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JSS1: MATHEMATICS - 1ST TERM

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  1. Whole Numbers I | Week 1
    3Topics
    |
    1 Quiz
  2. Whole Numbers II | Week 2
    1Topic
    |
    1 Quiz
  3. Counting in Base Two | Week 3
    4Topics
    |
    1 Quiz
  4. Arithmetic Operations | Week 4
    3Topics
    |
    1 Quiz
  5. Lowest Common Multiple (LCM) | Week 5
    1Topic
    |
    1 Quiz
  6. Highest Common Factor | Week 6
    1Topic
    |
    1 Quiz
  7. Fraction | Week 7
    7Topics
    |
    1 Quiz
  8. Basic Operations with Fractions I | Week 8
    3Topics
    |
    1 Quiz
  9. Basic Operations with Fractions II | Week 9
    1Topic
    |
    1 Quiz
  10. Directed Numbers | Week 10
    3Topics
    |
    1 Quiz
  11. Estimation and Approximation I | Week 11
    3Topics
    |
    1 Quiz
  12. Estimation and Approximation II | Week 12
    6Topics
    |
    1 Quiz
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Multiplication of Fractions:

To multiply fractions, you need to:

1. multiply the denominators and

2. reduce the result to its lowest value, if necessary.

Example 1

\(\frac{3 }{4}\: \times \: \frac{5 }{6} \\ = \frac{3 \: \times \: 5}{4 \: \times \: 6} \\ = \frac{15}{24} \)

= \( \frac{5}{8}\)

Example 2

i. \(\frac{2 }{7}\: \times \: \frac{4}{5} \)

Solution

\(\frac{2 }{7}\: \times \: \frac{4 }{5}\\ = \frac{2 \: \times \: 4}{7 \: \times \: 5} \)

= \( \frac{8}{35}\)

ii. \(\scriptsize 3 \normalsize \frac{5 }{17}\: \times \: \scriptsize 2 \normalsize \frac{5 }{6} \: \times \: \scriptsize 1 \normalsize \frac{4}{8}\)

Solution

= \(\frac{56 }{17}\: \times \: \frac{17}{6} \: \times \: \frac{12}{8} \\ = \scriptsize 7 \: \times \: 2 \\ = \scriptsize 14 \)

Division of Fractions:

In whole numbers, if we say 9 divided by 4.

It means or we write  9  ÷   4  or   9/4

Similarly 7 divided by  2/3 means   7   ÷  2/3

Or  \( \frac{7}{\frac{2}{3}} \)

To make the denominator equal to 1, multiply both the numerator and denominator by  3/2 .

i.e \( \frac{7 \: \times \: \frac{3}{2}}{\frac{2}{3} \: \times \: \frac{3}{2}} \\ = \frac{7 \: \times \: \frac{3}{2}}{1} \)

= \(\scriptsize 7 \: \times \: \normalsize \frac{3}{2} \)

Therfore, \(\scriptsize = 7 \: \div \: \normalsize \frac{2}{3} \\ \scriptsize = 7 \: \times \: \normalsize \frac{3}{2} \)

Notice that the sign  \( \scriptsize \div\) (division) changes to \( \scriptsize \times\)  (multiplication) and 2/3 is inverted (i.e. turned upside down)  to  3/2.

Thus, 3/2  is called the inverse or the reciprocal of 2/3.

Hence, to divide by a fraction, simply multiply by its inverse (or reciprocal).

Example 3

i. \(\frac{3}{7}\: \div \: \frac{2}{5} \)

Solution

\(\frac{3}{7}\: \div \: \frac{2}{5} \\ = \frac{3}{7}\: \times \: \frac{5}{2}\)

Did you notice that the sign changed to \( \scriptsize \times\) and \(\frac{2}{5}\) changed to \(\frac{5}{2}\)

We then Multiply

\(\frac{3 \: \times \: 5}{7\: \times \: 2}\\ = \frac{15}{14}\)

=\(\scriptsize 1 \normalsize \frac{1 }{14}\)

ii. \(\scriptsize 3 \normalsize \frac{2 }{3}\: \div \: \scriptsize 4 \normalsize \frac{3}{9} \)

Solution:

First, change these mixed fractions to importer fractions.

\(\frac{11}{3}\: \div \: \frac{39}{3} \)

\(\frac{11}{3}\: \times \: \frac{3}{39} = \frac{11}{39} \)

iii. \(\frac{15}{20} \scriptsize \: \div \: 5 \)

Solution:

This example illustrates how to divide a fraction by a whole number

\(\frac{15}{20} \scriptsize \: \div \: 5 \: means \: \normalsize \frac{15}{20}\scriptsize \: \div \: \normalsize \frac{5}{1}\)

This, \(\frac{15}{20} \scriptsize \: \div \: \normalsize \frac{5}{1} \\ = \frac{15}{20} \scriptsize \: \times \: \normalsize \frac{1}{5} \\ = \frac{3 \: \times \: 1}{20 \: \times \: 1}\\ = \frac{3}{20}\)

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