Math 8 Comparing and Ordering

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Presentation transcript:

Math 8 Comparing and Ordering -1/3 -0.08 Math 8 Comparing and Ordering Rational Numbers

Comping Numbers Decimals and Fractions There are 4 simple principles you can use to compare and order fractions and decimal numbers: Use points of reference Use common denominators Use common numerators Convert to fractions or decimal numbers.

Reference Points When we speak of reference points (benchmarks) be familiar with common fractions and their decimal equivalents as good reference points: 1/8 = 0.125 1/3 = 0.3333… 1/5 = 0.20 3/4 = 0.75 1/4 = 0.25 2/3 =0.6666… 1/2 = 0.5 1/10 = 0.1

A special pattern with denominator of « 9 » _ __ ___ 1/9 = 0.1 1/99 = 0.01 1/999 = 0.001 _ __ ___ 2/9 = 0.2 2/99 = 0.02 31/999 = 0.031 _ __ 3/9 = 0.3 3/99 = 0.03 _ __ 4/9 = 0.4 11/99 = 0.11 etc…… __ 12/99 = 0.12

What is the decimal value of this fraction? 1.25

What is the decimal value of this fraction? -2,333…

What is the decimal value of this fraction? 8.75

What is the decimal value of this fraction? -3.666…

What fraction is greater? If the 2 fractions are converted to decimals, it’s easy… 2/3 = 0.666… 3/4 = 0.75 Then 3/4 is greater.

What fraction is greater? Reference Points! 3/4 = 0.75 9/10 is closer to 1 So 9/10 is greater.

What fraction is greater? We can use ½ as a reference point. 3/7 < 1/2 5/8 > 1/2 So 5/8 is greater.

Comparing negative numbers If the numbers are negative, the numbers further left are smaller than numbers to the right on a number line. -0.5 is closer to zero so it is greater Example: What number is greater? -0.56 ou -0.5?

What number is greater? - 3/4 is closer to zero so it is greater +1 -1

Comparing with common denominators. +1 -1 If you compare - 4/7 and - 3/7 you see - 3/7 is closer to zero so it is greater.

Comparing with common denominators. You can also change the fraction to have common denominators to compare: Example: What fraction is greater?

What fraction is greater? When you find equivalent fractions - 7/21 is closer to zero so it is greater. +1 -1

Use common numerators to compare fractions. If the numerators are the same, the fraction with the smaller denominator is the greater absolute value.

What fraction is greater?

What fraction is greater? +1 -1 6/8 is greater because it is closer to zero

Compare fractions by converting to decimal numbers Example: What fraction is greater? So 1/8 is greater.

What fraction is greater? So, 1/13 is the greater fraction.

Place the row of numbers in order from least to greatest:

Place the row of numbers in order from least to greatest: