# Homework 11-2 Decomposing Fractions Calculator

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## Calculator Use

Do math calculations with mixed numbers (mixed fractions) performing operations on fractions, whole numbers, integers, mixed numbers, mixed fractions and improper fractions. The Mixed Numbers Calculator can add, subtract, multiply and divide mixed numbers and fractions.

### Mixed Numbers Calculator (also referred to as Mixed Fractions):

This online calculator handles simple operations on whole numbers, integers, mixed numbers, fractions and improper fractions by adding, subtracting, dividing or multiplying. The answer is provided in a reduced fraction and a mixed number if it exists.

Enter mixed numbers, whole numbers or fractions in the following formats:

- Mixed numbers: Enter as 1 1/2 which is one and one half or 25 3/32 which is twenty five and three thirty seconds. Keep exactly one space between the whole number and fraction and use a forward slash to input fractions. You can enter up to 3 digits in length for each whole number, numerator or denominator (123 456/789).
- Whole numbers: Up to 3 digits in length.
- Fractions: Enter as 3/4 which is three fourths or 3/100 which is three one hundredths. You can enter up to 3 digits in length for each the numerators and denominators (e.g., 456/789).

## Adding Mixed Numbers using the Adding Fractions Formula

- Convert the mixed numbers to improper fractions
- Use the algebraic formula for addition of fractions:

a/b + c/d = (ad + bc) / bd - Reduce fractions and simplify if possible

### Adding Fractions Formula

\( \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \times d) + (b \times c)}{b \times d} \)

### Example

Add 1 2/6 and 2 1/4

\( 1 \dfrac{2}{6} + 2 \dfrac{1}{4} = \dfrac{8}{6} + \dfrac{9}{4} \)

\( = \dfrac{(8 \times 4) + (9 \times 6)}{6 \times 4} \)

\( = \dfrac{32 + 54}{24} = \dfrac{86}{24} = \dfrac{43}{12} \)

\( = 3 \dfrac{7}{12} \)

1 2/6 + 2 1/4 = 8/6 + 9/4 = (8*4 + 9*6) / 6*4 = 86 / 24

So we get 86/24 and simplify to 3 7/12

## Subtracting Mixed Numbers using the Subtracting Fractions Formula

- Convert the mixed numbers to improper fractions
- Use the algebraic formula for subtraction of fractions: a/b - c/d = (ad - bc) / bd
- Reduce fractions and simplify if possible

### Subtracting Fractions Formula

\( \dfrac{a}{b} - \dfrac{c}{d} = \dfrac{(a \times d) - (b \times c)}{b \times d} \)

### Example

Subtract 2 1/4 from 1 2/6

1 2/6 - 2 1/4 = 8/6 - 9/4 = (8*4 - 9*6) / 6*4 = -22 / 24

Reduce the fraction to get -11/12

## Multiplying Mixed Numbers using the Multiplying Fractions Formula

- Convert the mixed numbers to improper fractions
- Use the algebraic formula for multiplying of fractions: a/b * c/d = ac / bd
- Reduce fractions and simplify if possible

### Multiplying Fractions Formula

\( \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d} \)

### Example

multiply 1 2/6 by 2 1/4

1 2/6 * 2 1/4 = 8/6 * 9/4 = 8*9 / 6*4 = 72 / 24

Reduce the fraction to get 3/1 and simplify to 3

## Dividing Mixed Numbers using the Dividing Fractions Formula

- Convert the mixed numbers to improper fractions
- Use the algebraic formula for division of fractions: a/b ÷ c/d = ad / bc
- Reduce fractions and simplify if possible

### Dividing Fractions Formula

\( \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a \times d}{b \times c} \)

### Example

divide 1 2/6 by 2 1/4

1 2/6 ÷ 2 1/4 = 8/6 ÷ 9/4 = 8*4 / 9*6 = 32 / 54

Reduce the fraction to get 16/27

### Related Calculators

To perform math operations on simple proper or improper fractions use our Fractions Calculator. This calculator simplifies improper fraction answers into mixed numbers.

If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator.

For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.

If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values.

Note:

This calculator performs the reducing calculation faster than others you might find. The primary reason is that the code utilizes Euclid's Theorem for reducing fractions which can be found at The Math Forum: LCD, LCM.

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