Comparing and Ordering Rational Numbers

The video tutorial covers comparing and ordering rational numbers, including fractions and decimals. It introduces formal methods like finding the least common multiple and equivalent fractions, as well as shortcut methods like cross-multiplication. The tutorial also addresses comparing decimals, especially those with repeating patterns, and ordering rational numbers, including negative values. It concludes with advanced examples and emphasizes using calculators for mixed fractions and decimals.

What is the first step in the formal method of comparing rational numbers?

• Use a number line

• Convert fractions to decimals

• Cross-multiply the fractions

• Find the least common multiple of the denominators

When comparing 7/8 and 5/6 using the shortcut method, what is the result?

• Cannot be determined

• 7/8 is greater than 5/6

• 7/8 is equal to 5/6

• 7/8 is less than 5/6

How do you handle repeating patterns when comparing decimals?

• Ignore the repeating pattern

• Round to the nearest whole number

• Convert to fractions

• Compare place value by place value

What is the result of comparing 0.428571 (repeating) to 0.44?

• 0.428571 is equal to 0.44

• 0.428571 is less than 0.44

• 0.428571 is greater than 0.44

• Cannot be determined

When ordering rational numbers, which of the following is true?

• Numbers to the left on a number line are greater

• Numbers to the right on a number line are less

• Negative numbers are always greater than positive numbers

• Negative numbers are always less than positive numbers

How do you compare negative fractions using the shortcut method?

• Convert them to decimals

• Use a number line

• Cross-multiply and compare the results

• Find a common denominator

What is the result of comparing -1/8 to -3/8?

• -1/8 is greater than -3/8

• -1/8 is less than -3/8

• -1/8 is equal to -3/8

• Cannot be determined

When comparing decimals without a number line, what should you do?

• Use a calculator

• Ignore the decimal point and compare as integers

• Round to the nearest whole number

• Convert to fractions

In a problem with both fractions and decimals, what is the best approach?

• Use the original forms and compare directly

• Use a number line

• Convert everything to decimals

• Convert everything to fractions

What is the correct order from greatest to least for 3/4, 5/7, and 0.64?

• 5/7, 3/4, 0.64

• 0.64, 5/7, 3/4

• 3/4, 0.64, 5/7

• 3/4, 5/7, 0.64