\[3+\frac{7}{4}+2+\frac{8}{7}\]

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Examples

Add the whole numbers first.

5+\frac{7}{4}+\frac{8}{7}

Find the Least Common Denominator (LCD) of

\frac{7}{4},\frac{8}{7}

. In other words, find the Least Common Multiple (LCM) of

4,7

Method 1: By Listing Multiples

List the multiples of each number.

Multiples of 4

: 4, 8, 12, 16, 20, 24, 28, ...

Multiples of 7

: 7, 14, 21, 28, ...

Find the smallest number that is shared by all rows above. This is the LCM.

LCM =

28

Method 2: By Prime Factors

List the prime factors of each number.

Prime Factors of 4

: 2, 2

Prime Factors of 7

: 7

Find the union of these primes.

2,2,7

Multiply these numbers:

2\times 2\times 7=28

. This is the LCM.

LCM =

28

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LCD =

28

Make the denominators the same as the LCD.

5+\frac{7\times 7}{4\times 7}+\frac{8\times 4}{7\times 4}

Simplify. Denominators are now the same.

5+\frac{49}{28}+\frac{32}{28}

Join the denominators.

5+\frac{49+32}{28}

Simplify.

5+\frac{81}{28}

Convert

\frac{81}{28}

to mixed fraction.

5+2\frac{25}{28}

Simplify.

7\frac{25}{28}

Done

Decimal Form: 7.892857

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