Ratios: Practice

Total parts: $3 + 5 = 8$. Each part is $72 \div 8 = 9$. The larger share is $5$ parts.

$5 \times 9 = 45$

So the larger share is $45$.

Write each as a fraction over the common denominator $88$: $\frac{5}{8} = \frac{55}{88}$ and $\frac{7}{11} = \frac{56}{88}$.

$\frac{56}{88} > \frac{55}{88}$

So $7 : 11$ is the larger ratio.

Total parts: $4 + 7 = 11$. Each part is $33 \div 11 = 3$. The smaller part is $4$ parts.

$4 \times 3 = 12$

So the smaller part is $12$.

The sugar went from $2$ to $8$, a scale factor of $4$, so flour is $5 \times 4 = 20$ cups. Add the two amounts.

$8 + 20 = 28$

So there are $28$ cups in total.

Write $1\frac{1}{2}$ as $\frac{3}{2}$, then multiply both parts by $2$ to clear the fraction and simplify.

$\tfrac{3}{2} : 3 = 3 : 6 = 1 : 2$

Compare them as decimals: $2 : 3 \approx 0.667$, $3 : 5 = 0.6$, and $4 : 7 \approx 0.571$.

$0.667 > 0.6 > 0.571$

So $2 : 3$ is the largest.

Total parts: $3 + 4 = 7$. Each part is $56 \div 7 = 8$, so the shares are $24$ and $32$. Subtract.

$32 - 24 = 8$

So the difference is $8$.

Total parts: $3 + 1 = 4$. Each part is $2 \div 4 = 0.5$ liter. Juice is $3$ parts.

$3 \times 0.5 = 1.5$

So there are $1.5$ liters of juice.

The smallest term is $2$ parts, worth $10$, so each part is $10 \div 2 = 5$. The total is all $4 + 3 + 2 = 9$ parts.

$9 \times 5 = 45$

So the total is $45$.

Total parts: $5 + 3 = 8$. Each part is $40 \div 8 = 5$ games. Wins are $5$ parts.

$5 \times 5 = 25$

So the team had $25$ wins.

Total parts: $1 + 2 + 3 = 6$. Each part is $120 \div 6 = 20$. The middle share is $2$ parts.

$2 \times 20 = 40$

So the middle share is $40$.

Total parts: $4 + 9 = 13$. Each part is $39 \div 13 = 3$ marbles. Blue is the $4$-part quantity.

$4 \times 3 = 12$

So there are $12$ blue marbles.