How to subtract fractions -20/53-22/25 = ? Result written As a negative improper fraction (numerator >= denominator): - 1,666/1,325 As a mixed number: - 1 341/1,325 As a decimal number: - 1.26 As a percentage:

How to: Adding ordinary (simple, common) math fractions. Steps.

There are two cases regarding the denominators when we add ordinary fractions:

A. the fractions have like denominators;
B. the fractions have unlike denominators.

A. How to add ordinary fractions that have like denominators?

Simply add the numerators of the fractions.
The denominator of the resulting fraction will be the common denominator of the fractions.
Reduce the resulting fraction.

An example of adding ordinary fractions that have like denominators, with explanations

³/₁₈ + ⁴/₁₈ + ⁵/₁₈ = ^{(3 + 4 + 5)}/₁₈ = ¹²/₁₈;
We simply added the numerators of the fractions: 3 + 4 + 5 = 12;
The denominator of the resulting fraction is: 18;
The resulting fraction is being reduced: ¹²/₁₈ = ^{(12 ÷ 6)}/_{(18 ÷ 6)} = ²/₃.
How to reduce (simplify) the common fraction ¹²/₁₈?

B. To add fractions with different denominators (unlike denominators), build up the fractions to the same denominator. How is it done?

1. Reduce the fractions to the lowest terms (simplifying).
- Factor the numerator and the denominator of each fraction down to prime factors (prime factorization).
- Factor numbers online down to their prime factors.
- Calculate GCF, the greatest common factor (also called GCD, greatest common divisor, HCF, greatest common factor) of each fraction's numerator and denominator.
- GCF is the product of all the unique common prime factors of the numerator and the denominator, taken by the lowest exponents.
- Calculate online the greatest common factor, GCF.
- Divide the numerator and the denominator of each fraction by their greatest common factor, GCF - after this operation the fraction is reduced to its lowest terms equivalent.
- Reduce (simplify) fractions online to their lowest terms, with explanations.
2. Calculate the least common multiple, LCM, of all the fractions' new denominators:
- LCM is going to be the common denominator of the added fractions.
- Factor all the new denominators of the reduced fractions (run the prime factorization).
- The least common multiple, LCM, is the product of all the unique prime factors of the denominators, taken by the largest exponents.
- Calculate LCM, the least common multiple of numbers.
3. Calculate each fraction's expanding number:
- The expanding number is the non-zero number that will be used to multiply both the numerator and the denominator of each fraction, in order to build all the fractions up to the same common denominator.
- Divide the least common multiple, LCM, calculated above, by each fraction's denominator, in order to calculate each fraction's expanding number.
4. Expand each fraction:
- Multiply each fraction's both numerator and denominator by expanding number.
- At this point, fractions are built up to the same denominator.
5. Add the fractions:
- In order to add all the fractions simply add all the fractions' numerators.
- The end fraction will have as a denominator the least common multiple, LCM, calculated above.
6. Reduce the end fraction to the lowest terms, if needed.
- Reduce (simplify) ordinary fractions to lowest terms.

- ²⁰/₅₃ - ²²/₂₅ = ?	Mar 02 04:29 UTC (GMT)
²⁰/₃₇ + ²⁹/₂₇ + ⁶/₈ - ¹⁰⁸/₇ + ³¹⁰/₇ = ?	Mar 02 04:29 UTC (GMT)
- ²²/₃₈ - ¹⁴/₁₉ = ?	Mar 02 04:29 UTC (GMT)
⁶¹/_18,250 - ⁶¹/₁₄ = ?	Mar 02 04:29 UTC (GMT)
⁵⁰/₂₂ - ³¹/₉₅₆ + ⁸²⁸/₈₃₀ + ²³/₁₂ = ?	Mar 02 04:29 UTC (GMT)
²⁰/₁₄ - ²²/₉ = ?	Mar 02 04:29 UTC (GMT)
⁵⁸/₇₈₉ - ^21,169/₃₃ - ⁸⁸/_1,582 + ¹⁷⁷/₃₉ = ?	Mar 02 04:29 UTC (GMT)
⁸/_831,071 - ²⁸/₁₈ - ⁹/_68,946 - ²⁴/_966,113 + 9 = ?	Mar 02 04:29 UTC (GMT)
⁴⁶/_4,246 + ^5,246/_482,969 + ²⁴/₈ + ⁴²/_5,142 - ^6,247/₇₂ + ⁵¹/₁₄ + ⁴⁷/₂₀ - ^765,818/₃₃ = ?	Mar 02 04:29 UTC (GMT)
- ³⁴/_662,993 + ²⁷/₅₈ = ?	Mar 02 04:29 UTC (GMT)
¹¹⁷/₄₄ - ¹⁹²/₃₀ = ?	Mar 02 04:29 UTC (GMT)
- ¹⁹/₁₅₃ + ³¹/₂₀ = ?	Mar 02 04:28 UTC (GMT)
⁴⁴/₆₇ + ⁵²/₈₁ - ^577,268/₂₀ + ⁶³/₂₃ = ?	Mar 02 04:28 UTC (GMT)
see more... added fractions

- 20/53 - 22/25 = ? Subtracting Ordinary (Simple, Common) Math Fractions Calculator, Subtraction Explained in Detail

- 20/53 - 22/25 = ?

Reduce (simplify) fractions to their lowest terms equivalents:

To reduce a fraction: divide the numerator and denominator by their greatest common factor, GCF.

Fraction: - 20/53 already reduced to the lowest terms. The numerator and denominator have no common prime factors. Their prime factorization: 20 = 22 × 5; 53 is a prime number; gcf (22 × 5; 53) = 1;

Fraction: - 22/25 already reduced to the lowest terms. The numerator and denominator have no common prime factors. Their prime factorization: 22 = 2 × 11; 25 = 52; gcf (2 × 11; 52) = 1;

To operate fractions, build up their denominators the same.

Calculate LCM, the least common multiple of the denominators of the fractions:

LCM will be the common denominator of the fractions that we work with.

The prime factorization of the denominators:

53 is a prime number;

25 = 52;

Multiply all the unique prime factors, by the largest exponents:

LCM (53; 25) = 52 × 53 = 1,325

Calculate the expanding number of each fraction:

Divide LCM by the numerator of each fraction.

For fraction: - 20/53 is 1,325 ÷ 53 = (52 × 53) ÷ 53 = 25;

For fraction: - 22/25 is 1,325 ÷ 25 = (52 × 53) ÷ 52 = 53;

Build up the fractions to the same denominator:

Expand each fraction - multiply the numerator and denominator by the expanding number.

Then work with the numerators of the fractions.

- 20/53 - 22/25 =

- (25 × 20)/(25 × 53) - (53 × 22)/(53 × 25) =

- 500/1,325 - 1,166/1,325 =

( - 500 - 1,166)/1,325 =

- 1,666/1,325

Reduce (simplify) the fraction to its lowest terms equivalent:

To reduce a fraction: divide the numerator and denominator by their greatest common factor, GCF.

- 1,666/1,325 already reduced to the lowest terms.

The numerator and denominator have no common prime factors.

Their prime factorization:

1,666 = 2 × 72 × 17;

1,325 = 52 × 53;

gcf (2 × 72 × 17; 52 × 53) = 1;

Rewrite the fraction

As a mixed number (also called a mixed fraction):

Mixed number = a whole number and a proper fraction, of the same sign.

Proper fraction = numerator smaller than denominator.

- 1,666 ÷ 1,325 = - 1 and remainder = - 341 =>

- 1,666 = - 1 × 1,325 - 341 =>

- 1,666/1,325 =

( - 1 × 1,325 - 341)/1,325 =

- 1 - 341/1,325 =

- 1 341/1,325

As a decimal number:

- 1 - 341/1,325 =

- 1 - 341 ÷ 1,325 ≈

- 1.257358490566 ≈

- 1.26

As a percentage:

- 1.257358490566 =

- 1.257358490566 × 100/100 =

( - 1.257358490566 × 100)/100 =

- 125.735849056604/100 ≈

- 125.735849056604% ≈

- 125.74%

The final answer::: written in four ways ::

As a negative improper fraction (numerator >= denominator): - 20/53 - 22/25 = - 1,666/1,325

As a mixed number (also called a mixed fraction): - 20/53 - 22/25 = - 1 341/1,325

As a decimal number: - 20/53 - 22/25 ≈ - 1.26

As a percentage: - 20/53 - 22/25 ≈ - 125.74%

More operations of this kind:

Writing numbers: comma ',' used as a thousands separator; point '.' used as a decimal mark; numbers rounded to max. 12 decimals (whenever the case);

Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; ≈ approximation;

Add ordinary fractions, online calculator

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How to: Adding ordinary (simple, common) math fractions. Steps.

A. How to add ordinary fractions that have like denominators?

An example of adding ordinary fractions that have like denominators, with explanations

3/18 + 4/18 + 5/18 = (3 + 4 + 5)/18 = 12/18;

The resulting fraction is being reduced: 12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3.

How to reduce (simplify) the common fraction 12/18?

B. To add fractions with different denominators (unlike denominators), build up the fractions to the same denominator. How is it done?

1. Reduce the fractions to the lowest terms (simplifying).

2. Calculate the least common multiple, LCM, of all the fractions' new denominators:

3. Calculate each fraction's expanding number:

4. Expand each fraction:

5. Add the fractions:

6. Reduce the end fraction to the lowest terms, if needed.

More on ordinary (common) math fractions theory:

- ²⁰/₅₃ - ²²/₂₅ = ? Subtracting Ordinary (Simple, Common) Math Fractions Calculator, Subtraction Explained in Detail

- ²⁰/₅₃ - ²²/₂₅ = ?

Fraction: - ²⁰/₅₃ already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
20 = 2² × 5;
53 is a prime number;
gcf (2² × 5; 53) = 1;

Fraction: - ²²/₂₅ already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
22 = 2 × 11;
25 = 5²;
gcf (2 × 11; 5²) = 1;

25 = 5²;

LCM (53; 25) = 5² × 53 = 1,325

For fraction: - ²⁰/₅₃ is 1,325 ÷ 53 = (5² × 53) ÷ 53 = 25;

For fraction: - ²²/₂₅ is 1,325 ÷ 25 = (5² × 53) ÷ 5² = 53;

- ²⁰/₅₃ - ²²/₂₅ =

- ^{(25 × 20)}/_{(25 × 53)} - ^{(53 × 22)}/_{(53 × 25)} =

- ⁵⁰⁰/_1,325 - ^1,166/_1,325 =

^{( - 500 - 1,166)}/_1,325 =

- ^1,666/_1,325

- ^1,666/_1,325 already reduced to the lowest terms.

1,666 = 2 × 7² × 17;

1,325 = 5² × 53;

gcf (2 × 7² × 17; 5² × 53) = 1;

- ^1,666/_1,325 =

^{( - 1 × 1,325 - 341)}/_1,325 =

- 1 - ³⁴¹/_1,325 =

- 1 ³⁴¹/_1,325

- 1 - ³⁴¹/_1,325 =

- 1.257358490566 × ¹⁰⁰/₁₀₀ =

^{( - 1.257358490566 × 100)}/₁₀₀ =

^{- 125.735849056604}/₁₀₀ ≈

The final answer:
:: written in four ways ::

As a negative improper fraction (numerator >= denominator):
- ²⁰/₅₃ - ²²/₂₅ = - ^1,666/_1,325

As a mixed number (also called a mixed fraction):
- ²⁰/₅₃ - ²²/₂₅ = - 1 ³⁴¹/_1,325

As a decimal number:
- ²⁰/₅₃ - ²²/₂₅ ≈ - 1.26

As a percentage:
- ²⁰/₅₃ - ²²/₂₅ ≈ - 125.74%

³/₁₈ + ⁴/₁₈ + ⁵/₁₈ = ^{(3 + 4 + 5)}/₁₈ = ¹²/₁₈;

The resulting fraction is being reduced: ¹²/₁₈ = ^{(12 ÷ 6)}/_{(18 ÷ 6)} = ²/₃.

How to reduce (simplify) the common fraction ¹²/₁₈?