Digits, Grade 7, Volume 1, Homework Helper

1-3: Subtracting Rational Numbers

Key Concept

You subtract a fraction or a decimal the same way you subtract an integer.

For any rational numbers a and b:

ab = a + (− b)

a − (− b) = a + b

table with 4 rows and 3 columns , row1 column 1 , cap writesubtractionasaddingtheopposite. , column 2 minus , 3 fifths , minus , 4 fifths , column 3 equals negative , 3 fifths , plus . open , negative , 4 fifths , close , row2 column 1 , cap addnumberswiththesamesign. , column 2 , column 3 equals negative , 7 fifths , row3 column 1 , cap writesubtractionasaddingtheopposite. , column 2 negative 9.1 minus . open , negative 7.6 , close , column 3 equals negative 9.1 plus 7.6 , row4 column 1 , cap addnumberswithdifferentsigns. , column 2 , column 3 equals negative 1.5 , end table

Part 1

Example Predicting The Sign of Differences of Rational Numbers

Determine if each difference is negative, zero, or positive.

  • a. 1 half , minus . open , negative , 1 fourth , close

  • b. negative 5 minus . open . negative 3 , and 3 fourths . close

  • c. negative 4.7 minus . open , negative 4.7 , close

  • d. 5.7 minus 8 , and 1 half

  • e. − 2.6 − (− 3.1)

  • f. negative 3 , and 1 half , minus . open . negative 3 , and 1 half . close

  • g. negative , 4 thirds , minus . open , negative , 2 thirds , close

  • h. negative 0.8 minus 0.8

Solution

Rewrite the subtraction as adding the opposite. Then think about the relationship of the addends.

  • a. The sum of two positives is positive.

  • b. The sum of two negatives is negative.

  • c. The sum of two additive inverses is zero.

  • d. The absolute value of negative eight and a half is greater then the absolute value of 5.7, so the sum is negative.

  • e. The absolute value of 3.1 is greater than the absolute value of −2.6, so the sum is positive.


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Table of Contents

Digits, Grade 7, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Expressions, Equations, and Relationships Unit C: Measurement and Geometry Unit D: Proportionality English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties