Ratio Problem Solving Flashcards

All 14 cards in this deck

How do you express one quantity as a fraction of another?
e.g. express 3 kg as a fraction of 12 kg

Write the first quantity over the second, then simplify.
$\frac{3}{12} = \frac{1}{4}$

When is one quantity expressed as a fraction of another greater than 1?

When the first quantity is bigger than the second.
e.g. 15 m as a fraction of 10 m is $\frac{15}{10} = \frac{3}{2}$

$\frac{2}{5}$ of a class are boys and the rest are girls. What is the ratio boys : girls?

$2:3$
2 parts out of 5 are boys, so the other 3 parts are girls.

What are the steps to write a ratio from a percentage?
e.g. 20% of an area is land and the rest is water — find land : water

1. Find the other percentage: $100 - 20 = 80\%$
2. Write as a ratio: $20:80$
3. Simplify: $1:4$

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 match — LCM of 5 and 4 is 20
2. Scale each ratio: $A:B = 8:20$ and $B:C = 20:5$
3. Combine: $A:B:C = 8:20:5$

What are the steps to solve a ratio problem when you are given the difference between two shares instead of the total?
e.g. $R:M:I = 4:7:15$ and Ibrahim has 24 more stickers than Matilda

1. Difference in parts: $15 - 7 = 8$ parts
2. Value of one part: $24 \div 8 = 3$
3. Multiply each person's parts by 3: $12:21:45$

True or false? If the same number of counters is added to both colours in a bag where red : blue $= 3:5$, the ratio is still $3:5$.

False. Adding the same amount to each part changes the ratio; only multiplying both parts by the same number gives an equivalent ratio.

True or false? The greatest number of batches of a recipe you can make is decided by the ingredient you have the smallest amount of.

False. It is decided by the ingredient that gives the fewest batches when compared with the amount the recipe needs.

What are the steps to find the dimensions of a rectangle from a ratio and its perimeter?
e.g. length : width $= 3:1$ and the perimeter is 32 cm

1. Perimeter in parts: $3 + 1 + 3 + 1 = 8$ parts
2. One part: $32 \div 8 = 4$ cm
3. Length $= 3 \times 4 = 12$ cm, width $= 4$ cm

True or false? If there are twice as many blue cubes as yellow cubes, then blue : yellow $= 2:1$.

True.
"Twice as many blue" means for every 1 yellow there are 2 blue, so blue : yellow $= 2:1$.

How do you find what percentage of the whole each part of a ratio is?

e.g. the ratio $3:1$

Write each part as a fraction of the total, then convert to a percentage.

$3:1$ gives $\frac{3}{4} = 75\%$ and $\frac{1}{4} = 25\%$.

True or false? If 20% of an area is land and the rest is water, then land : water $= 20 : 100$.

False. The water is $100\% - 20\% = 80\%$, so land : water $= 20 : 80$ (or $1:4$).

Given $y = 0.4x$, what is the ratio $y : x$ in its simplest form?

$2 : 5$

$0.4 : 1 = 4 : 10 = 2 : 5$.

What are the steps to find a ratio when the quantities are linked by equations?

e.g. $n = 2m$ and $p = 5n$ — find $m : p$

1. Choose the simplest value for the first quantity: $m = 1$.
2. Substitute through the equations: $n = 2$, so $p = 5 \times 2 = 10$.
3. Write the ratio asked for: $m : p = 1 : 10$.