Ratios: Practice

Order matters: oranges are named first this time.

$\text{oranges} : \text{apples} = 5 : 4$

So the ratio is $5 : 4$.

A ratio is written as a fraction by putting the first quantity on top and the second on the bottom, keeping the same order.

$3 : 7 = \frac{3}{7}$

The greatest common factor of $4$ and $6$ is $2$. Divide both parts by $2$.

$4 : 6 = (4 \div 2) : (6 \div 2) = 2 : 3$

Multiply both parts of $2 : 5$ by the same number. Doubling each part gives

$2 : 5 = (2 \times 2) : (5 \times 2) = 4 : 10.$

The greatest common factor of $10$ and $5$ is $5$. Divide both parts by $5$.

$10 : 5 = (10 \div 5) : (5 \div 5) = 2 : 1$

Multiply each part by $4$.

$5 : 1 = (5 \times 4) : (1 \times 4) = 20 : 4$

Oil is named first, so it is written first.

$\text{oil} : \text{water} = 1 : 3$

A ratio is simplest when the two parts share no common factor beyond $1$. Check each: $6 : 8$ shares $2$, $4 : 10$ shares $2$, and $9 : 12$ shares $3$, but $3$ and $5$ share only $1$.

$\gcd(3, 5) = 1$

So $3 : 5$ is already simplest.

Add the parts to get the whole.

$2 + 3 = 5$

So the mix is $5$ parts in all.

Multiply each part by $2$.

$3 : 4 = (3 \times 2) : (4 \times 2) = 6 : 8$

The ratio of roses to tulips is $8 : 4$. Divide both parts by their greatest common factor, $4$.

$8 : 4 = (8 \div 4) : (4 \div 4) = 2 : 1$

A ratio is written as a fraction with the first quantity on top and the second on the bottom, in the same order.

$5 : 6 = \frac{5}{6}$