Lesson 3 of 4
Use common denominators and preserve restrictions through every operation.
Subject to changeOptional future study, outside the current course sequence. This lesson and its homework preview are unassigned and may change.
One idea at a time. Try the example, then keep going.
Big ideas · 1 of 8
Big ideas
Do this: Read one idea, then explain it in your own words.
With the same nonzero denominator, add or subtract the whole numerators and keep the denominator. Subtraction applies to every term in the second numerator.
Factor different denominators and use each needed factor at its highest power. Multiply both numerator and denominator by the same missing factor before combining.
Multiplication combines numerators and denominators. Division multiplies by the reciprocal of the divisor; the divisor itself must also be nonzero.
Restrictions come from every original denominator and from a divisor's nonzero requirement. Cancellation at the end does not restore forbidden inputs.
Step-through
Do this: Step through the example. Predict the next step before revealing it.
Worked example: add different denominators
Whole picture, 4 steps
4 steps. Tap a number or Show me how it works.
Do this: Cover the next step and try it yourself.
Both original exclusions remain.
Do this: Cover the next step and try it yourself.
Do this: Explain why the tempting shortcut fails.
Wrong idea: . Adding fractions requires a common denominator; for nonzero and the sum is . Numerators and denominators do not add independently.
Tip
Do this: Use paper. State the definition before you calculate.
Explain why for .
Worked example
Do this: Work on paper and explain each step before checking it.
Combine .
Watch
Do this: Watch the public lesson, pause to try a step, then return to your practice.
The linked video is free to watch. The creator may offer optional paid resources; they are not needed for this lesson. If YouTube is blocked, use the lesson notes and worked examples here.
Ready when you are.
Activity 1 of 7 · 0 of 7 activities done
Flashcards
Do this: Say the answer and a reason before you flip.
Card 1 of 8
0 Know it0 Still learning
Keep the shared denominator.
On the card: Enter or Space flips. Left and Right move. After revealing, 1 marks Still learning and 2 marks Know it. Tab reaches every control.
Add for .
.
Subtract for .
.
What is a common denominator for and ?
.
How do you subtract a numerator with two terms?
Put it in parentheses and distribute the subtraction sign to both terms.
How do you divide by a nonzero rational expression?
Multiply by its reciprocal.
What extra inputs can rational division exclude?
Zeros of the divisor's numerator, in addition to all original denominator zeros.
Can canceled denominator factors erase original exclusions?
No.
What should you do after combining rational expressions?
Factor if useful, simplify legal common factors and state the retained restrictions.
True or false
Do this: Choose true or false; explain what would make a false statement correct.
Self-test
Do this: Try each problem without a timer. Read the feedback before moving on.
6 questions. One at a time.
Practice, not a grade. No timer. Your best score stays in this browser.
Self-test
Do this: Try each problem without a timer. Read the feedback before moving on.
6 questions. One at a time.
Practice, not a grade. No timer. Your best score stays in this browser.
Write it
Do this: Write two or three sentences, then compare with the model.
Start here if it helps: I would first identify...
Your answer is not saved anywhere. It disappears when you leave the page.
Write it
Do this: Try the extension on paper, then explain your reasoning here.
Your answer is not saved anywhere. It disappears when you leave the page.
Match
Do this: Choose a word, then choose its meaning.
Connect the ideas
0 / 4 connectedChoose a term, then its meaning. Or drag its grip. Use Tab and Enter or Space; Escape clears.
Subject to changeOptional preview. This page does not mean this homework is assigned. Only turn it in if your teacher asks.
Optional practice preview · 3 points if assigned
Opening your homework…
Practice it: You did 0 of 7 activities.
You decide when you have finished. This is your study progress, not a grade.
Not marked finished yet.
