Problem Solving with Ratios Flashcards

All 13 cards in this deck

What fraction of the whole does each part of a ratio represent?
e.g. $3:5$

Each part over the total number of parts.
e.g. $\frac{3}{8}$ and $\frac{5}{8}$

True or false? In the ratio $1:4$, the first part is $\frac{1}{4}$ of the whole.

False. It is $\frac{1}{5}$ of the whole, because there are $1+4=5$ parts altogether.

True or false? If 30% of a class are boys, then boys : girls $= 3 : 10$.

False. The percentages compare to the whole, so boys : girls $= 30:70 = 3:7$.

Two quantities are in the fixed ratio $x : y = 2 : 3$. How do you write $x$ in terms of $y$?

$x = \frac{2}{3}y$ — the first part over the second part.

Abby : Ben $= 2 : 7$ and Chloe gets 1.5 times the amount Abby gets. What parts do you use for Abby : Ben : Chloe?

$2 : 7 : 3$, since $1.5 \times 2 = 3$.

What are the steps to find $A:B$ when a fraction of $A$ equals a fraction of $B$?
e.g. $\frac{2}{3}$ of $A$ $=$ $\frac{1}{2}$ of $B$

1. Write the equation: $\frac{2}{3}A = \frac{1}{2}B$
2. Rearrange to a fraction: $\frac{A}{B} = \frac{1/2}{2/3} = \frac{3}{4}$
3. Write as a ratio: $A:B = 3:4$

What are the steps to combine $A:B$ and $B:C$ into a single ratio $A:B:C$?
e.g. $A:B = 2:5$ and $B:C = 4:1$

1. Make the $B$ parts equal, using their LCM: $B = 20$
2. Scale each ratio: $2:5 \to 8:20$ and $4:1 \to 20:5$
3. Write the three-part ratio: $A:B:C = 8:20:5$

Given a combined three-part ratio in its simplest whole-number form, what is the smallest possible total number of items?
e.g. $A:B:C = 8:20:5$

The sum of the parts: $8+20+5 = 33$.
Every possible total is a multiple of this.

How do you find the greatest possible number of one type of item when a combined ratio is known and the total must be less than 100?
e.g. $A:B:C = 8:20:5$

Use the largest whole-number multiplier $k$ with $k \times$ (total parts) $< 100$: $33 \times 3 = 99$, so greatest $C = 5 \times 3 = 15$.

True or false? If $B$ lies on the line $AC$ and $AB:BC = 1:2$, then $AB:AC = 1:3$.

True. $AC = AB + BC$, so the whole line is $1+2 = 3$ parts.

What are the steps to find how many items are moved when a ratio changes but the total stays the same?
e.g. 240 stamps shared $3:7$, then $3:5$

1. Share using the first ratio: $240 \div 10 \times 3 = 72$
2. Share using the second ratio: $240 \div 8 \times 3 = 90$
3. Subtract the two amounts: $90 - 72 = 18$ stamps moved

What are the steps to find the fraction of all the counters that are red and square?

e.g. red : blue $= 3:2$ and $\frac{1}{3}$ of the red counters are square

1. Red as a fraction of the whole: $\frac{3}{5}$
2. Multiply by the fraction of the red ones that are square: $\frac{1}{3}\times\frac{3}{5}$
3. Red squares $= \frac{1}{5}$ of all the counters

In a two-way ratio problem (two properties at once), what total number of items should you choose so all the working stays in whole numbers?

e.g. red : blue $= 3:2$ and $\frac{1}{4}$ of the red counters are square

A common multiple of the total number of parts and the fraction denominators.

e.g. take 20 counters: 12 red, 8 blue, and 3 red squares.