How to write a ratio in math

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A ratio compares two quantities by division. The order matters: the ratio of red tiles to blue tiles is different from the ratio of blue tiles to red tiles unless the two numbers are equal.

Ratios can be written with words, a colon, or a fraction. For example, $6$ wins to $9$ losses can be written as $6$ to $9$, $6:9$, or $\frac{6}{9}$. All three forms describe the same comparison.

To write a ratio clearly, identify the two quantities, put them in the requested order, make the units match when needed, and simplify by dividing each term by the greatest common factor.

For example, the ratio of $18$ minutes to $1$ hour is not $18:1$, because the units differ. Change $1$ hour to $60$ minutes, then simplify $18:60$ to $3:10$.

Writing Ratios

Think of this lesson as more than a rule to memorize. Writing Ratios is about comparisons, scaling, and equal ratios. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.

A ratio compares quantities, and a proportion says two ratios are equal. Cross products help because $\frac{a}{b}=\frac{c}{d}$ implies $ad=bc$.

Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.

Read what is given and what is being asked.
Choose the rule that connects them.
Substitute carefully and simplify in small steps.
Check the final answer against the original question.

A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.

Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.

When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.

On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.

Free printable Worksheets

Exercises for Writing Ratios

1) Write the ratio of $8$ red tiles to $12$ blue tiles in colon form.

2) Write the ratio of $9$ correct answers to $15$ questions as a fraction in simplest form.

3) A class has $14$ girls and $10$ boys. Write the ratio of boys to girls in simplest form.

4) Write the ratio of $18$ minutes to $1$ hour in simplest form.

5) A recipe uses $3$ cups of flour and $2$ cups of sugar. Write the ratio of flour to total cups.

6) A bag has $6$ green marbles, $9$ yellow marbles, and $15$ purple marbles. Write the ratio of green marbles to all marbles.

7) A car travels $150$ miles on $5$ gallons of gas. Write the unit rate as miles per gallon.

8) A store charges $\$24$ for $6$ notebooks. Write the unit price as dollars per notebook.

9) Write the ratio $0.75$ meters to $1.5$ meters in simplest form.

10) A map scale says $2$ inches represents $25$ miles. Write the ratio of inches to miles.

11) In a survey, $32$ students prefer soccer and $48$ prefer basketball. Write soccer to basketball in simplest form.

12) A mixture has $250$ milliliters of juice and $750$ milliliters of water. Write juice to water in simplest form.

13) A team wins $12$ games and loses $8$ games. Write the ratio of wins to total games.

14) A rectangle is $18$ centimeters wide and $30$ centimeters long. Write width to perimeter in simplest form.

15) A jar has pennies, nickels, and dimes in the ratio $4:3:2$. Write the ratio of nickels to all coins.

16) A printer makes $84$ pages in $7$ minutes. Write the unit rate as pages per minute.

17) A trail rises $450$ feet over $1.5$ miles. Write the rate in feet per mile.

18) A punch recipe uses lemon juice, tea, and water in amounts $1.5$, $2.5$, and $6$ cups. Write lemon juice to total punch in simplest whole-number form.

19) A scale drawing uses $3.2$ centimeters for an actual length of $4$ meters. Write drawing length to actual length in centimeters.

20) A school has $126$ freshmen, $98$ sophomores, and $56$ juniors in an activity. Write freshmen to non-freshmen in simplest form.

Answers

1) There are $8$ red tiles and $12$ blue tiles, so write red to blue as $8:12$. Simplify by dividing both numbers by $4$: $8 \div 4 = 2$ and $12 \div 4 = 3$. The ratio is $\color{red}{2:3}$.

2) Use correct answers over total questions: $\frac{9}{15}$. The greatest common factor is $3$, so $\frac{9 \div 3}{15 \div 3}=\frac{3}{5}$. The ratio is $\color{red}{\frac{3}{5}}$.

3) The order is boys to girls, so start with $10:14$. Divide both terms by $2$: $10 \div 2 = 5$ and $14 \div 2 = 7$. The ratio is $\color{red}{5:7}$.

4) Use the same units first: $1$ hour is $60$ minutes. The ratio is $18:60$. Divide both terms by $6$: $18 \div 6 = 3$, $60 \div 6 = 10$. The ratio is $\color{red}{3:10}$.

5) The total cups are $3+2=5$. Flour to total is $3:5$. Since $3$ and $5$ have no common factor greater than $1$, the ratio is $\color{red}{3:5}$.

6) First find the total: $6+9+15=30$. Green to total is $6:30$. Divide by $6$: $6 \div 6 = 1$, $30 \div 6 = 5$. The ratio is $\color{red}{1:5}$.

7) Miles per gallon means miles divided by gallons: $150 \div 5 = 30$. The ratio $150:5$ becomes $30:1$. The unit rate is $\color{red}{30}$ miles per gallon.

8) Dollars per notebook means $24 \div 6$. Since $24 \div 6 = 4$, the ratio $24:6$ becomes $4:1$. The unit price is $\color{red}{\$4}$ per notebook.

9) Both terms are already in meters. Clear decimals by multiplying by $100$: $0.75:1.5 = 75:150$. Divide both terms by $75$: $75 \div 75 = 1$, $150 \div 75 = 2$. The ratio is $\color{red}{1:2}$.

10) The order is inches to miles, so write $2:25$. The numbers share no common factor greater than $1$. The ratio is $\color{red}{2:25}$.

11) Start with $32:48$. The greatest common factor is $16$. Divide both terms: $32 \div 16 = 2$, $48 \div 16 = 3$. The ratio is $\color{red}{2:3}$.

12) The ratio is $250:750$. Divide both terms by $250$: $250 \div 250 = 1$, $750 \div 250 = 3$. The ratio is $\color{red}{1:3}$.

13) Total games are $12+8=20$. Wins to total is $12:20$. Divide by $4$: $12 \div 4 = 3$, $20 \div 4 = 5$. The ratio is $\color{red}{3:5}$.

14) The perimeter is $2(18+30)=96$ centimeters. Width to perimeter is $18:96$. Divide by $6$: $18 \div 6 = 3$, $96 \div 6 = 16$. The ratio is $\color{red}{3:16}$.

15) The parts add to $4+3+2=9$. Nickels represent $3$ of the $9$ total parts, so nickels to all coins is $3:9$. Divide by $3$ to get $\color{red}{1:3}$.

16) Pages per minute means $84 \div 7$. Since $84 \div 7 = 12$, the ratio $84:7$ becomes $12:1$. The unit rate is $\color{red}{12}$ pages per minute.

17) Feet per mile means divide feet by miles: $450 \div 1.5 = 300$. The ratio $450:1.5$ becomes $300:1$. The rate is $\color{red}{300}$ feet per mile.

18) Total punch is $1.5+2.5+6=10$ cups. Lemon to total is $1.5:10$. Multiply by $2$ to clear the decimal: $3:20$. The ratio is $\color{red}{3:20}$.

19) Convert $4$ meters to $400$ centimeters. The ratio is $3.2:400$. Multiply by $10$: $32:4000$. Divide by $32$: $1:125$. The ratio is $\color{red}{1:125}$.

20) Non-freshmen are $98+56=154$. Freshmen to non-freshmen is $126:154$. The greatest common factor is $14$, so $126 \div 14 = 9$ and $154 \div 14 = 11$. The ratio is $\color{red}{9:11}$.