The document outlines the learning objectives for mastering fractions and decimals in mathematics for grade 8, including recognizing equivalent fractions and estimating mixed numbers. It explains the concepts of terminating and recurring decimals with examples, emphasizing the conversion of recurring decimals. Additionally, it addresses the use of arithmetic laws and order of operations when working with decimals and fractions.

1. FRACTIONS
AND
DECIMALS
Mathematics 8

2. Learning objectives
 Recognize fractions that are equivalent to recurring decimals.
 Estimate and subtract mixed numbers, and write the answer as a mixed number in its simplest
form.
 Estimate and multiply an integer by a mixed number, and divide an integer by a proper fraction.
 Use knowledge of the laws of arithmetic and order of operations (including brackets) to simplify
calculations containing decimals or fractions
 Understand the relative size of quantities to compare and order decimals and fractions (positive
and negative), using the symbols =, , >, <,

3. Types of decimal numbers
Terminating decimals
• Some
decimals terminate which
means the decimals do not
recur, they just stop.
• For example, = 0.75.
Recurring decimals
• A decimal number that has
digit(s) that repeat forever.
Examples:
1/3 = 0.333... (the 3 repeats forever)
1/7 = 0.142857142857... ( the
"142857" repeats forever)

4. Converting recurring decimals
Convert to a recurring decimal.
• Divide 5 by 6. 5 divided by 6 is 0,
remainder 5, so carry the 5 to the tenths
column.
• 50 divided by 6 is 8, remainder 2.
• 20 divided by 6 is 3 remainder 2.
• Because the remainder is 2 again, the
digit 3 is going to recur:
0.83333…
0 . 8 3 3…..
6) 5 .0 0 0
- 0
5 0
- 4 8
2 0
- 1 8
2 0
- 1 8
2
6x8=48
6x3=18
6x3=18

5. Terminating and recurring decimals