Skip to content
Request a demo

Grade 10 · Core Mathematics · Lesson 9 of 11

Reciprocal Methods for Rates

A Grade 10 Core Mathematics CBE lesson from the sub-strand Real Numbers. In it, learners interpret reciprocal quantities in a rate context.

Strand Numbers and AlgebraSub-strand Real NumbersLesson code 10CM-11-L940 minutes · 2 slides

KICD learning outcome (e)

Apply reciprocal of real numbers in mathematical computations.

By the end of this lesson, learners should be able to

  1. Interpret reciprocal quantities in a rate context.
  2. Solve multi-step expressions containing fraction division.
  3. Check whether the final value and units are reasonable.

Key vocabulary

Rate
A comparison of two quantities measured in related units.
A rate of three litres per minute compares volume and time.
Unit rate
A rate expressed for one unit of the second quantity.
Four kilometres in two hours gives unit rate two kilometres hourly.

Lesson preview

Slide 1 · Reciprocal Rates Exchange RolesOpening · 18 min
A gear diagram displaying the fractions ten over one and one over ten alongside labels for amount and time.
Figure 1: A gear diagram displaying the fractions ten over one and one over ten alongside labels for amount and time.

A rate written as amount per time becomes time per amount when reciprocated, provided the same quantities are exchanged. The numerical reciprocal is meaningful only when the units change with it. Use Figure 1 to discuss why the numerical reciprocal is meaningful only when the units change.

  • Read the numerator and denominator units before calculating.
  • Swapping units requires taking the numerical reciprocal.
  • A reciprocal rate answers a different practical question.
  • Estimate the result from the original rate.
Worked example. The numerical rate is five items per minute. Exchange the units and take the reciprocal: one-fifth. Attach the new unit order: minutes per item. Answer: The reciprocal rate is one-fifth minute per item..

Check question: What happens to the units of a given rate when the numerical rate is reciprocated?

  1. The numerator and denominator units exchange positions.
  2. The units remain exactly the same.
  3. Only the unit in the denominator changes.
  4. The units cancel out completely.
Show answer

The numerator and denominator units exchange positions. The reciprocal reverses both the numerical division and the quantity relationship. For example, reciprocating 'items per minute' changes the units to 'minutes per item'.

Slide 2 · Solve a Multi-Step RateCheck · 22 min
A diagram illustrating the steps to calculate a unit rate by dividing three-quarters of a tank by two-fifths of an hour.
Figure 2: A diagram illustrating the steps to calculate a unit rate by dividing three-quarters of a tank by two-fifths of an hour.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

  • Both slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 10 lessons in this sub-strand
See the school projectorWhatsApp us

All 11 lessons in Real Numbers

  1. 1Sorting Whole Numbers by StructureClassify whole numbers as odd, even, prime and composite in different situations
  2. 2Classifying Numbers in SituationsClassify whole numbers as odd, even, prime and composite in different situations
  3. 3Recognising Rational and Irrational NumbersClassify real numbers as rational and irrational in different situations
  4. 4Justifying Real-Number ClassificationsClassify real numbers as rational and irrational in different situations
  5. 5Finding Reciprocals by DivisionDetermine the reciprocal of real numbers by division
  6. 6Reciprocals with Signs and DecimalsDetermine the reciprocal of real numbers by division
  7. 7Using Tools to Find ReciprocalsDetermine the reciprocal of real numbers by use of mathematical tables and calculators
  8. 8Reciprocals in Fraction ComputationApply reciprocal of real numbers in mathematical computations
  9. 9Reciprocal Methods for RatesApply reciprocal of real numbers in mathematical computations
  10. 10Real Numbers in Daily DecisionsPromote the use of real numbers in day-to-day activities
  11. 11Communicating Real-Number SolutionsPromote the use of real numbers in day-to-day activities