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Arithmetic
Question

3. Multiply or divide. Draw a model to explain you...

3. Multiply or divide. Draw a model to explain your thinking. \(4 \div \frac { 1 } { 3 }\)\(\frac { 1 } { 2 } \div 3\)

Answer

\(4 \div \frac { 1 } { 3 } = 12 \) 

Steps 

\( 4 \div \frac { 1 } { 3 } \) 

Convert element to fraction: \( 4 = \frac { 4 } { 1 } \) 

\( = \frac { 4 } { 1 } \div \frac { 1 } { 3 } \) 

Apply the fraction rule: \( \frac { a } { b } \div \frac { c } { d } = \frac { a } { b } \times \frac { d } { c } \) 

\( = \frac { 4 } { 1 } \times \frac { 3 } { 1 } \) 

Apply rule \( \frac { a } { 1 } = a \) 

\( = 4 \times 3 \) 

Multiply the numbers: \( 4 \times 3 = 12 \) 

\( = 12\) 

\(\frac { 1 } { 2 } \div 3 = \frac { 1 } { 6 } \) 

Steps 

\( \frac { 1 } { 2 } \div 3 \) 

Convert element to fraction: \( 3 = \frac { 3 } { 1 } \) 

\( = \frac { 1 } { 2 } \div \frac { 3 } { 1 }\) 

Apply the fraction rule: \( \frac { a } { b } \div \frac { c } { d } = \frac { a } { b } \times \frac { d } { c } \) 

\( = \frac { 1 } { 2 } \times \frac { 1 } { 3 } \) 

Multiply fractions: \( \frac { a } { b } \times \frac { c } { d } = \frac { a \times c } { b \times d } \) 

\( = \frac { 1 \times 1 } { 2 \times 3 } \) 

Multiply the numbers: \( 1 \times 1 = 1\) \(= \frac { 1 } { 2 \times 3 } \) 

Multiply the numbers: \( 2 \times 3 = 6 \) 

\( = \frac { 1 } { 6 }\) 

Solution
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