Fractions · Capstone · C1

Pick the right move.

The last skill is choosing: simplify, find a common denominator to add or subtract, multiply across, or keep–flip–multiply to divide — and always reduce the answer.

01 / THE IDEA

See it work.

Watch the method

Pick the right move

Read the operation, then apply the right method.

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.

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— / WHY IT WORKS

The idea underneath.

The decision

Adding/subtracting needs a common denominator; multiplying does not; dividing flips the second fraction. Reduce at the end.

Why it works

Pick the right tool for the sign.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve 3/5 ÷ 2/3

1

Flip the divisor

Dividing means multiplying by the reciprocal. 3/5 \times 3/2

2

Multiply across

Tops times tops, bottoms times bottoms. 9/10

EX 2medium

Solve 1/2 + 1/3

1

Find the LCD

The least common denominator of 2 and 3 is 6. \text{LCD}(2,3)=6

2

Rewrite each fraction

Give both the LCD. 3/6 + 2/6

3

Add the numerators

Keep the LCD. 5/6

EX 3hard

Solve 2/3 + 4/5

1

Find the LCD

The least common denominator of 3 and 5 is 15. \text{LCD}(3,5)=15

2

Rewrite each fraction

Give both the LCD. 10/15 + 12/15

3

Add the numerators

Keep the LCD. 22/15

04 / COMMON TRAPS

Where students slip.

Trap

Finding an LCD to multiply.

Fix

Only adding/subtracting needs a common denominator.

Trap

Leaving the answer unreduced.

Fix

Always simplify the result.

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

Solve 3/5 ÷ 2/3

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.
C2

Solve 1/3 ÷ 2/4

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.
C3

Solve 2/3 - 1/2

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.
C4

Solve 1/2 + 4/5

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.
Apply

Apply (4)

A1

Solve 1/2 + 1/3

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.
A2

Solve 1/2 + 1/3

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.
A3

Solve 24/30

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.
A4

Solve 9/21

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.
Extension

Extension (4)

E1

Solve 2/3 + 4/5

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.
E2

Solve 10/35

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.
E3

Solve 2/3 - 2/4

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.
E4

Solve 2/4 + 1/3

Need a hint?
  • Look at the operation first.
  • Add/subtract → LCD; multiply → across; divide → flip.