What is 22/48 plus 15/21? (Answer: 197/168)

Exact Answer

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Problem: What is 22/48 plus 15/21?
Formula / Expression: 22/48 + 15/21
Final Answer: 1 29/168 (197/168)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 48 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 48 × 21 = 1008, keeping the calculation simpler).
Working: LCD(48, 21) = 336

Step 2: Convert to Equivalent Fractions with Common Denominator 336
Multiply the numerator and denominator of 22/48 by 7, and multiply the numerator and denominator of 15/21 by 16 so both fractions share the common base 336.
Working: 22 × 7/48 × 7 = 154/336 and 15 × 16/21 × 16 = 240/336

Step 3: Add the Numerators
Now add the numerators (154 + 240 = 394) and keep the common denominator 336 unchanged.
Working: 154 + 240/336 = 394/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 394 and 336, which is 2. Divide both the numerator and denominator by 2.
Working: 394 ÷ 2/336 ÷ 2 = 197/168

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (197) is greater than the denominator (168), divide 197 by 168: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/168.
Working: 197/168 = 1 29/168

Step 6: Decimal & Percentage Representation
Dividing the numerator 197 by denominator 168 produces a repeating decimal (approximately 1.172619, or 117.2619%).
Working: 197 ÷ 168 = 1.172619 (117.2619%)

Key Values:
- Simplified Fraction: 197/168
- Mixed Number Form: 1 29/168
- Decimal Value: 1.172619
- Percentage: 117.2619%

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Solved with FractionsCalc:
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22/48 + 15/21 = 197/168

Simplified Fraction

197/168

Mixed Number

1 29/168

Decimal Value

1.172619

Percentage

117.2619%

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Step-by-Step Solution: 22/48 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 48 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 48 × 21 = 1008, keeping the calculation simpler).

LCD(48, 21) = 336

Step 2

Convert to Equivalent Fractions with Common Denominator 336

Multiply the numerator and denominator of 22/48 by 7, and multiply the numerator and denominator of 15/21 by 16 so both fractions share the common base 336.

22 × 7/48 × 7 = 154/336 and 15 × 16/21 × 16 = 240/336

Step 3

Add the Numerators

Now add the numerators (154 + 240 = 394) and keep the common denominator 336 unchanged.

154 + 240/336 = 394/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 394 and 336, which is 2. Divide both the numerator and denominator by 2.

394 ÷ 2/336 ÷ 2 = 197/168

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (197) is greater than the denominator (168), divide 197 by 168: it goes in 1 whole time(s) with a remainder of 29, giving the mixed number 1 29/168.

197/168 = 129/168

Step 6

Decimal & Percentage Representation

Dividing the numerator 197 by denominator 168 produces a repeating decimal (approximately 1.172619, or 117.2619%).

197 ÷ 168 = 1.172619 (117.2619%)

Visual Representation

The diagram below illustrates 22/48 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`197/168`
Mixed Number Form	`1 29/168`
Decimal Form	`1.172619`
Percentage	`117.2619%`

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Frequently Asked Questions

What is 22/48 plus 15/21 as a fraction?

22/48 + 15/21 in simplest fraction form is 197/168 (or 1 29/168 as a mixed number).

What is 22/48 plus 15/21 as a decimal?

22/48 + 15/21 converted to a decimal is 1.172619.

What is 22/48 plus 15/21 as a percentage?

22/48 + 15/21 expressed as a percentage is 117.2619%.

How do you write 22/48 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 197/168 can be written as the mixed number 1 29/168.

Does 22/48 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.172619...) because the denominator contains prime factors other than 2 and 5.