Add Rational Numbers
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Warm Up
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Add Rational Numbers
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Warm Up
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Add Rational Numbers
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7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.A.1.A
Describe situations in which opposite quantities combine to make 0.
Standards for Mathematical Content
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Add Rational Numbers
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Standards for Mathematical Content
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Add Rational Numbers
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7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
Standards for Mathematical Content
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Add Rational Numbers
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7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers.
Standards for Mathematical Content
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Add Rational Numbers
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Standards for Mathematical Practice
MP1
Make sense of problems and persevere in solving them.
MP2
Reason abstractly and quantitatively.
MP3
Construct viable arguments and critique the reasoning of others.
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Add Rational Numbers
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Standards for Mathematical Practice
MP4
Model with mathematics.
MP6
Attend to precision.
MP7
Look for and make use of structure.
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Add Rational Numbers
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Students will demonstrate application of the additive inverse, and an understanding of addition of rational numbers.
Lesson Goal
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Add Rational Numbers
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Learn�Rational Numbers and Additive Inverses
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Add Rational Numbers
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Learn�Rational Numbers and Additive Inverses
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Add Rational Numbers
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Example 1�Find Additive Inverses
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Add Rational Numbers
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Example 1�Find Additive Inverses
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Add Rational Numbers
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Example 1�Find Additive Inverses
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Add Rational Numbers
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Example 1�Find Additive Inverses
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Add Rational Numbers
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Example 2�Find Additive Inverses
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Example 2�Find Additive Inverses
Think About It!
Should Annalise’s babysitting and part-time job money be represented with positive or negative numbers?
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Add Rational Numbers
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Example 2�Find Additive Inverses
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Add Rational Numbers
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Example 1�Find Additive Inverses
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Add Rational Numbers
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Example 1�Find Additive Inverses
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Add Rational Numbers
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Example 1�Find Additive Inverses
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Add Rational Numbers
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Example 1�Find Additive Inverses
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Add Rational Numbers
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Example 1�Find Additive Inverses
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Add Rational Numbers
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Example 1�Find Additive Inverses
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Example 1�Find Additive Inverses
A
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The rules that apply to adding fractions and decimals also apply to rational numbers. The rules for adding integers also apply to positive and negative rational numbers.
Use the chart to see some strategies for how to add rational numbers written in different forms.
Learn�Add Rational Numbers
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Add Rational Numbers
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Learn�Add Rational Numbers
Words | Example |
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If the fractions are decimals that terminate, use decimals or fractions to add. | |
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Add Rational Numbers
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Learn�Add Rational Numbers
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If the fractions are decimals that repeat nonzero digits, use fractions to add. | |
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Add Rational Numbers
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Learn�Add Rational Numbers
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Add Rational Numbers
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Example 3�Add Rational Numbers
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Example 3�Add Rational Numbers
Think About It!
Because the signs are different, what do you need to do to the mixed numbers before adding them?
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Example 3�Add Rational Numbers
| Rewrite the mixed numbers as improper fractions. |
| Add the numerators. Assign any negative signs to the numerator. |
| Add. |
| Simplify and rename as a mixed number. |
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Add Rational Numbers
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Example 3�Add Rational Numbers
Talk About It!
Why is it important when adding rational numbers to rewrite mixed numbers as improper fractions?
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Add Rational Numbers
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Example 3�Add Rational Numbers
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Add Rational Numbers
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Example 3�Add Rational Numbers
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Add Rational Numbers
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Example 4�Add Rational Numbers
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Add Rational Numbers
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Example 4�Add Rational Numbers
| Rewrite the mixed number as an improper fraction. |
| The LCD of 4 and 6 is 12. |
| Add the numerators. Assign any negative sign to the numerator. |
| Add and rename as a mixed number. |
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Add Rational Numbers
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Example 4�Add Rational Numbers
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Add Rational Numbers
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Example 4�Add Rational Numbers
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Add Rational Numbers
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Example 5�Add Rational Numbers
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Example 5�Add Rational Numbers
Think About It!
How would you begin evaluating this expression?
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Example 5�Add Rational Numbers
Method 1 Write both addends as decimals.
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| Simplify. |
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Example 5�Add Rational Numbers
Talk About It!
In Method 1, you wrote both addends as decimals before adding. Give an example of when Method 1 is not the best method to use. Explain your reasoning.
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Example 5�Add Rational Numbers
Method 2 Write both addends as fractions.
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Example 5�Add Rational Numbers
| Rewrite the decimal as a mixed number. |
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| Add the numerators. Assign the negative sign to the numerator. |
| Add and rename as a mixed number. |
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Add Rational Numbers
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Example 5�Add Rational Numbers
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Add Rational Numbers
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Example 5�Add Rational Numbers
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Add Rational Numbers
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When adding three or more rational numbers, use the Commutative Property to group numbers by signs or forms.
Grouping numbers with the same form can help simplify the expression.
Learn�Add Rational Numbers
| Write the expression. |
| Identify each number’s form as either a fraction or a decimal. |
| Rewrite the expression, grouping the numbers by their form. |
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Add Rational Numbers
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Talk About It!
How does grouping numbers by like forms help in simplifying an addition expression?
Learn�Add Rational Numbers
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Add Rational Numbers
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Example 6�Add Rational Numbers
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Add Rational Numbers
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Example 6�Add Rational Numbers
Think About It!
Would it be more beneficial to convert the decimals to fractions, or fractions to decimals? Be able to justify your reasoning.
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Add Rational Numbers
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Example 6�Add Rational Numbers
| Rewrite as an improper fraction. |
| The LCD of 3, 4, and 8 is 24. |
| Add the numerators. |
| Associative Property |
| Add. |
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Add Rational Numbers
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Example 6�Add Rational Numbers
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Add Rational Numbers
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Example 6�Add Rational Numbers
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Add Rational Numbers
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Example 7�Add Rational Numbers
The lowest recorded elevation in the contiguous United States, 282 feet below sea level, is in Death Valley. Suppose you began a hike in the parking area near Badwater Basin at 266 feet below sea level. The stopping points of the hike and the elevation traveled are shown in the table.
What is the elevation of your stopping point?
Stop | Elevation Traveled (ft) |
1 | |
2 | |
3 | |
4 | |
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Example 7�Add Rational Numbers
Think About It!
How will you represent the starting point of the hike in the expression?
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Example 7�Add Rational Numbers
| Write the �expression |
| Write fractions as decimals. |
| Commutative �Property |
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Example 7�Add Rational Numbers
| Associative Property |
| Simplify. |
| Add. |
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Add Rational Numbers
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Example 7�Add Rational Numbers
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Add Rational Numbers
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Apply�Animal Care
Time (hr) | Altitude Change (m) |
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Apply�Animal Care
Time (hr) | Altitude Change (m) |
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Think about scenarios, when adding rational numbers, where it would be beneficial to change all the numbers to decimals, or all to fractions. Give examples.
Pause and Reflect�
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Apply
Animal Care
Month | Change from Previous Month (lb) |
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Apply
Animal Care
Talk About It!
Why is it more efficient in this problem to write each of the values as a decimal before adding?
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Apply
Animal Care
Year | Change in Area (acres) |
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Add Rational Numbers
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Apply
Animal Care
Year | Change in Area (acres) |
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Add Rational Numbers
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Exit Ticket
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Exit Ticket
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Exit Ticket
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Add Rational Numbers
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