Ratios 4

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Ratios 4

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Question 1 of 4

1. Question
Simplify

$60 cents : $ 2$ $60 \text(cents):$2$
- (3) $:$ $:$ (10)
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A ratio compares quantities of the same type given in the same units.

First, convert the dollars into cents

$$ 1$ $$1$ $=$ $=$ $100 cents$ $100 \text(cents)$

$2 \times \frac{100}{1}$ $2xx(100)/1$ $=$ $=$ $200$ $200$

$60$ $60$ $:$ $:$ $200$ $200$

Finally, divide both sides by their highest common factor

$60$ $60$ $:$ $:$ $200$ $200$

$60$ $60$ $\div 20$ $divide20$ $:$ $:$ $200$ $200$ $\div 20$ $divide20$ $20$ $20$ is the highest common factor

$3$ $3$ $:$ $:$ $10$ $10$

$3 : 10$ $3:10$
Question 2 of 4

2. Question
Simplify

$700 kg : 2 t$ $700 \text(kg):2 \text(t)$
- (7) $:$ $:$ (20)
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A ratio compares quantities of the same type given in the same units.

First, convert the tons into kilograms

$1 ton$ $1 \text(ton)$ $=$ $=$ $1000 kilograms$ $1000 \text(kilograms)$

$2 \times \frac{1000}{1}$ $2xx(1000)/1$ $=$ $=$ $2000$ $2000$

$700$ $700$ $:$ $:$ $2000$ $2000$

Finally, divide both sides by their highest common factor

$700$ $700$ $:$ $:$ $2000$ $2000$

$700$ $700$ $\div 100$ $divide100$ $:$ $:$ $2000$ $2000$ $\div 100$ $divide100$ $100$ $100$ is the highest common factor

$7$ $7$ $:$ $:$ $20$ $20$

$7 : 20$ $7:20$
Question 3 of 4

3. Question
Simplify

$\frac{1}{x} : x$ $1/x:x$
- 1. $1 : x^{2}$ $1:x^2$
- 2. $2 : x$ $2:x$
- 3. $1 : x$ $1:x$
- 4. $1 : 2 x$ $1:2x$
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A ratio compares quantities of the same type given in the same units.

Remove the fraction by cancelling out the denominator

$\frac{1}{x}$ $1/x$ $:$ $:$ $x$ $x$

$\frac{1}{x}$ $1/x$ $\times x$ $timesx$ $:$ $:$ $x$ $x$ $\times x$ $timesx$ Multiply both sides by $x$ $x$

$1$ $1$ $:$ $:$ $x^{2}$ $x^2$ $\frac{x}{x} = 1$ $x/x=1$

$1 : x^{2}$ $1:x^2$
Question 4 of 4

4. Question
Simplify

$8 a b : 2 a c$ $8ab:2ac$
- (4b) $:$ $:$ (c)
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A ratio compares quantities of the same type given in the same units.

Simplify the ratio by dividing common factors to each side.

$8 a b$ $8ab$ $:$ $:$ $2 a c$ $2ac$

$8 a b$ $8ab$ $\div 2$ $divide2$ $:$ $:$ $2 a c$ $2ac$ $\div 2$ $divide2$ Divide both sides by $2$ $2$

$4 a b$ $4ab$ $\div a$ $dividea$ $:$ $:$ $a c$ $ac$ $\div a$ $dividea$ Divide both sides by $a$ $a$

$4 b$ $4b$ $:$ $:$ $c$ $c$

$4 b : c$ $4b:c$

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Quiz summary

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1. Question

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2. Question

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3. Question

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4. Question

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Quizzes

$2 \times \frac{100}{1}$ $2xx(100)/1$	$=$ $=$	$200$ $200$

$60$ $60$	$:$ $:$	$200$ $200$

$2 \times \frac{1000}{1}$ $2xx(1000)/1$	$=$ $=$	$2000$ $2000$

$700$ $700$	$:$ $:$	$2000$ $2000$

$\frac{1}{x}$ $1/x$	$:$ $:$	$x$ $x$

$\frac{1}{x}$ $1/x$ $\times x$ $timesx$	$:$ $:$	$x$ $x$ $\times x$ $timesx$	Multiply both sides by $x$ $x$

$1$ $1$	$:$ $:$	$x^{2}$ $x^2$	$\frac{x}{x} = 1$ $x/x=1$

$8 a b$ $8ab$	$:$ $:$	$2 a c$ $2ac$
$8 a b$ $8ab$ $\div 2$ $divide2$	$:$ $:$	$2 a c$ $2ac$ $\div 2$ $divide2$	Divide both sides by $2$ $2$
$4 a b$ $4ab$ $\div a$ $dividea$	$:$ $:$	$a c$ $ac$ $\div a$ $dividea$	Divide both sides by $a$ $a$
$4 b$ $4b$	$:$ $:$	$c$ $c$