Evaluate: \(-\frac{3}{4}+\frac{1}{2}\)
- A \(-\frac{5}{4}\)
- B \(-\frac{1}{4}\)
- C \(\frac{1}{4}\)
- D \(\frac{5}{4}\)
Check answer and explanation
Answer B: \(-\frac{1}{4}\)
Find a common denominator: \(-\frac{3}{4}+\frac{2}{4}=-\frac{1}{4}\).
CH03-04 lesson
Adding and Subtracting Rational Numbers Learning Activity
A focused Grade 7 learning session for Adding and Subtracting Rational Numbers using visual models, worked examples, strategy guidance, and a short mastery check.
- 15
- minutes
- 6
- lesson parts
- 11
- practice items
Students will build Grade 7 mastery of adding and subtracting rational numbers using models, equations, and test-style reasoning.
Student goal: I can solve problems involving adding and subtracting rational numbers.
Helpful first:
Subtracting Integers
Learn the Idea
Adding and Subtracting Rational Numbers is part of Grade 7 The Number System. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of adding and subtracting rational numbers using models, equations, and test-style reasoning.
See the Math
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Follow a Worked Example
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Adding and Subtracting Rational Numbers, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Connect It to a Real Situation
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
Avoid Mistakes and Choose a Strategy
- Underline the exact question before solving.
- Label units, variables, or graph axes when they appear.
- Estimate first so unreasonable answers are easier to catch.
- Review missed questions and write the reason for each mistake.
Remember the Key Idea
I can solve problems involving adding and subtracting rational numbers.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsWhat is \(-\frac{3}{5}+\frac{4}{5}\)?
- A \(-\frac{7}{5}\)
- B \(\frac{1}{5}\)
- C \(\frac{3}{5}\)
- D \(-\frac{1}{5}\)
Check answer and explanation
Answer B: \(\frac{1}{5}\)
When denominators are the same, add the numerators: \(-\frac{3}{5}+\frac{4}{5}=\frac{1}{5}\).
guided
1 questionEvaluate: \(5.2 - 7.1\)
- A \(-1.9\)
- B \(1.9\)
- C \(12.3\)
- D \(-12.3\)
Check answer and explanation
Answer A: \(-1.9\)
Since \(5.2 < 7.1\), the difference is negative: \(5.2 - 7.1 = -1.9\).
practice
5 questionsAdd: \(1\frac{1}{3} + 2\frac{1}{6}\)
- A \(4\frac{1}{6}\)
- B \(3\frac{1}{6}\)
- C \(2\frac{1}{2}\)
- D \(3\frac{1}{2}\)
Check answer and explanation
Answer D: \(3\frac{1}{2}\)
Convert to common denominator 6: \(1\frac{2}{6} + 2\frac{1}{6} = 3\frac{3}{6} = 3\frac{1}{2}\).
Which expression is equivalent to \(8 - 3\)?
- A \(8 + 3\)
- B \(8 + (-3)\)
- C \(-8 + 3\)
- D \(3 - 8\)
Check answer and explanation
Answer B: \(8 + (-3)\)
Subtraction can be rewritten as adding the opposite: \(8 - 3 = 8 + (-3) = 5\).
Evaluate: \(-\frac{5}{6} - \frac{1}{3}\)
- A \(\frac{7}{6}\)
- B \(-\frac{1}{2}\)
- C \(-\frac{5}{6}\)
- D \(-1\frac{1}{6}\)
Check answer and explanation
Answer D: \(-1\frac{1}{6}\)
Common denominator is 6: \(-\frac{5}{6} - \frac{2}{6} = -\frac{7}{6} = -1\frac{1}{6}\).
Use the number line below. Start at \(-2\) and add \(3\). Where do you end?
- A \(-5\)
- B \(1\)
- C \(-1\)
- D \(5\)
Check answer and explanation
Answer B: \(1\)
Starting at \(-2\) and moving right 3 units: \(-2 + 3 = 1\).
Use the number line to find \(-2.5 + 4.7\).
- A \(-7.2\)
- B \(-2.2\)
- C \(2.2\)
- D \(7.2\)
Check answer and explanation
Answer C: \(2.2\)
Starting at \(-2.5\) and moving right \(4.7\) units: \(-2.5 + 4.7 = 2.2\).
exit
3 questionsSubtract: \(\frac{7}{8} - \frac{1}{4}\)
- A \(\frac{3}{4}\)
- B \(\frac{6}{8}\)
- C \(\frac{1}{2}\)
- D \(\frac{5}{8}\)
Check answer and explanation
Answer D: \(\frac{5}{8}\)
Common denominator is 8: \(\frac{7}{8} - \frac{2}{8} = \frac{5}{8}\).
Evaluate: \(-3.6 + (-2.4)\)
- A \(-6.0\)
- B \(-1.2\)
- C \(1.2\)
- D \(6.0\)
Check answer and explanation
Answer A: \(-6.0\)
Adding two negatives: \(-3.6 + (-2.4) = -(3.6 + 2.4) = -6.0\).
What is \(\frac{3}{10} + \frac{4}{10}\)?
- A \(\frac{7}{20}\)
- B \(\frac{1}{2}\)
- C \(\frac{12}{10}\)
- D \(\frac{7}{10}\)
Check answer and explanation
Answer D: \(\frac{7}{10}\)
Same denominator: \(\frac{3}{10} + \frac{4}{10} = \frac{7}{10}\).
