How to Divide Mixed Numbers
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Example 1) Work out \[ 3 {1 \over 3} ÷ 1 {5 \over 6} \]

Step 1)

We need to convert each of the mixed numbers into improper fractions.

\[ 3 {1 \over 3} \; = \; {10 \over 3} \] and \[ 1{ 5 \over 6} \; = \; {11 \over 6} \]

Now we have: \[ 3 {1 \over 3} ÷ 1 {5 \over 6} \; = \; {10 \over 3} ÷ {11 \over 6} \]

Step 2)

We need to invert the dividend fraction and change the operator to multiplication.

This gives us: \[ {10 \over 3} ÷ {11 \over 6} \; = \; {10 \over 3} \times {6 \over 11} \]

Step 3) Multiply the fractions

\[ {10 \over 3} \times {6 \over 11} \; = \; {10 \times 6 \over 3 \times 11} \; = \; {60 \over 33} \]

Step 4) Simplify the answer

We can simplify the answer by dividing the numerator and denominator by 3.

\[ {60 \over 33} \; = \; {60 ÷ 3 \over 33 ÷ 3} = {20 \over 11} \]

Now convert back to a mixed number.

\[ {20 \over 11} = 1 {9 \over 11} \]

Final answer: \[ 3 {1 \over 3} ÷ 1 {5 \over 6} \; = \; 1 {9 \over 11} \]

Example 2) Work out \[ 1 {3 \over 4} ÷ 2 {2 \over 5} \]

Step 1)

We need to convert each of the mixed numbers into improper fractions.

\[ 1 {3 \over 4} \; = \; {7 \over 4} \] and \[ 2{ 2 \over 5} \; = \; {12 \over 5} \]

Now we have: \[ 1 {3 \over 4} ÷ 2 {2 \over 5} \; = \; {7 \over 4} ÷ {12 \over 5} \]

Step 2)

We need to invert the dividend fraction and change the operator to multiplication.

This gives us: \[ {7 \over 4} ÷ {12 \over 5} \; = \; {7 \over 4} \times {5 \over 12} \]

Step 3) Multiply the fractions

\[ {7 \over 4} \times {5 \over 12} \; = \; {7 \times 5 \over 4 \times 12} \; = \; {35 \over 48} \]

Step 4) Simplify the answer

This fraction is already in simplest form.

Final answer: \[ 1 {3 \over 4} ÷ 2 {2 \over 5} \; = \; {35 \over 48} \]

Example 3) Work out \[ 4 ÷ 2 {1 \over 3} \]

Step 1)

We need to convert the mixed numbers into an improper fraction and put any integers over a denominator of 1.

\[ 2 {1 \over 3} \; = \; {7 \over 3} \]

Now we have: \[ 4 ÷ 2 {1 \over 3} \; = \; {4 \over 1} ÷ {7 \over 3} \]

Step 2)

We need to invert the dividend fraction and change the operator to multiplication.

This gives us: \[ {4 \over 1} ÷ {7 \over 3} \; = \; {4 \over 1} \times {3 \over 7} \]

Step 3) Multiply the fractions

\[ {4 \over 1} \times {3 \over 7} \; = \; {4 \times 3 \over 1 \times 7} \; = \; {12 \over 7} \]

Step 4) Simplify and convert.

This fraction is already in simplest form.

Now convert back to a mixed number.

\[ {12 \over 7} = 1 {5 \over 7} \]

Final answer: \[ 4 ÷ 2 {1 \over 3} \; = \; 1 {5 \over 7} \]