Base — Grade 7 Math, what it means and where it is taught
The number being multiplied. In 53 the base is 5.
Taught in Grade 7 Math.
Where it is taught
What uses it later
This idea is needed for:
- Exponent — How many times the base is used as a factor. In 53 the exponent is 3.
- Pyramid — A base tapering to a point. V = 13 Bh.
- Common log — Base 10, usually written log with no base shown.
- Natural log — Base e ≈ 2.718, written ln.
- Change of base — logb x = log xlog b, which is how a calculator handles any base.
Practise this idea
41 questions in the course bank use Base, in Proportional Reasoning with Percents, Positive & Negative Rational Number Operations, Length and Area in 2-D Figures, Plane Sections of 3-D Figures, Volume & Surface Area of 3-D Figures, Geometric Construction. The first 8 are below; the rest are in those units.
Problem 1
A stock drops 20%. By what percent must it rise to return to its original value?
Worked answer
25
Say it started at 100; after the drop it is 80
It needs to gain 20
2080 = 0.25 = 25%
The gain is measured from the smaller number, so the percent is larger.
Problem 2
Compute (-3)2.
Worked answer
9
(-3)(-3) = 9
Same signs, positive.
Problem 3
Find the area of a rectangle 7 cm by 9 cm.
Worked answer
63
7 × 9 = 63 cm2
Problem 4
Find the area of a triangle with base 10 and height 6.
Worked answer
30
12(10)(6) = 30
Problem 5
Find the area of a parallelogram with base 12 and height 5.
Worked answer
60
12 × 5 = 60
Problem 6
A triangle has area 54 cm2 and base 12 cm. Find its height.
Worked answer
9
54 = 12(12)h = 6h
h = 9 cm
Problem 7
A triangle has its base along the full 12-unit side of a 12 × 8 rectangle, with its third vertex on the opposite side. Find its area.
Worked answer
48
Base = 12, height = 8
12(12)(8) = 48
Exactly half the rectangle — and it does not matter where along the side the apex sits.
Problem 8
A cylinder is sliced parallel to its base. What shape is the cross section?
- A rectangle
- A circle
- An oval
- A triangle
Worked answer
A circle
A circle, the same size as the base.