Adding Fractions: The Common Ground

What you do

You shape the function y = x/2 + x/k and watch the graph answer.

Challenges to clear

• Make the second piece thirds: slide k to 3. Then check that x = 6 gives y = 5 — because 1/2 + 1/3 = 5/6, and 6 of those sixths make 5.
• The common ground holds everywhere: check that x = 12 gives y = 10 (12 × 5/6).
• Both fractions are yours now. Make the first piece thirds — slide m to 3.
• Now the second piece. Slide k until x = 12 gives 7, because 1/3 + 1/4 = 7/12 and 12 of those twelfths make 7.

Check yourself

Why can't you add 1/2 + 1/3 directly?

So what is 1/2 + 1/3?

• The pieces are different sizes — you must first cut both into sixths. — correct
• Because 2 + 3 = 5 is an odd number.
• You can: 1/2 + 1/3 = 2/5.
• Fractions can only be multiplied, never added.
• 5/6 — correct
• 2/5
• 1/5
• 3/6

Think about it

• If x = 6, then x/2 = 3. When k = 3, x/k = 2. What should y = x/2 + x/k show at x = 6?