation simpler).

LCD(18, 21) = 126

Step 2

Convert to Equivalent Fractions with Common Denominator 126

Multiply the numerator and denominator of 4/18 by 7, and multiply the numerator and denominator of 7/21 by 6 so both fractions share the common base 126.

4 × 7/18 × 7 = 28/126 and 7 × 6/21 × 6 = 42/126

Step 3

Add the Numerators

Now add the numerators (28 + 42 = 70) and keep the common denominator 126 unchanged.

28 + 42/126 = 70/126

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 70 and 126, which is 14. Divide both the numerator and denominator by 14.

70 ÷ 14/126 ÷ 14 = 5/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).

5 ÷ 9 = 0.555556 (55.5556%)

Visual Representation

The diagram below illustrates 4/18 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/9`
Mixed Number Form	`5/9`
Decimal Form	`0.555556`
Percentage	`55.5556%`

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Frequently Asked Questions

What is 4/18 plus 7/21 as a fraction?

4/18 + 7/21 in simplest fraction form is 5/9.

What is 4/18 plus 7/21 as a decimal?

4/18 + 7/21 converted to a decimal is 0.555556.

What is 4/18 plus 7/21 as a percentage?

4/18 + 7/21 expressed as a percentage is 55.5556%.

Does 4/18 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.555556...) because the denominator contains prime factors other than 2 and 5.