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Arithmetic
Question

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

$$4 \div \frac { 1 } { 3 } = 12$$

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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