6 1 2 7 8 divided by 5 11 16

6\frac{1}{2}-\frac{7}{8}\div 5\frac{11}{16}6​2​​1​​−​8​​7​​÷5​16​​11​​

1



Convert 6\frac{1}{2}6​2​​1​​ to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}a​c​​b​​=​c​​ac+b​​

\frac{6\times 2+1}{2}-\frac{7}{8}\div 5\frac{11}{16}​2​​6×2+1​​−​8​​7​​÷5​16​​11​​


2



Simplify 6\times 26×2 to 1212

\frac{12+1}{2}-\frac{7}{8}\div 5\frac{11}{16}​2​​12+1​​−​8​​7​​÷5​16​​11​​


3



Simplify 12+112+1 to 1313

\frac{13}{2}-\frac{7}{8}\div 5\frac{11}{16}​2​​13​​−​8​​7​​÷5​16​​11​​


4



Convert 5\frac{11}{16}5​16​​11​​ to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}a​c​​b​​=​c​​ac+b​​

\frac{13}{2}-\frac{7}{8}\div \frac{5\times 16+11}{16}​2​​13​​−​8​​7​​÷​16​​5×16+11​​


5



Simplify 5\times 165×16 to 8080

\frac{13}{2}-\frac{7}{8}\div \frac{80+11}{16}​2​​13​​−​8​​7​​÷​16​​80+11​​


6



Simplify 80+1180+11 to 9191

\frac{13}{2}-\frac{7}{8}\div \frac{91}{16}​2​​13​​−​8​​7​​÷​16​​91​​


7



Use this rule: a\div \frac{b}{c}=a\times \frac{c}{b}a÷​c​​b​​=a×​b​​c​​

\frac{13}{2}-\frac{7}{8}\times \frac{16}{91}​2​​13​​−​8​​7​​×​91​​16​​


8



Use this rule: \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}​b​​a​​×​d​​c​​=​bd​​ac​​

\frac{13}{2}-\frac{7\times 16}{8\times 91}​2​​13​​−​8×91​​7×16​​


9



Simplify 7\times 167×16 to 112112

\frac{13}{2}-\frac{112}{8\times 91}​2​​13​​−​8×91​​112​​


10



Simplify 8\times 918×91 to 728728

\frac{13}{2}-\frac{112}{728}​2​​13​​−​728​​112​​


11



Simplify \frac{112}{728}​728​​112​​ to \frac{2}{13}​13​​2​​

\frac{13}{2}-\frac{2}{13}​2​​13​​−​13​​2​​


12



Find the Least Common Denominator (LCD) of \frac{13}{2}, \frac{2}{13}​2​​13​​,​13​​2​​

Method 1: By Listing Multiples

List out all multiples of each denominator, and find the first common one.

Multiples of 2

: 2, 4, 6 ... 22, 24, 26, ...

Multiples of 13

: 13, 26, ...

Therefore, the LCD is 2626.

Method 2: By Prime Factors

Since 2,132,13 are prime numbers themselves, we simply multiply them to get the LCD.

Therefore, the LCD is 2\times 13=262×13=26.

LCD = 2626


13



Make the denominators the same as the LCD

\frac{13\times 13}{2\times 13}-\frac{2\times 2}{13\times 2}​2×13​​13×13​​−​13×2​​2×2​​


14



Simplify. Denominators are now the same

\frac{169}{26}-\frac{4}{26}​26​​169​​−​26​​4​​


15



Join the denominators

\frac{169-4}{26}​26​​169−4​​


16



Simplify

\frac{165}{26}​26​​165​​


17



Convert to mixed fraction

6\frac{9}{26}6​26​​9​​

Decimal Form: 6.346154



i know this is too long but is your teachers fault am so sorry.