Ratios: Practice

The flour went from $3$ to $15$, a scale factor of $15 \div 3 = 5$. Multiply the sugar part by $5$.

$1 \times 5 = 5$

So you need $5$ cups of sugar.

Total parts: $1 + 3 = 4$. Each part is worth $24 \div 4 = 6$ dollars. The larger share is $3$ parts.

$3 \times 6 = 18$

So the larger share is $18.

The greatest common factor of $18$ and $24$ is $6$. Divide both parts by $6$.

$18 : 24 = (18 \div 6) : (24 \div 6) = 3 : 4$

The dogs went from $7$ to $21$, a scale factor of $21 \div 7 = 3$. Multiply the cats part by $3$.

$2 \times 3 = 6$

So there are $6$ cats.

The juice went from $2$ to $10$, a scale factor of $10 \div 2 = 5$. Multiply the water part by $5$.

$5 \times 5 = 25$

So there are $25$ cups of water.

Total parts: $5 + 3 = 8$. Each part is $40 \div 8 = 5$ marbles. Red is $5$ parts.

$5 \times 5 = 25$

So $25$ marbles are red.

First simplify the right side: $10 : 15 = 2 : 3$. Now match $\square : 6$ to $2 : 3$. The second part went from $3$ to $6$, a factor of $2$.

$2 \times 2 = 4$

So the blank is $4$.

Each equivalent ratio scales $3 : 4$ by the same factor: $6 : 8$ ($\times 2$), $9 : 12$ ($\times 3$), $12 : 16$ ($\times 4$). Test $8 : 9$ by simplifying.

$\gcd(8, 9) = 1 \Rightarrow 8 : 9 \ne 3 : 4$

So $8 : 9$ is not equivalent.

Total parts: $3 + 2 = 5$. Each part is $25 \div 5 = 5$ games. Wins are $3$ parts.

$3 \times 5 = 15$

So they won $15$ games.

The greatest common factor of $16$ and $40$ is $8$. Divide both parts by $8$.

$16 : 40 = (16 \div 8) : (40 \div 8) = 2 : 5$

The old width went from $2$ to $6$, a scale factor of $6 \div 2 = 3$. Multiply the new part by $3$.

$5 \times 3 = 15$

So the new width is $15$ cm.

Total parts: $4 + 5 = 9$. Each part is $45 \div 9 = 5$ dollars. The larger share is $5$ parts.

$5 \times 5 = 25$

So the larger share is $25.