What is 7/21 plus 5/9? (Answer: 8/9)

Exact Answer

==================================================
Problem: What is 7/21 plus 5/9?
Formula / Expression: 7/21 + 5/9
Final Answer: 8/9
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).
Working: LCD(21, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 7/21 by 3, and multiply the numerator and denominator of 5/9 by 7 so both fractions share the common base 63.
Working: 7 × 3/21 × 3 = 21/63 and 5 × 7/9 × 7 = 35/63

Step 3: Add the Numerators
Now add the numerators (21 + 35 = 56) and keep the common denominator 63 unchanged.
Working: 21 + 35/63 = 56/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 56 and 63, which is 7. Divide both the numerator and denominator by 7.
Working: 56 ÷ 7/63 ÷ 7 = 8/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 9 produces a repeating decimal (approximately 0.888889, or 88.8889%).
Working: 8 ÷ 9 = 0.888889 (88.8889%)

Key Values:
- Simplified Fraction: 8/9
- Mixed Number Form: 8/9
- Decimal Value: 0.888889
- Percentage: 88.8889%

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

7/21 + 5/9 = 8/9

Simplified Fraction

8/9

Mixed Number

Proper (8/9)

Decimal Value

0.888889

Percentage

88.8889%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 7/21 + 5/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).

LCD(21, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 7/21 by 3, and multiply the numerator and denominator of 5/9 by 7 so both fractions share the common base 63.

7 × 3/21 × 3 = 21/63 and 5 × 7/9 × 7 = 35/63

Step 3

Add the Numerators

Now add the numerators (21 + 35 = 56) and keep the common denominator 63 unchanged.

21 + 35/63 = 56/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 56 and 63, which is 7. Divide both the numerator and denominator by 7.

56 ÷ 7/63 ÷ 7 = 8/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 9 produces a repeating decimal (approximately 0.888889, or 88.8889%).

8 ÷ 9 = 0.888889 (88.8889%)

Visual Representation

The diagram below illustrates 7/21 plus 5/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/9`
Mixed Number Form	`8/9`
Decimal Form	`0.888889`
Percentage	`88.8889%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 7/21 plus 5/9 as a fraction?

7/21 + 5/9 in simplest fraction form is 8/9.

What is 7/21 plus 5/9 as a decimal?

7/21 + 5/9 converted to a decimal is 0.888889.

What is 7/21 plus 5/9 as a percentage?

7/21 + 5/9 expressed as a percentage is 88.8889%.

Does 7/21 plus 5/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.888889...) because the denominator contains prime factors other than 2 and 5.