What is 7/18 plus 9/21? (Answer: 103/126)

Exact Answer

==================================================
Problem: What is 7/18 plus 9/21?
Formula / Expression: 7/18 + 9/21
Final Answer: 103/126
==================================================

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 7/18 by 7, and multiply the numerator and denominator of 9/21 by 6 so both fractions share the common base 126.
Working: 7 × 7/18 × 7 = 49/126 and 9 × 6/21 × 6 = 54/126

Step 3: Add the Numerators
Now add the numerators (49 + 54 = 103) and keep the common denominator 126 unchanged.
Working: 49 + 54/126 = 103/126

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 103 and 126 is 1, confirming that 103/126 cannot be reduced further—it is already in its simplest irreducible form.
Working: 103/126

Step 5: Decimal & Percentage Representation
Dividing the numerator 103 by denominator 126 produces a repeating decimal (approximately 0.81746, or 81.746%).
Working: 103 ÷ 126 = 0.81746 (81.746%)

Key Values:
- Simplified Fraction: 103/126
- Mixed Number Form: 103/126
- Decimal Value: 0.81746
- Percentage: 81.746%

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

7/18 + 9/21 = 103/126

Simplified Fraction

103/126

Mixed Number

Proper (103/126)

Decimal Value

0.81746

Percentage

81.746%

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: 7/18 + 9/21

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 7/18 by 7, and multiply the numerator and denominator of 9/21 by 6 so both fractions share the common base 126.

7 × 7/18 × 7 = 49/126 and 9 × 6/21 × 6 = 54/126

Step 3

Add the Numerators

Now add the numerators (49 + 54 = 103) and keep the common denominator 126 unchanged.

49 + 54/126 = 103/126

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 103 and 126 is 1, confirming that 103/126 cannot be reduced further—it is already in its simplest irreducible form.

103/126

Step 5

Decimal & Percentage Representation

Dividing the numerator 103 by denominator 126 produces a repeating decimal (approximately 0.81746, or 81.746%).

103 ÷ 126 = 0.81746 (81.746%)

Visual Representation

The diagram below illustrates 7/18 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`103/126`
Mixed Number Form	`103/126`
Decimal Form	`0.81746`
Percentage	`81.746%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 7/18 plus 9/21 as a fraction?

7/18 + 9/21 in simplest fraction form is 103/126.

What is 7/18 plus 9/21 as a decimal?

7/18 + 9/21 converted to a decimal is 0.81746.

What is 7/18 plus 9/21 as a percentage?

7/18 + 9/21 expressed as a percentage is 81.746%.

Does 7/18 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.81746...) because the denominator contains prime factors other than 2 and 5.