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a Numbers which can be expressed in the form , b where a and b are integers and b is not equal to 0 are called rational numbers. Rational numbers may appear in different forms but all of them can be written as a fraction in the form a over b. 0.9 0.66 Number 2 1 4 5 a Form b 2 1 21 5 9 10 2 3 Rational 0 1 1 8 4 1 2 1 The number line can be used to compare numbers with exactly one of the following being true: a<b a would be to the left of b. a=b They are at the same position and have the same value. a>b a is to the right of b. While using the number line works well for many numbers and some familiar fractions, how else can we compare rational numbers? • A Fraction consists of two numbers separated by a line. • The top number (or numerator) tells how many fractional pieces there are. In the fraction 3/8, we have three pieces. • The denominator of a fraction tells how many pieces an object was divided into. The fraction 3/8 tells us that the whole object was divided into 8 pieces. • If the denominators of two fractions are the same, the fraction with the largest numerator is the larger fraction. • For example 5/8 is larger than 3/8 because all of the pieces are the same and five pieces are more than three pieces. • If the numerators of two fractions are the same, the fraction with the smaller denominator is the larger fraction. • For example 5/8 is larger than 5/16 because each fraction says there are five pieces. If an object is divided into 8 pieces, each piece will be larger than if the object were split into 16 pieces. Therefore five larger pieces are more than five smaller pieces a c For any rational numbers and , with b > 0 and d > 0 b d 1. a c if , then ad bc , and b d 2. a c if ad bc , then . b d 3 2 Compare and . 8 5 Set up the problem as follows: 3 < 2 ____ 8 5 Multiply the numerator on the left by the denominator on 15 the right. Multiply the numerator on the right by the denominator on the left. 16 15 < 16 therefore, 3/8 is less than 2/5. • Just convert each fraction to decimals, and then compare the decimals. • For Example: Which is bigger: 3/8 or 5/12 ? • You need to convert each fraction to a decimal. You can do this using your calculator (3÷8 and 5÷12), • 3/8 = 0.375, and 5/12 = 0.4166... • So, 5/12 > 3/8 • Use > or < or = to make the statement true • 1) 7 8 • 3) 6 8 5 8 5 7 3 7 3 13 3 4) 5 6 9 2)