Fractions · Add & subtract · 6.3

Add with the LCD.

Different denominators must be made the same first. Find the least common denominator, rewrite both fractions, then add the numerators.

01 / THE IDEA

See it work.

Watch the method

Add with the LCD

1/2 + 1/3: LCD 6 → 3/6 + 2/6 = 5/6.

1 / 3
12+13\frac{1}{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.

36+26\frac{3}{6} + \frac{2}{6}
3

Add the numerators

Keep the LCD.

56\frac{5}{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
best 0
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— / WHY IT WORKS

The idea underneath.

Least common denominator

The LCD is the smallest common multiple of the denominators. Rewrite both over it, then add the tops.

Why it works

Cut both bars into the same-size pieces.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Add 3/4 + 3/6

1

Find the LCD

The least common denominator of 4 and 6 is 12. \text{LCD}(4,6)=12

2

Rewrite each fraction

Give both the LCD. 9/12 + 6/12

3

Add the numerators

Keep the LCD. 15/12

4

Simplify

Reduce to lowest terms. 11/4

EX 2medium

Add 3/4 + 2/6

1

Find the LCD

The least common denominator of 4 and 6 is 12. \text{LCD}(4,6)=12

2

Rewrite each fraction

Give both the LCD. 9/12 + 4/12

3

Add the numerators

Keep the LCD. 13/12

EX 3hard

Add 3/4 + 5/6

1

Find the LCD

The least common denominator of 4 and 6 is 12. \text{LCD}(4,6)=12

2

Rewrite each fraction

Give both the LCD. 9/12 + 10/12

3

Add the numerators

Keep the LCD. 19/12

04 / COMMON TRAPS

Where students slip.

Trap

Adding across different denominators.

Fix

Find the LCD first.

Trap

Forgetting to rewrite the numerators.

Fix

Scale the tops to match the new bottom.

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 3/4 + 3/6

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.
C2

Add 2/3 + 2/6

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.
C3

Add 2/3 + 5/6

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.
C4

Add 1/2 + 4/5

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.
Apply

Apply (4)

A1

Add 3/4 + 2/6

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.
A2

Add 3/4 + 1/5

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.
A3

Add 2/4 + 3/5

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.
A4

Add 2/4 + 1/3

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.
Extension

Extension (4)

E1

Add 3/4 + 5/6

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.
E2

Add 2/3 + 4/5

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.
E3

Add 2/3 + 1/5

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.
E4

Add 2/3 + 2/5

Need a hint?
  • Find the LCD.
  • Rewrite both, then add the tops.