Fractions · Add & subtract · 6.1

Add, same denominator.

When denominators match, the pieces are the same size: add the numerators and keep the denominator. Simplify if you can.

01 / THE IDEA

See it work.

Picture it

Shaded parts out of the whole.

1
5

Watch the method

Add, same denominator

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

1 / 1
15+25\frac{1}{5} + \frac{2}{5}
1

Add the numerators

Same denominator — keep it, combine the tops.

1+25=35\frac{1 + 2}{5} = \frac{3}{5}
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.

Add the counts

n/d + m/d = (n+m)/d — you are counting unit fractions.

Why it works

One fifth plus two fifths is three fifths.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Add 1/3 + 1/3

1

Add the numerators

Same denominator — keep it, combine the tops. \frac{1 + 1}{3} = 2/3

EX 2medium

Add 1/5 + 3/5

1

Add the numerators

Same denominator — keep it, combine the tops. \frac{1 + 3}{5} = 4/5

EX 3hard

Add 4/7 + 2/7

1

Add the numerators

Same denominator — keep it, combine the tops. \frac{4 + 2}{7} = 6/7

04 / COMMON TRAPS

Where students slip.

Trap

Adding the denominators too.

Fix

Keep the denominator; only add the tops.

Trap

Forgetting to simplify.

Fix

Reduce the result if possible.

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 1/3 + 1/3

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.
C2

Add 2/6 + 4/6

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.
C3

Add 1/3 + 2/3

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.
C4

Add 2/9 + 7/9

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.
Apply

Apply (4)

A1

Add 1/5 + 3/5

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.
A2

Add 1/5 + 3/5

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.
A3

Add 3/7 + 3/7

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.
A4

Add 3/6 + 1/6

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.
Extension

Extension (4)

E1

Add 4/7 + 2/7

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.
E2

Add 1/5 + 3/5

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.
E3

Add 2/5 + 2/5

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.
E4

Add 6/8 + 1/8

Need a hint?
  • Add the numerators.
  • Keep the denominator; simplify.