1 Work these out. $$ \begin{array}{lll} ext { a) } 14 \div \frac{1}{2} & ext { (i) } 16 \div \frac{2}{3} & ext { c) } 18 \div \frac{3}{5} \ 2 ext { Work these out. Give each answer as a mixed number i } \ ext { In all parts, cancel before you do any calculations. } \ \begin{array}{lll} ext { a) } 22 \div \frac{4}{7} & ext { b) } 10 \div \frac{4}{5} & ext { (d) } 21 \div \frac{14}{31}\end{array}\end{array} $$

Question

1 Work these out. $$ \begin{array}{lll}	ext { a) } 14 \div \frac{1}{2} & 	ext { (i) } 16 \div \frac{2}{3} & 	ext { c) } 18 \div \frac{3}{5} \ 2 	ext { Work these out. Give each answer as a mixed number i } \ 	ext { In all parts, cancel before you do any calculations. } \ \begin{array}{lll}	ext { a) } 22 \div \frac{4}{7} & 	ext { b) } 10 \div \frac{4}{5} & 	ext { (d) } 21 \div \frac{14}{31}\end{array}\end{array}> $$

UpStudy AI · Accepted Answer

**1. Work these out.**

**a)**  
We have  
$$
14 \div \frac{1}{2} = 14 \times \frac{1}{\frac{1}{2}} = 14 \times 2 = 28.
$$

**(i)**  
We have  
$$
16 \div \frac{2}{3} = 16 \times \frac{3}{2}.
$$  
Before multiplying, note that  
$$
16 \times \frac{3}{2} = \frac{16 \times 3}{2} = \frac{48}{2} = 24.
$$

**c)**  
We have  
$$
18 \div \frac{3}{5} = 18 \times \frac{5}{3}.
$$  
Simplify by canceling common factors before multiplying:  
$$
18 \times \frac{5}{3} = \frac{18 \times 5}{3} = \frac{90}{3} = 30.
$$

---

**2. Work these out. Give each answer as a mixed number. In all parts, cancel before you do any calculations.**

**a)**  
We have  
$$
22 \div \frac{4}{7} = 22 \times \frac{7}{4}.
$$  
Multiply:  
$$
22 \times \frac{7}{4} = \frac{154}{4}.
$$  
Simplify by dividing numerator and denominator by 2:  
$$
\frac{154}{4} = \frac{77}{2}.
$$  
Convert to a mixed number:  
$$
\frac{77}{2} = 38 \frac{1}{2}.
$$

**b)**  
We have  
$$
10 \div \frac{4}{5} = 10 \times \frac{5}{4}.
$$  
Multiply:  
$$
10 \times \frac{5}{4} = \frac{50}{4}.
$$  
Simplify by dividing numerator and denominator by 2:  
$$
\frac{50}{4} = \frac{25}{2}.
$$  
Convert to a mixed number:  
$$
\frac{25}{2} = 12 \frac{1}{2}.
$$

**(d)**  
We have  
$$
21 \div \frac{14}{31} = 21 \times \frac{31}{14}.
$$  
Before multiplying, cancel common factors. Factorize:
$$
21 = 3 \times 7 \quad \text{and} \quad 14 = 2 \times 7.
$$  
Cancel the common factor $$7$$:
$$
21 \times \frac{31}{14} = \frac{3 \times 7 \times 31}{2 \times 7} = \frac{3 \times 31}{2} = \frac{93}{2}.
$$  
Convert to a mixed number:  
$$
\frac{93}{2} = 46 \frac{1}{2}.
$$
**1. Work these out.** **a)** $$ 14 \div \frac{1}{2} = 28 $$ **(i)** $$ 16 \div \frac{2}{3} = 24 $$ **c)** $$ 18 \div \frac{3}{5} = 30 $$ --- **2. Work these out. Give each answer as a mixed number.** **a)** $$ 22 \div \frac{4}{7} = 38 \frac{1}{2} $$ **b)** $$ 10 \div \frac{4}{5} = 12 \frac{1}{2} $$ **(d)** $$ 21 \div \frac{14}{31} = 46 \frac{1}{2} $$

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