Ratio — Grade 7 Accelerated, what it means and where it is taught
A comparison of two quantities, like 3 cups flour to 2 cups water.
Taught in Grade 7 Accelerated.
Where it is taught
What uses it later
This idea is needed for:
- Rate — A ratio of two different units, like miles per hour or dollars per pound.
- Proportional — Two quantities with a constant ratio: yx = k always.
- SSS similarity — All three pairs of sides in the same ratio.
- SAS similarity — Two pairs of sides in ratio with the included angles congruent.
- Equivalent ratios — Ratios naming the same relationship, like 2:3 and 4:6.
Practise this idea
29 questions in the course bank use Ratio, in Proportional Reasoning with Scale Drawings, What Is a Function?, Exponential Functions & Growth, Sequences, Explicit & Recursive, Similarity & Proportionality, Right Triangle Trigonometry. The first 8 are below; the rest are in those units.
Problem 1
Two similar figures have areas 25 cm2 and 64 cm2. The smaller has perimeter 20 cm. Find the larger perimeter.
Worked answer
32
k2 = 6425, so k = 85
Perimeter is a length, so it scales by k
20 × 85 = 32 cm
Problem 2
Is this table linear? x: 1, 2, 3, 4; y: 2, 6, 18, 54. Answer yes or no.
Worked answer
no
Differences: 4, 12, 36 — not constant
Ratios: 3, 3, 3 — constant
So it is exponential, not linear
Problem 3
Is 4, 12, 36, 108 linear or exponential?
Worked answer
exponential
12 ÷ 4 = 3
36 ÷ 12 = 3
Constant ratio, so exponential
Problem 4
Write the exponential rule for the table x: 0, 1, 2, 3 and y: 6, 18, 54, 162.
Worked answer
y = 6 * 3^x
a = 6
Ratio = 3
y = 6 · 3x
Problem 5
Classify 2, 10, 50, 250, … as arithmetic or geometric.
Worked answer
geometric
Ratio is 5 each time
So geometric
Problem 6
Two similar figures have sides in ratio 2:3. Find the ratio of their areas.
Worked answer
4:9
k = 32, so k2 = 94
Ratio 4:9
Problem 7
Two similar triangles have areas 9 and 81. Find the ratio of their sides.
Worked answer
1:3
k2 = 9
k = 3, so sides are 1:3
Problem 8
Two pairs of sides in ratio with the included angles congruent proves
- SAS similarity
- SSS similarity
- AA similarity
- congruence
Worked answer
SAS similarity
Two sides in ratio plus the angle between them.
That is SAS similarity.