Ratios: Additional Practice (Set 1)

Total parts: $3 + 2 + 5 = 10$. Each part is $400 \div 10 = 40$ grams. Cashews are $2$ parts.

$2 \times 40 = 80$

So there are $80$ grams of cashews.

Blue's $7$ parts are $77$ tiles, so one part is $77 \div 7 = 11$. The total is all $4 + 7 = 11$ parts.

$11 \times 11 = 121$

So there are $121$ tiles altogether.

The butter went from $2$ to $3$, a scale factor of $3 \div 2 = 1.5$. Multiply the flour part by $1.5$.

$5 \times 1.5 = 7.5$

So you need $7.5$ cups of flour.

The largest share is $4$ parts, worth $48, so one part is $48 \div 4 = 12$ dollars. The total is $2 + 3 + 4 = 9$ parts.

$9 \times 12 = 108$

So the total shared is $108.

Write both parts over the common denominator $9$: $\frac{2}{3} = \frac{6}{9}$ and $\frac{4}{9}$. Compare the numerators, then simplify.

$\tfrac{6}{9} : \tfrac{4}{9} = 6 : 4 = 3 : 2$

Total parts: $3 + 4 = 7$. Each part is $35 \div 7 = 5$ students. Girls exceed boys by $4 - 3 = 1$ part.

$1 \times 5 = 5$

So there are $5$ more girls than boys.

Compare as decimals: $7 : 9 \approx 0.778$, $5 : 6 \approx 0.833$, and $8 : 11 \approx 0.727$.

$0.833 > 0.778 > 0.727$

So $5 : 6$ is the largest.

Total parts: $1 + 2 + 3 = 6$. Each part is $60 \div 6 = 10$ dollars. The largest is $3$ parts and the smallest is $1$ part, a gap of $2$ parts.

$2 \times 10 = 20$

So the largest gets $20 more.

The width went from $3$ to $12$, a scale factor of $12 \div 3 = 4$. Multiply the length part by $4$.

$5 \times 4 = 20$

So the length is $20$ cm.

Make the yellow part match in both ratios. Red to yellow is $3 : 4$, and yellow to blue is $2 : 5$; scaling the second so yellow is $4$ turns it into $4 : 10$. Now red to yellow to blue lines up as $3 : 4 : 10$.

$\text{red} : \text{blue} = 3 : 10$

So red to blue is $3 : 10$.

Total parts: $4 + 1 = 5$. Each part is $20 \div 5 = 4$ liters. Red is $1$ part.

$1 \times 4 = 4$

So there are $4$ liters of red.

Total parts: $3 + 7 = 10$. Each part is $250 \div 10 = 25$ people. Adults are $3$ parts.

$3 \times 25 = 75$

So there are $75$ adults.