Ratio and Proportion Practice Problems

Vocabulary practice flashcards covering word problems and mathematical concepts in ratio and proportion.

Sharing a Quantity in a Given Ratio (Question 1)

The method of dividing a total amount by the sum of ratio parts to find the value of one part; when $£80$ is shared between Will and Olly in the ratio $3 : 2$, one part is $£16$, giving Will $£48$ and Olly $£32$.

Three-Part Ratio Sharing (Question 2)

The process of dividing an amount into three proportional shares; sharing $42\text{ sweets}$ among Molly, Paige, and Demi in the ratio $3 : 2 : 1$ gives $6$ total parts at $7\text{ sweets}$ per part, resulting in $21\text{ sweets}$ for Molly, $14\text{ sweets}$ for Paige, and $7\text{ sweets}$ for Demi.

Straight Line Segment Ratio (Question 3)

A geometric ratio application on a line $ABC$ where segment $BC$ is three times the length of $AB$; since total length $AC = 80\text{ metres}$ represents $4$ equal parts, the length of $BC$ is $60\text{ metres}$.

Difference in Ratio Shares (Question 4)

Finding individual values when given the difference between shares; Carly and James share money in the ratio $5 : 3$ where Carly gets $£70$ more ($2\text{ parts}$ difference), meaning each part is worth $£35$ and James gets $£105$.

Single Known Share Ratio (Question 5)

Calculating an unknown share when one person's exact amount is given; Jerry and Mick share money in the ratio $2 : 3$ where Mick's $3\text{ parts}$ equal $£900$, making one part $£300$ and Jerry's share $£600$.

Comparative Part Difference (Question 6)

Determining an individual's total based on an excess quantity; Ali and Steve share sweets in the ratio $2 : 7$ where Steve gets $30$ more sweets than Ali ($5\text{ parts}$ difference), giving $6\text{ sweets}$ per part and a total of $42\text{ sweets}$ for Steve.

Recipe Ingredient Proportion (Question 7)

Scaling ingredients proportionally from a fixed quantity; Dave mixes flour, butter, and sugar in the ratio $6 : 4 : 1$, so using $160\text{ grams}$ of butter ($4\text{ parts}$ at $40\text{ grams}$ per part) requires $240\text{ grams}$ of flour and $40\text{ grams}$ of sugar.

Fractional Redistribution of Shares (Question 8)

Determining a combined fractional share received from multiple portions; Alvin and Simon share $£540$ in the ratio $4 : 5$ ($£240$ and $£300$), giving Theo half of Alvin's share ($£120$) and one-tenth of Simon's share ($£30$) for a total of $£150$, which simplifies to $\frac{5}{18}$ of the $£540$.

Subsegment Length Determination (Question 9)

Calculating total line length from a multiple of a subsegment; on straight line $ABC$, the length of $BC$ is four times $AB$, so if $BC = 100\text{ metres}$, then $AB = 25\text{ metres}$ and the total length $AC$ is $125\text{ metres}$.

Mixture Feasibility Analysis (Question 10)

Assessing whether available stocks meet proportional mixture requirements; producing $750\text{ ml}$ of orange paint in the ratio $5 : 4 : 1$ requires $375\text{ ml}$ red, $300\text{ ml}$ yellow, and $75\text{ ml}$ white, meaning Bob has enough paint since his supplies ($400\text{ ml}$, $300\text{ ml}$, and $200\text{ ml}$) meet or exceed each requirement.

Limiting Component Ratio (Question 11)

The ingredient that constrains the maximum total volume produced in a fixed ratio; mixing $2\text{ parts}$ fruit juice with $5\text{ parts}$ sparkling water from $180\text{ ml}$ juice and $400\text{ ml}$ water is restricted by water to $80\text{ ml}$ per part, resulting in a maximum drink volume of $560\text{ ml}$.

Probability from Ratios (Question 12)

Deducing missing probabilities using a ratio of remaining outcomes; with $P(\text{Red}) = 0.35$, the remaining probability of $0.65$ divided between blue and white counters in the ratio $2 : 3$ gives $P(\text{Blue}) = 0.26$ and $P(\text{White}) = 0.39$.

Compound Three-Way Ratio (Question 13)

Combining proportional statements into a unified ratio; Al and Tom share in the ratio $5 : 4$ and Joe gets $1.5$ times Tom's amount ($6\text{ parts}$), forming the ratio $5 : 4 : 6$, which divides $€3000$ into $15\text{ parts}$ ($€200$ per part) so Tom receives $€800$.

Internal Transfer Between Ratios (Question 14)

Calculating the quantity transferred between two parties while total count remains constant; Harry and Gary have $300\text{ stickers}$ originally in ratio $7 : 3$ ($210$ to $90$) and shift to ratio $8 : 7$ ($160$ to $140$), requiring Harry to give Gary $50\text{ stickers}$.

Pack Size to Item Count Ratio (Question 15)

Solving total items when pack sizes and pack ratios differ; small packs contain $4\text{ bars}$ and large packs contain $9\text{ bars}$, sold in a pack ratio of $5 : 2$ ($38\text{ bars}$ per set), meaning $190\text{ total bars}$ corresponds to $5\text{ sets}$ and $100\text{ small chocolate bars}$ sold.