Reciprocal — Grade 7 Accelerated, what it means and where it is taught
The flip of a fraction. The reciprocal of 35 is 53.
Taught in Grade 7 Accelerated.
Where it is taught
What uses it later
This idea is needed for:
- Perpendicular — Slopes multiply to -1 — negative reciprocals.
- Frequency — How many full cycles fit in a given interval. The reciprocal of the period.
Practise this idea
9 questions in the course bank use Reciprocal, in Slope & the Forms of a Line, Right Triangle Trigonometry, Rational Expressions & Equations, Trigonometric Identities & Equations, Dividing Fractions, One-Step Equations. The first 8 are below; the rest are in those units.
Problem 1
A line perpendicular to y = 4x + 1 has what slope?
Worked answer
-1/4
Reciprocal of 4 is 14
Negated: -14
Problem 2
A line perpendicular to y = -25x + 3 has what slope?
Worked answer
5/2
Reciprocal: -52
Negated: 52
Problem 3
sin-1(0.5) means
- the angle whose sine is 0.5
- 1sin 0.5
- sin(0.5) doubled
- half of sin
Worked answer
the angle whose sine is 0.5
It undoes the sine.
sin-1(0.5) = 30°.
Problem 4
Simplify x3 ÷ x6.
Worked answer
2
x3 · 6x
=63=2
Keep the original domain restriction: x≠0.
Problem 5
If sinθ=14, find cscθ.
Worked answer
4
11/4=4
Problem 6
If cosθ=12, find secθ.
Worked answer
2
11/2=2
Problem 7
Give the reciprocal of 35.
Worked answer
5/3
53
Problem 8
Give the reciprocal of 4.
Worked answer
1/4
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