TOPIC 2 DECIMALS (and INTRODUCTION TO FRACTIONS) WEEK 3

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Abigayle Walters
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1 TOPIC DECIMALS (and INTRODUCTION TO FRACTIONS) WEEK 3 Association between Fractions and Decimals is a fraction. It means divided by. If we divide by the result is not a whole number. It is a half of whole number. As a decimal we refer to it as 0.5. ie One half of the circle is shaded, or we can say that 0.5 or that 50% of the circle is shaded. To convert the fraction into a decimal, we divided the denominator into the numerator. 3 is a fraction. It means 3 5. The answer will not be a whole number. 5 What does 3 5 To Convert Decimal to Fractions and back again Write the decimal as a decimal fraction, then simplify: eg DECIMAL FRACTION Divide the denominator into the numerator normally. Making Equivalent Fractions This is where the numerator and the denominator are multiplied by the same number. 3 5 as an equivalent fraction, as a decimal, as a percentage. Make an equivalent fraction with a denominator of WEEK 3

2 Decimal Numbers A number like is a decimal number. It has a part which is whole numbers and another part which is part of a whole number. Hundreds Tens Units tenths Hundredths Thousandths ten thousandths decimal places after the decimal point (6 x 00) + (7 x Addition and Subtraction of Decimals Write the numbers with their place values (and the decimal point) lined up vertically. Add zeros to any empty place values. Add and subtract normally without forgetting the decimal point. For example _ Multiplying and Dividing by multiples of 0 Multiples of ten are numbers like 00 or 000. To multiply, move the decimal point to the right the same number of places as the number of zeros in the multiple of 0. Any empty place values are filled with zeros..35 x x x 0000 WEEK 3

3 To Divide, to move the decimal point to the left the same number of decimal places as zeros in the multiple of 0. Any empty place values are filled with zeros Multiplication of Other Decimals Numbers For example 3. x.7 Multiply the numbers normally ignoring the decimal point Count the number of decimal places to the right of the decimal point in both numbers. Give the final answer with that same number of decimal places to the right of the decimal point. 3 There are... decimal places to the right in both numbers. x 7 Therefore the answer is... An estimate of the answer could be... Calculate the exact answer to x As an estimate the answer could be... WEEK 3 3

4 Dividing Decimal Numbers by Whole Numbers eg Work so that place values are lined up vertically. Divide normally making sure to include the decimal point in the answer Dividing Decimals by other Decimals eg Adjust both numbers so that the divisor becomes a whole number. In this case the number 0.0 would become. That means that 0.0 has been multiplied by 00. We need to then adjust the numerator so that it is also multiplied by 00. So the sum becomes Then operate as you would for dividing a decimal number by a whole number. Don t forget the decimal point in the answer. Try Round off your answer to the nearest whole number... Round of your answer to the nearest ten... WEEK 3

5 Rounding Decimals and other Numbers Eg Round to the nearest tenth (ie one decimal place)... Rounded to the nearest hundredth it will become... Rounded to the nearest thousandth it will become... We round off numbers so that we make estimates (in our head) to operations that would otherwise take time with paper and pencil. At times we only need a quick estimate x More on Equivalent Fractions Multiply the numerator and denominator by the same number Simplifying Fractions Divide the numerator and denominator by the same factor of both numbers WEEK 3 5

6 Proper and Improper Fractions, and Mixed Numbers. Proper Fractions The numerator is smaller in value than the denominator. All the fractions that we have dealt with so far have been proper fractions. or 3 or 6 00 Mixed Numbers Where the number is a mixture of whole numbers and a part of a whole number. eg.5 can be written as or 3 Improper Fractions A fraction where the numerator is larger than the denominator. How many halves in? How many quarters in 3? Changing between Mixed numbers and Improper fractions. Multiply the whole number by the denominator and add the part number Mixed Number Improper Fraction Divide by the denominator Mixed Number Improper Fraction Mixed Number Improper Fraction WEEK 3 6

To be able to count up and down in tenths

To be able to count up and down in tenths Progression Grid: Year Year 2 Year 3 Year Year Year 6 Counting in Fractional steps To be able to count in fractions up to 0, starting from any number and using the/2 and 2/ equivalence on the number line