JHS1 Mathematics · Term 1 Week 10: Fractions, Decimals and Percentages

Lesson notes

Learning Objectives

Indicator: B7.1.3.3.1 - Explain the process of multiplying a fraction (i.e. common, percent and decimal fractions up to thousandths) by a whole number and by a fraction.

By the end of the lesson, learners can:

Explain the difference between reading multiplication as “times” (whole number × fraction) and as “of” (fraction × whole number or fraction × fraction).
Multiply a whole number by a proper fraction and by a mixed number, simplifying the result to lowest terms.
Multiply a proper fraction by a whole number, interpreting the operation as “finding a fraction of” the whole number.
Multiply a common fraction by another common fraction, simplifying the product where possible.
Calculate percentages of whole numbers by converting the percentage to a common fraction or decimal, and round answers to the nearest tenth when required.

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Curriculum details

Strand: Number (Strand 1)
Sub-strand: Fractions, Decimals and Percentages (1.3)
Content standard: B7.1.3.3 - Demonstrate an understanding of the process of multiplying and dividing positive fractions and apply this in solving problems
Indicator: B7.1.3.3.1 - Explain the process of multiplying a fraction (i.e. common, percent and decimal fractions up to thousandths) by a whole number and by a fraction.
Suggested placement: Term 1, Week 10 (Week 10 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: Mathematics, Common Core Programme (JHS1-JHS3), 2023, p. 20
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g. 1. To multiply a whole number by a fraction, the multiplication is read as 'times'. For instance, 3 × 2 2 means 3 times 2 2 or 3 groups of 2 2 ;
3 3 3
i.e. 3 × (2 + 2 ) or 3 × 8 . The product can be obtained by (i) changing 3 3
all into common fraction; (ii) multiplying all numerators and denominators; (iii) simplifying the results. Find 1. 15 × 2 2. 12 × 3 . 3 8
E.g. 2. To multiply a fraction by a whole number, the multiplication is read as 'of'. for instance, 2 × 5 means 2 of 5 or i.e. 2 × 5 = 2 ×5 = 10 = 3 3 3 1 3 ×1 3
3 1 . The product can be obtained by (i) changing all into common 3
fraction; (ii) multiplying all numerators and denominators; (iii) simplifying the results. [Note: (ii) and (iii) can be alternated] Find (i) 2 × 240 (ii). 3 × 480 3 8
E.g. 3. Calculate the following (when necessary, round your answer to the nearest tenth): a. 28% of 40 b. 234% of 8 c. 3½ % of 50 d. 0.2% of 15000 e. 8.25% of 62
E.g. 4. To multiply a fraction by a fraction, the multiplication is read as 'of'. For instance, 2 × 1 means 2 of 1 or i.e. 2 × 1 = 2 ×1 = 2 = 1 . The 3 2 3 2 3 2 3 ×2 6 3
product can be obtained by (i) changing all into common fraction; (ii) multiplying all numerators and denominators; (iii) simplifying the results. [Note: (ii) and (iii) can be alternated] Find (i) 2 × 3 (ii) 3 × 5
3 5 8 6