What is 1/49 plus 3/21? (Answer: 8/49)

Exact Answer

==================================================
Problem: What is 1/49 plus 3/21?
Formula / Expression: 1/49 + 3/21
Final Answer: 8/49
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).
Working: LCD(49, 21) = 147

Step 2: Convert to Equivalent Fractions with Common Denominator 147
Multiply the numerator and denominator of 1/49 by 3, and multiply the numerator and denominator of 3/21 by 7 so both fractions share the common base 147.
Working: 1 × 3/49 × 3 = 3/147 and 3 × 7/21 × 7 = 21/147

Step 3: Add the Numerators
Now add the numerators (3 + 21 = 24) and keep the common denominator 147 unchanged.
Working: 3 + 21/147 = 24/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 24 and 147, which is 3. Divide both the numerator and denominator by 3.
Working: 24 ÷ 3/147 ÷ 3 = 8/49

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 49 produces a repeating decimal (approximately 0.163265, or 16.3265%).
Working: 8 ÷ 49 = 0.163265 (16.3265%)

Key Values:
- Simplified Fraction: 8/49
- Mixed Number Form: 8/49
- Decimal Value: 0.163265
- Percentage: 16.3265%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-49-plus-3-21/
==================================================

1/49 + 3/21 = 8/49

Simplified Fraction

8/49

Mixed Number

Proper (8/49)

Decimal Value

0.163265

Percentage

16.3265%

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: 1/49 + 3/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).

LCD(49, 21) = 147

Step 2

Convert to Equivalent Fractions with Common Denominator 147

Multiply the numerator and denominator of 1/49 by 3, and multiply the numerator and denominator of 3/21 by 7 so both fractions share the common base 147.

1 × 3/49 × 3 = 3/147 and 3 × 7/21 × 7 = 21/147

Step 3

Add the Numerators

Now add the numerators (3 + 21 = 24) and keep the common denominator 147 unchanged.

3 + 21/147 = 24/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 24 and 147, which is 3. Divide both the numerator and denominator by 3.

24 ÷ 3/147 ÷ 3 = 8/49

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 49 produces a repeating decimal (approximately 0.163265, or 16.3265%).

8 ÷ 49 = 0.163265 (16.3265%)

Visual Representation

The diagram below illustrates 1/49 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/49`
Mixed Number Form	`8/49`
Decimal Form	`0.163265`
Percentage	`16.3265%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 1/49 plus 3/21 as a fraction?

1/49 + 3/21 in simplest fraction form is 8/49.

What is 1/49 plus 3/21 as a decimal?

1/49 + 3/21 converted to a decimal is 0.163265.

What is 1/49 plus 3/21 as a percentage?

1/49 + 3/21 expressed as a percentage is 16.3265%.

Does 1/49 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.163265...) because the denominator contains prime factors other than 2 and 5.