Ratios: Additional Practice (Set 2)

Multiply both parts by $10$ to clear the decimals, then simplify by dividing by the common factor $5$.

$0.5 : 1.5 = 5 : 15 = 1 : 3$

Ann's $5$ parts are worth $45, so one part is $45 \div 5 = 9$ dollars. Ben gets $4$ parts.

$4 \times 9 = 36$

So Ben gets $36.

Total parts: $2 + 3 + 5 = 10$. Each part is $100 \div 10 = 10$. The largest is $5$ parts.

$5 \times 10 = 50$

So the largest share is $50$.

Cars exceed trucks by $7 - 2 = 5$ parts, and that difference is $20$ vehicles, so one part is $20 \div 5 = 4$. Cars are $7$ parts.

$7 \times 4 = 28$

So there are $28$ cars.

The cats went from $5$ to $35$, a scale factor of $35 \div 5 = 7$. Multiply the dogs part by $7$.

$5 : 2 = 35 : 14$

So there are $14$ dogs.

Simplify each fraction by dividing out the greatest common factor.

$\frac{6}{10} = \frac{3}{5}, \qquad \frac{9}{15} = \frac{3}{5}$

Both reduce to $3 : 5$, so the ratios are equivalent.

Divide both parts by their greatest common factor, $25$.

$25 : 100 = (25 \div 25) : (100 \div 25) = 1 : 4$

Yes went from $9$ to $126$, a scale factor of $126 \div 9 = 14$. Multiply the no part by $14$.

$5 \times 14 = 70$

So $70$ people answered no.

The flour went from $5$ to $20$, a scale factor of $20 \div 5 = 4$. Multiply the cocoa part by $4$.

$3 : 5 = 12 : 20$

So you need $12$ cups of cocoa.

Blue is never touched, so it stays at $3$ parts. Making the ratio $1 : 1$ means red must equal blue, so red has to rise from $2$ parts to $3$ parts. The $4$ added red counters fill exactly that $1$-part gap, so $1$ part is $4$ counters. Blue is $3$ parts.

$3 \times 4 = 12$

So there are $12$ blue counters.

Multiply both parts by $10$ to clear the decimals, then divide by the common factor $4$.

$1.2 : 0.8 = 12 : 8 = 3 : 2$

Gear A went from $4$ to $36$, a scale factor of $36 \div 4 = 9$. Multiply gear B's part by $9$.

$9 \times 9 = 81$

So gear B makes $81$ turns.