Write a ratio from counts

Start a set of 8

1 OF 10

Ovals: \(\displaystyle 11\)
Hexagons: \(\displaystyle 7\)

Write hexagons to ovals using the actual counts

Count the whole display

A display contains only the listed cards

The table includes every recorded item once, in exactly one category

Category	Count (cards)
Landscape	\(17\)
Portrait	\(12\)
Square	\(6\)

Write Landscape to all cards using the actual counts

For all cards, add the included categories

17 + 12 + 6 = 35

The first term uses Landscape: \(17\)

The second term uses all cards: \(35\)

Write the actual counts in the requested order

17 : 35

Reorder three counts

A collection contains only the listed decorations

The table includes every recorded item once, in exactly one category

Category	Count (items)
Patches	\(13\)
Badges	\(8\)
Ribbons	\(5\)

3 marks

Write badges to ribbons to patches using the actual counts

first term second term third term

Choose the requested groups

The tray contains only these tiles

The table includes every recorded item once, in exactly one category

Category	Count (tiles)
Triangles	\(8\)
Squares	\(5\)
Hexagons	\(10\)
Circles	\(6\)

2 marks

Write triangles and squares combined to all non-circle tiles, using actual counts

first term second term

Read two recorded counts

A community market classified each stall by its main product

The table includes every recorded item once, in exactly one category

Category	Count (stalls)
Baked goods	\(4\)
Fresh produce	\(10\)

2 marks

What is the ratio of Baked goods to Fresh produce? Use the actual counts; do not simplify

first term second term

Compare a part with the whole

A hardware store counted its stock of fasteners

The table includes every recorded item once, in exactly one category

Category	Count (boxes)
Hex bolts	\(16\)
Wing nuts	\(5\)
Phillips-head screws	\(17\)

2 marks

Express Wing nuts to the total number of boxes counted as a ratio, in that order. Use the actual counts; do not simplify

first term second term

Compare a category with a selected whole

A school counted the vehicles in the staff car park one morning

The table includes every recorded item once, in exactly one category

Category	Count (vehicles)
Car	\(19\)
Motorbike	\(11\)
Ute	\(3\)
Bicycle	\(9\)

2 marks

Write the ratio of Motorbike to Car, Motorbike and Ute combined. Use the actual counts; do not simplify

first term second term

Year 9, Chapter 1, 3 difficulty levels, Calculator allowedBuild a worksheet

Write a ratio from counts

Identify each requested category or group, then write its count in the named order

Part to part Use only the two named parts
Part to whole The whole includes the part itself
Selected whole Include exactly the categories named. Do not automatically use every item in the table

Common mistakes

Using the other part as the whole

✕\(\displaystyle \text{Drummers to all}=9:14\)✓\(\displaystyle \text{Drummers to all}=9:23\)

There are 9 drummers and 14 other members. Add them to get 23 members in all

Difficulty levels

introWrite a ratio of two recorded counts

standardReorder three categories or compare a part with the whole

challengeCompare one category or a combined part with a selected whole

Questions about this topic

Should the largest number go first?+

No. The question sets the order

Should I always use the total of the table?+

No. A selected whole may leave out one or more categories

Can I use a calculator?+

A calculator is allowed unless a question is marked no calculator

Which year level and chapter is this?+

Year 9 Mathematics, chapter 1: Number and financial mathematics

In this chapter

Evaluate an integer expression Factors, multiples, HCF, LCM and primes Round to decimal places or significant figures Estimate an expression using rounded inputs Convert between fractions, mixed numbers and decimals Classify real numbers and compare exact values Add, subtract, multiply and divide fractions and mixed numbers Write a ratio from counts Write ratios in simplest form Complete equivalent ratios Use a constant rate Divide a quantity in a given ratio Decide which option is the better value Convert between fractions, decimals and percentages Find a percentage of a quantity Express one quantity as a percentage of another 1F Percentages and money: Find the original amount from a percentage Increase or decrease a quantity by a percentage Find percentage change Percentage error against a reference value 1G Percentage change and percentage error: Find the original amount from a percentage Profit, mark-up and discount Income and tax Simple interest Compound interest (optional extension)