Simplify the following ratios: 50 mm : 25 mm, 15 kg : 21000 g, 120 sec : 8 min, 49 months : 7 years

Question

ScanSolve AI Tutor · Accepted Answer

Right Chosen, let's solve these ratios again.

Simplify $50 \text{ mm} : 25 \text{ mm}$

The units are already the same.
Divide both sides by the greatest common divisor, which is 25.
$$ \frac{50}{25} : \frac{25}{25} $$
Simplify the division.
$$ 2 : 1 $$ The simplified ratio is $\boxed{\text{2:1}}$.
2. Simplify $15 \text{ kg} : 21000 \text{ g}$
Convert kilograms to grams.
( $1 \text{ kg} = 1000 \text{ g}$ ) $15 \text{ kg} = 15 \times 1000 \text{ g} = 15000 \text{ g}$
Write the ratio with the same units.
$$ 15000 \text{ g} : 21000 \text{ g} $$
Divide both sides by 1000.
$$ 15 : 21 $$
Divide both sides by their greatest common divisor, which is 3.
$$ \frac{15}{3} : \frac{21}{3} $$ $$ 5 : 7 $$ The simplified ratio is $\boxed{\text{5:7}}$.
3. Simplify $120 \text{ sec} : 8 \text{ min}$
Convert minutes to seconds.
( $1 \text{ min} = 60 \text{ sec}$ ) $8 \text{ min} = 8 \times 60 \text{ sec} = 480 \text{ sec}$
Write the ratio with the same units.
$$ 120 \text{ sec} : 480 \text{ sec} $$
Divide both sides by their greatest common divisor, which is 120.
$$ \frac{120}{120} : \frac{480}{120} $$ $$ 1 : 4 $$ The simplified ratio is $\boxed{\text{1:4}}$.
4. Simplify $49 \text{ months} : 7 \text{ years}$
Convert years to months.
( $1 \text{ year} = 12 \text{ months}$ ) $7 \text{ years} = 7 \times 12 \text{ months} = 84 \text{ months}$
Write the ratio with the same units.
$$ 49 \text{ months} : 84 \text{ months} $$
Divide both sides by their greatest common divisor, which is 7.
$$ \frac{49}{7} : \frac{84}{7} $$ $$ 7 : 12 $$ The simplified ratio is $\boxed{\text{7:12}}$.
5. Simplify $7.5 \text{ litres} : 700 \text{ millilitres}$
Convert litres to millilitres.
( $1 \text{ litre} = 1000 \text{ millilitres}$ ) $7.5 \text{ litres} = 7.5 \times 1000 \text{ millilitres} = 7500 \text{ millilitres}$

Write the ratio with the same units.

$$
7500 \text{ millilitres} : 700 \text{ millilitres}
$$

Divide both sides by their greatest common divisor, which is 100.

$$
\frac{7500}{100} : \frac{700}{100}
$$
$$
75 : 7
$$
The simplified ratio is $\boxed{\text{75:7}}$.

Simplify the following ratios: 50 mm : 25 mm, 15 kg : 21000 g, 120 sec : 8 min, 49 months : 7 years

Step-by-step solution

The units are already the same.

Divide both sides by the greatest common divisor, which is 25.

Simplify the division.

Convert kilograms to grams.

Write the ratio with the same units.

Divide both sides by 1000.

Divide both sides by their greatest common divisor, which is 3.

Convert minutes to seconds.

Write the ratio with the same units.

Divide both sides by their greatest common divisor, which is 120.

Convert years to months.

Write the ratio with the same units.

Divide both sides by their greatest common divisor, which is 7.

Convert litres to millilitres.

Write the ratio with the same units.

Divide both sides by their greatest common divisor, which is 100.

Still stuck on this one?

More Mathematics Questions