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Grade 7 · lesson 3 of 4

Combine Signed Fractional Amounts

Equivalent fractions put both quantities into the same-size parts.

About 20 minutes, plus any extended practice

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Supplied materials

  • Paper or a browser scratch area; a calculator is optional unless rounding is requested.
  • Supplied teaching case: Compute −2/3 + 3/4 exactly. Candidate answers: (A) -2/7 (B) 1/12 (C) 1/7 (D) 17/12.
  • Independent check inputs: Compute −3/3 + 4/4 exactly. Candidate answers: (A) -3/7 (B) 0 (C) 1/7 (D) 2.

Learn the idea

Rational numbers can be represented as ratios of integers with nonzero denominator. Their decimal forms terminate or repeat, and negative quantities can be compared by their positions to the left of zero. Equivalent fractions put both quantities into the same-size parts. Signed numerators can then be added while the common denominator continues naming the size of each part.

Here is the method on the supplied teaching case. Rename both fractions in twelfths: −8/12+9/12=(1)/12=1/12. The sign belongs to the numerator.

Add the signed numerators only after choosing a common denominator. Adding denominators creates a different part size; keep the minus sign attached to its quantity during renaming.

  1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
  2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
  3. Solve the independent check with its changed inputs before revealing feedback.
  4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
Worked example

See the method in action

Teaching case: Compute −2/3 + 3/4 exactly. Candidate answers: (A) -2/7 (B) 1/12 (C) 1/7 (D) 17/12. Solution: Rename both fractions in twelfths: −8/12+9/12=(1)/12=1/12. The sign belongs to the numerator. The final answer is 1/12. Add the signed numerators only after choosing a common denominator. Adding denominators creates a different part size; keep the minus sign attached to its quantity during renaming.

Your turn

Check your reasoning

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Helpful tips
  • Equivalent fractions put both quantities into the same-size parts.
  • Add the signed numerators only after choosing a common denominator.
Compute −3/3 + 4/4 exactly.

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

0

Rename both fractions in twelfths: −12/12+12/12=(0)/12=0. The sign belongs to the numerator.

Take it further

Changed-input task: Compute −9/3 + 10/4 exactly. Candidate answers: (A) -1/2 (B) -9/7 (C) 1/7 (D) 11/2. Show the mathematical reason, not only the selected answer. Expected result: -1/2. Rename both fractions in twelfths: −36/12+30/12=(-6)/12=-1/2. The sign belongs to the numerator.

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More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. Compute −4/3 + 5/4 exactly.
Need a hint?
  • Equivalent fractions put both quantities into the same-size parts.
  • Add the signed numerators only after choosing a common denominator.
2. Compute −5/3 + 6/4 exactly.
Need a hint?
  • Equivalent fractions put both quantities into the same-size parts.
  • Add the signed numerators only after choosing a common denominator.
3. Compute −6/3 + 7/4 exactly.
Need a hint?
  • Equivalent fractions put both quantities into the same-size parts.
  • Add the signed numerators only after choosing a common denominator.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.