EXERCISE 13.5 1. Calculate these numbers. Afterwards, check your answers using your calculator. a) $$ 5 \div \frac{1}{2} $$ b) $$ 3 \div \frac{5}{6} $$ c) $$ 22 \div \frac{2}{3} $$ d) $$ 45 \div \frac{7}{5} $$ 2. What do I have to multiply 5 with to get 7 ? 3. How many times does $$ \frac{2}{3} $$ go into 4 ?

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UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{2}{3}x=4$$
- step1: Multiply by the reciprocal:
  $$\frac{2}{3}x\times \frac{3}{2}=4\times \frac{3}{2}$$
- step2: Multiply:
  $$x=6$$
Calculate or simplify the expression $$ 22 \div \frac{2}{3} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$22\div \frac{2}{3}$$
- step1: Multiply by the reciprocal:
  $$22\times \frac{3}{2}$$
- step2: Reduce the numbers:
  $$11\times 3$$
- step3: Multiply the numbers:
  $$33$$
Calculate or simplify the expression $$ 45 \div \frac{7}{5} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$45\div \frac{7}{5}$$
- step1: Multiply by the reciprocal:
  $$45\times \frac{5}{7}$$
- step2: Multiply:
  $$\frac{45\times 5}{7}$$
- step3: Multiply:
  $$\frac{225}{7}$$
Solve the equation $$ 5x=7 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$5x=7$$
- step1: Divide both sides:
  $$\frac{5x}{5}=\frac{7}{5}$$
- step2: Divide the numbers:
  $$x=\frac{7}{5}$$
Calculate or simplify the expression $$ 5 \div \frac{1}{2} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5\div \frac{1}{2}$$
- step1: Multiply by the reciprocal:
  $$5\times 2$$
- step2: Multiply the numbers:
  $$10$$
Calculate or simplify the expression $$ 3 \div \frac{5}{6} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$3\div \frac{5}{6}$$
- step1: Multiply by the reciprocal:
  $$3\times \frac{6}{5}$$
- step2: Multiply:
  $$\frac{3\times 6}{5}$$
- step3: Multiply:
  $$\frac{18}{5}$$
Let's solve the problems step by step.

### 1. Calculate these numbers.

a) $$ 5 \div \frac{1}{2} $$

To divide by a fraction, we multiply by its reciprocal:
$$
5 \div \frac{1}{2} = 5 \times 2 = 10
$$

b) $$ 3 \div \frac{5}{6} $$

Using the same method:
$$
3 \div \frac{5}{6} = 3 \times \frac{6}{5} = \frac{18}{5} = 3\frac{3}{5} = 3.6
$$

c) $$ 22 \div \frac{2}{3} $$

Again, multiplying by the reciprocal:
$$
22 \div \frac{2}{3} = 22 \times \frac{3}{2} = 33
$$

d) $$ 45 \div \frac{7}{5} $$

Using the reciprocal:
$$
45 \div \frac{7}{5} = 45 \times \frac{5}{7} = \frac{225}{7} \approx 32\frac{1}{7} \approx 32.14
$$

### Summary of Results:
- a) $$ 10 $$
- b) $$ 3.6 $$
- c) $$ 33 $$
- d) $$ 32\frac{1}{7} $$ or approximately $$ 32.14 $$

### 2. What do I have to multiply 5 with to get 7?

We can set up the equation:
$$
5x = 7
$$
Solving for $$ x $$:
$$
x = \frac{7}{5} = 1.4
$$

### 3. How many times does $$ \frac{2}{3} $$ go into 4?

We can set up the equation:
$$
\frac{2}{3}x = 4
$$
Solving for $$ x $$:
$$
x = 4 \times \frac{3}{2} = 6
$$

### Final Answers:
1. a) $$ 10 $$, b) $$ 3.6 $$, c) $$ 33 $$, d) $$ 32\frac{1}{7} $$
2. $$ 1.4 $$
3. $$ 6 $$
1. a) 10, b) 3.6, c) 33, d) 32.14 2. Multiply 5 by 1.4 to get 7. 3. $$ \frac{2}{3} $$ goes into 4 six times.

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