Fractions · Add & subtract · 6.6

Add mixed numbers.

Add mixed numbers by adding the whole parts and the fraction parts (with the LCD), then combining — carrying a whole if the fractions make more than 1.

01 / THE IDEA

See it work.

Watch the method

Add mixed numbers

1 1/2 + 2 1/3 = 3 + 5/6 = 3 5/6.

1 / 3
112+2131\frac{1}{2} + 2\frac{1}{3}
1

Find the LCD

The least common denominator of 2 and 3 is 6.

LCD(2,3)=6\text{LCD}(2,3)=6
2

Rewrite each fraction

Give both the LCD.

96+146\frac{9}{6} + \frac{14}{6}
3

Add the numerators

Keep the LCD.

236\frac{23}{6}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a fraction like 3/4 or 1 1/2.

streak 0
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— / WHY IT WORKS

The idea underneath.

Parts together

Combine wholes with wholes and fractions with fractions; if the fraction part is improper, carry a whole.

Why it works

Stack the wholes, then the pieces.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Add 1 2/3 + 1 1/3

1

Add the numerators

Same denominator — keep it, combine the tops. \frac{5 + 4}{3} = 9/3

2

Simplify

Reduce to lowest terms. 3

EX 2medium

Add 2 1/2 + 2 1/2

1

Add the numerators

Same denominator — keep it, combine the tops. \frac{5 + 5}{2} = 10/2

2

Simplify

Reduce to lowest terms. 5

EX 3hard

Add 1 2/3 + 3 2/3

1

Add the numerators

Same denominator — keep it, combine the tops. \frac{5 + 11}{3} = 16/3

04 / COMMON TRAPS

Where students slip.

Trap

Ignoring the LCD for the fraction parts.

Fix

Add the fractions over a common denominator.

Trap

Forgetting to carry.

Fix

If the fractions exceed 1, carry into the wholes.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Add 1 2/3 + 1 1/3

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.
C2

Add 1 3/4 + 3 3/4

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.
C3

Add 3 3/4 + 3 3/4

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.
C4

Add 1 3/4 + 1 2/4

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.
Apply

Apply (4)

A1

Add 2 1/2 + 2 1/2

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.
A2

Add 1 1/4 + 2 2/4

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.
A3

Add 1 3/4 + 1 2/4

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.
A4

Add 2 2/4 + 1 1/4

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.
Extension

Extension (4)

E1

Add 1 2/3 + 3 2/3

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.
E2

Add 2 1/4 + 2 2/4

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.
E3

Add 1 2/3 + 1 1/3

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.
E4

Add 3 1/2 + 1 1/2

Need a hint?
  • Add wholes; add fractions with the LCD.
  • Carry if the fraction part is over 1.