Grade 10 · Core Mathematics · Lesson 5 of 11

Finding Reciprocals by Division

A Grade 10 Core Mathematics CBE lesson from the sub-strand Real Numbers. In it, learners define reciprocal as the multiplicative inverse of a nonzero number.

Strand Numbers and AlgebraSub-strand Real NumbersLesson code 10CM-11-L540 minutes · 2 slides

KICD learning outcome (c)

Determine the reciprocal of real numbers by division.

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

Define reciprocal as the multiplicative inverse of a nonzero number.
Calculate reciprocals of integers and positive fractions by division.
Check an answer by multiplying the number and its reciprocal.

Key vocabulary

Reciprocal: A nonzero number that multiplies with another to make one.; The reciprocal of eight is one-eighth because their product is one.
Inverse: A value that reverses a mathematical operation or relationship.; The multiplicative inverse of a number is its reciprocal.

Lesson preview

Slide 1 · Reciprocal Means Product OneOpening · 18 min

Figure 1: A visual model demonstrating how nonzero input numbers are converted into reciprocal fractions, verified by multiplication.

Definition: The reciprocal of a nonzero real number is the value that produces one when multiplied by the original. Division gives it directly: reciprocal of x equals 1 divided by x. Study Figure 1 to see how multiplying a number by its reciprocal always equals one.

Only nonzero real numbers have multiplicative reciprocals.
One is its own reciprocal because one times one equals one exactly.
Reciprocal language describes multiplication relationships, not addition.
Always preserve the original number while checking the product.

Worked example. Apply one divided by five. Write the result as one-fifth. Check by multiplying five by one-fifth. Answer: The reciprocal of five is one-fifth, and their product is one..

Check question: What is the reciprocal of $1$ ?

$1$
$0$
$- 1$
Undefined

Show answer

$1$ . The reciprocal of a nonzero number is $1$ divided by that number. Therefore, the reciprocal of $1$ is $1 \div 1 = 1$ . You can verify this because $1 \times 1 = 1$ .

Slide 2 · Division Makes the Flip VisibleModel · 22 min

Figure 2: A conveyor belt diagram illustrating how dividing one by a fraction flips the numerator and denominator.

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

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