Order Rational Numbers on a Number Line
Compare the supplied signed values by locating them relative to zero and each other.
About 20 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: Compare −3/4 and −1/2.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Rational numbers include fractions and terminating decimals, positive or negative. On an increasing horizontal line, farther right means greater. For negative values, a larger distance from zero places the value farther left. Rewrite fractions as comparable values when helpful without losing their signs.
Compare the supplied signed values by locating them relative to zero and each other. Use equivalent fractions or decimals to clarify their positions. Select the greater number and explain with left-right order rather than magnitude alone.
Use number-line position for greater and less. For negative values, a larger absolute value can mean a smaller signed value. Use a common denominator or decimal model and keep every sign visible.
- Use a common denominator or decimal model and keep every sign visible.
- Work through the supplied example and label what each number or attribute represents.
- Compare the supplied signed values by locating them relative to zero and each other.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
Compare −3/4 and −1/2. Their decimal forms are −0.75 and −0.5. Minus one half lies to the right, so −1/2 is greater. Although three fourths is the larger positive magnitude, its negative location is farther left. Use number-line position for greater and less. For negative values, a larger absolute value can mean a smaller signed value. Use a common denominator or decimal model and keep every sign visible.
Check your reasoning
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Helpful tips
- Use number-line position for greater and less.
- For negative values, a larger absolute value can mean a smaller signed value.
See the answer and explanation
-0.4
Minus 0.4 is nearer zero on the right of minus 0.7.
Take it further
Order −1,−0.6,0,0.4 from least to greatest. Expected: that same order.
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Check the subject sources
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