Practice Maths

L14 — Representing Ratios

What is a Ratio?

A ratio is a way to compare two or more quantities that are measured in the same units. We state ratios without units.

Key Terms

ratio
a comparison of two or more quantities of the same type, written using a colon (e.g. 3 : 5)
colon (:)
the symbol used to separate the parts of a ratio; read as "to" (e.g. 3 : 5 is read as "three to five")
order
in a ratio, position matters — the first number must correspond to the first quantity named in the question
part
one of the quantities being compared in a ratio (e.g. in 3 : 5, there are two parts: 3 and 5)
total
the sum of all parts in a ratio (e.g. in the ratio 3 : 5, the total is 3 + 5 = 8)
The Colon Symbol (:) In Maths, we use a colon to represent a ratio. For example, if there are 3 blue pens and 1 red pen, the ratio is written as 3 : 1.
We say this aloud as "three to one".

Important Rule: Order Matters!

The order of the numbers must match the description. If we ask for the ratio of apples to oranges, the number of apples must come first.

Worked Example

Write the ratio of 8 blue marbles to 5 red marbles.

Step 1 — Identify the two quantities: 8 blue, 5 red.

Step 2 — Write as a ratio: 8 : 5

Step 3 — Order matters: always write in the order stated in the question.

What Is a Ratio?

A ratio compares two or more quantities of the same type. Instead of saying “there are 3 red marbles and 5 blue marbles,” we write this as 3 : 5 (read as “3 to 5”). The colon (:) is the ratio symbol. Ratios are a shorthand way of showing how amounts relate to each other.

Unlike fractions, ratios don’t have to represent a part of a whole — they compare quantities to each other. For example, a recipe might call for flour and sugar in a ratio of 2 : 1, meaning you use twice as much flour as sugar.

Order Matters in a Ratio

The order of a ratio is very important. If a class has 12 girls and 8 boys, the ratio of girls to boys is 12 : 8. The ratio of boys to girls is 8 : 12. These are different ratios! Always check what order the question asks for.

If you are asked for “the ratio of red to blue,” always write red first, then blue. Getting the order wrong gives an incorrect answer even if your numbers are right.

Ratios Have No Units

When both quantities are in the same unit, the ratio has no units. For example:

  • A recipe uses 200 g of butter and 400 g of flour. The ratio of butter to flour is 200 : 400, which simplifies to 1 : 2. There are no grams in the ratio — just the numbers.
  • A map has a scale of 1 : 50 000. This means 1 cm on the map = 50 000 cm in real life. No units needed because they cancel.

Reading Ratios from Visual Contexts

Ratios often appear in pictures or diagrams. For example, if you see a group of 4 circles and 6 squares:

  • Ratio of circles to squares: 4 : 6
  • Ratio of squares to circles: 6 : 4
  • Ratio of circles to total shapes: 4 : 10

Count carefully and match the order to what the question asks.

Key tip: Ratios always need context — “3 : 5” by itself means nothing. You need to know what the 3 and 5 represent. When writing a ratio, always say what each part refers to, for example “the ratio of red to blue is 3 : 5.” In exam questions, read the wording carefully to know which quantity goes first.

Practice Questions

  1. Basic Visual Ratios Fluency

    A bag contains 5 blue marbles and 2 green marbles.

    1. What is the ratio of blue marbles to green marbles?
    2. What is the ratio of green marbles to blue marbles?
    3. What is the ratio of blue marbles to the total number of marbles?
    4. What is the ratio of green marbles to the total number of marbles?
    5. If 3 more blue marbles are added to the bag, what is the new ratio of blue to green?

  2. The Classroom Context Fluency

    In a classroom, 12 students are wearing hats and 8 students are not.

    1. Write the ratio of hats to no hats.
    2. Write the ratio of no hats to hats.
    3. Write the ratio of hat-wearers to the total number of students.
    4. Write the ratio of non-hat-wearers to the total number of students.
    5. If 4 more students arrive and all are wearing hats, write the new ratio of hats to no hats.

  3. Order Awareness Fluency

    A recipe uses 3 cups of flour and 5 cups of sugar.

    1. Write the ratio of sugar to flour.
    2. If a student writes the ratio as 3 : 5, which ingredient are they putting first?
    3. Write the ratio of flour to the total cups used in the recipe.
    4. Write the ratio of sugar to the total cups used in the recipe.
    5. If 1 more cup of sugar is added to the recipe, write the new ratio of sugar to flour.

  4. Family Ratios Fluency

    In the Smith family, there are 2 parents, 3 daughters, and 1 son.

    1. What is the ratio of parents to children?
    2. What is the ratio of daughters to the total number of people in the family?
    3. What is the ratio of sons to the total number of people in the family?
    4. What is the ratio of children to parents?
    5. What is the ratio of daughters to sons?

  5. School Uniforms Fluency

    Out of 10 students, 7 are wearing the school uniform and 3 are in casual clothes.

    1. What is the ratio of uniform to casual?
    2. What is the ratio of casual to uniform?
    3. What is the ratio of uniform wearers to the total number of students?
    4. If 2 more students arrive in uniform, write the new ratio of uniform to casual.

  6. Interpreting Symbols Understanding

    Read the following ratios and write how you would say them in words (e.g., "___ to ___"):

    1. 4 : 9
    2. 15 : 2
    3. 1 : 100
    4. Write the following as a ratio using a colon: "seven to three".

  7. Real-World Comparison Understanding

    A garden has 10 yellow flowers and 14 red flowers.

    1. Write the ratio of yellow flowers to red flowers.
    2. If 2 more yellow flowers bloom, write the new ratio of yellow to red.
    3. After the 2 new flowers bloom, write the ratio of red flowers to the total number of flowers in the garden.
    4. How many more yellow flowers would need to bloom so that the ratio of yellow to red becomes 1 : 1?

  8. Unit Awareness Understanding

    Write each of the following as a ratio. Convert to the same unit first where needed.

    1. 50 mL of cordial to 200 mL of water.
    2. 5 kg of dog food to 20 kg weight of the dog.
    3. 30 cm of ribbon to 1.2 m of ribbon. (Hint: Convert to cm.)
    4. 45 minutes of exercise compared to 3 hours of the day. (Hint: Convert to minutes.)

  9. Consolidation: Total Parts Understanding

    The ratio of boys to girls in a club is 5 : 3.

    1. How many total “parts” are there in the ratio?
    2. If there are 8 children in the club, how many are boys?
    3. If there are 40 children in the club, how many are boys?
    4. If there are 15 boys in the club, how many girls are there?

  10. The Science Experiment Problem Solving

    A student mixes red and blue food colouring in a ratio of 2 : 5 to make purple.

    1. Write the ratio of red colouring to the total colouring used.
    2. If the student uses 8 mL of red colouring, how much blue colouring is needed?
    3. A second student makes purple using 10 mL of red and 30 mL of blue. Is this the same shade of purple? Compare the ratios and explain your answer.
    4. A third student wants to make exactly 35 mL of purple using the original ratio of 2 : 5. How much red and how much blue colouring are needed?
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