basic 12 and 20 P Find the GCF and LCM O D advanced 32, 68 GCF= 4 LCM= 60 GCF= 4 LCM= 544

Compare and Order Rational Numbers

A

rational number

is a number that can be expressed as a ratio of two integers written as a fraction, in which the denominator is not zero. Common fractions, terminating and repeating decimals, percents, and integers are all rational numbers.

Not all numbers are rational. The Greek letter π (pi) represents a non-repeating, non-terminating number whose first few digits are 3.14… This number is an irrational number

Comparing rational numbers To compare fractions you can find the least common denominator (LCD). The LCD is the LCM of the denominators. You can also use a number line.

Ex: 1 Use <, >, or = to compare 7 12 The LCD of the denominators 12 and 18 is 36.

8 18 7 × 3 12 × 3 8 × 2 18 × 2 = = 21 36 16 36 Since 21 36 > 16 36 , 7 12 > 8 18

Ex. 2 Use <, >, or = to compare -1 5 6 Graph each rational number on a number line.

1 Mark off equal size increments of between -2 and -1 -1 1 6 -2 -1 5 6 -1 4 6 -1 3 6 -1 2 6 -1 1 6 -1 The number line shows that -1 5 6 < -1 1 6

Ex. 3 In Mr. Huang’s class, 20% of students own i-phones. In Mrs. Trevino’s class, 5 out of 29 students own i-phones. In which class does a greater fraction of students own i-phones?

Express each number as a decimal and then compare.

20% = 0.2

5 29 = 5 ÷ 29 ≈ 0.1724

5 Since 0.2 > 0.1724, 20% > 29

Remember

1. Don’t compare apples to oranges (fractions to decimals, or decimals to percents…) , convert.

2. When comparing fractions, find an LCD.

3. When using a number line, the number to the right is greater.

4. When comparing decimals, use place value to see which is greater.

Whiteboard time Use <, >, or = to compare 4 5 and 1 5 use a number line -1 4 5 3 5 2 5 1 5 0 4 5 < 1 5

Elliot and Shanna are both soccer goalies. Elliot saves 3 goals out of 4. Shanna saves 7 goals out of 11. Who has the better average? Explain.

Elliot; 3 out of four has an average of 0.75. Shanna’s 7 out of 11 has an average of 0.64

The lengths of four insects are 0.02 inch, 1/8 inch, 0.1 inch, and 2/3 inch. List the lengths from least to greatest.

0.02, 0.1, 1/8, 2/3