What is 1/7 plus 7/21? (Answer: 10/21)

Exact Answer

==================================================
Problem: What is 1/7 plus 7/21?
Formula / Expression: 1/7 + 7/21
Final Answer: 10/21
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 21 is an exact multiple of 7 (7 × 3 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.
Working: LCD(7, 21) = 21

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 1/7 by 3, and multiply the numerator and denominator of 7/21 by 1 so both fractions share the common base 21.
Working: 1 × 3/7 × 3 = 3/21 and 7 × 1/21 × 1 = 7/21

Step 3: Add the Numerators
Now add the numerators (3 + 7 = 10) and keep the common denominator 21 unchanged.
Working: 3 + 7/21 = 10/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 10 and 21 is 1, confirming that 10/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 10/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 21 produces a repeating decimal (approximately 0.47619, or 47.619%).
Working: 10 ÷ 21 = 0.47619 (47.619%)

Key Values:
- Simplified Fraction: 10/21
- Mixed Number Form: 10/21
- Decimal Value: 0.47619
- Percentage: 47.619%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-7-plus-7-21/
==================================================

1/7 + 7/21 = 10/21

Simplified Fraction

10/21

Mixed Number

Proper (10/21)

Decimal Value

0.47619

Percentage

47.619%

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: 1/7 + 7/21

Step 1

Find the Least Common Denominator (LCD)

Notice that 21 is an exact multiple of 7 (7 × 3 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.

LCD(7, 21) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 1/7 by 3, and multiply the numerator and denominator of 7/21 by 1 so both fractions share the common base 21.

1 × 3/7 × 3 = 3/21 and 7 × 1/21 × 1 = 7/21

Step 3

Add the Numerators

Now add the numerators (3 + 7 = 10) and keep the common denominator 21 unchanged.

3 + 7/21 = 10/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 10 and 21 is 1, confirming that 10/21 cannot be reduced further—it is already in its simplest irreducible form.

10/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 21 produces a repeating decimal (approximately 0.47619, or 47.619%).

10 ÷ 21 = 0.47619 (47.619%)

Visual Representation

The diagram below illustrates 1/7 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/21`
Mixed Number Form	`10/21`
Decimal Form	`0.47619`
Percentage	`47.619%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/7 plus 7/21 as a fraction?

1/7 + 7/21 in simplest fraction form is 10/21.

What is 1/7 plus 7/21 as a decimal?

1/7 + 7/21 converted to a decimal is 0.47619.

What is 1/7 plus 7/21 as a percentage?

1/7 + 7/21 expressed as a percentage is 47.619%.

Does 1/7 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.47619...) because the denominator contains prime factors other than 2 and 5.