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Premium UnlockedChallenge55 min

Maths • Number & Operations: Fractions

Fraction Operations Studio

Add, subtract, multiply, and divide fractions using real-world problems and visual models.

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Activities

Learning Goals

✓Add fractions with unlike denominators.
✓Subtract mixed numbers with regrouping.
✓Multiply fractions using an area model.
✓Multiply a whole number by a fraction using a set model.
✓Divide unit fractions by whole numbers.
✓Divide whole numbers by unit fractions.

Mini Lesson

1Unlike denominators must be converted to common denominators before adding or subtracting.
2Mixed numbers sometimes require regrouping one whole into fractional parts.
3Fraction multiplication can be shown with overlapping shaded areas.
4A unit fraction names one equal part of a whole.
5Dividing by a unit fraction asks how many of those fractional pieces fit.

unlike denominatorsmixed numberregroupingunit fractionfraction multiplicationfraction divisionsimplify

Interactive Activities

Tap an answer choice. The card will show feedback, the correct answer, visual model, and step-by-step explanation.

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Activity 1Add Fractions with Unlike Denominatorsfraction-lcd

Pizza Fraction Addition

Question

Liam ate 1/3 of a pizza, and Jenny ate 2/5 of the same pizza. How much of the pizza did they eat combined?

Instruction

Find a common denominator for thirds and fifths, convert both fractions, then add.

💡 Teacher Hint

The LCD of 3 and 5 is 15.

Fraction LCD Helper

LCD

Left

5/15

Right

6/15

Final

11/15

👁️ Show Visual Model: Fraction Bar Model

Model Type: fraction-bar

Liam:  1/3 = 5/15
[ X ][ X ][ X ][ X ][ X ][   ][   ][   ][   ][   ][   ][   ][   ][   ][   ]

Jenny: 2/5 = 6/15
[ O ][ O ][ O ][ O ][ O ][ O ][   ][   ][   ][   ][   ][   ][   ][   ][   ]

Total:
[ X ][ X ][ X ][ X ][ X ][ O ][ O ][ O ][ O ][ O ][ O ][   ][   ][   ][   ]

Answer: 11/15 of the pizza

✅ Show Step-by-Step Answer

1Find the LCD of 3 and 5.
2The LCD is 15.
3Convert 1/3 to 5/15.
4Convert 2/5 to 6/15.
5Add 5/15 + 6/15.
6The total is 11/15.

CCSS 5.NF.A.1

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Activity 2Subtract Mixed Numbers with Regroupingquiz

Baker's Flour Regrouping

Question

A baker has 4 1/4 cups of flour. He uses 2 3/4 cups for a cake recipe. How much flour does he have left?

Instruction

Regroup one whole cup into fourths, then subtract the mixed numbers.

💡 Teacher Hint

Change 4 1/4 into 3 5/4 before subtracting.

👁️ Show Visual Model: Mixed Number Decomposition

Model Type: fraction-bar

Start:
[████] [████] [████] [████] [█░░░]  = 4 1/4

Regroup one whole:
3 wholes and 5/4

Subtract:
3 5/4 - 2 3/4 = 1 2/4

Simplify:
1 2/4 = 1 1/2 cups

✅ Show Step-by-Step Answer

1Start with 4 1/4.
2You cannot subtract 3/4 from 1/4 without regrouping.
3Borrow 1 whole from 4 wholes.
4That gives 3 wholes and 5/4.
5Subtract 2 3/4 from 3 5/4.
63 - 2 = 1 and 5/4 - 3/4 = 2/4.
71 2/4 simplifies to 1 1/2 cups.

CCSS 5.NF.A.1

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Activity 3Multiply Fractionsquiz

Garden Fraction Multiplication

Question

A garden takes up 2/3 of a backyard. Flowers are planted in 4/7 of that garden space. What fraction of the entire backyard is planted with flowers?

Instruction

Multiply 2/3 × 4/7. Use the overlapping shaded area as the model.

💡 Teacher Hint

Multiply numerators: 2 × 4. Multiply denominators: 3 × 7.

👁️ Show Visual Model: Grid Area Model

Model Type: grid-model

Columns: 3 sections, 2 shaded
Rows:    7 sections, 4 shaded

Overlap = 2 × 4 = 8 squares
Total   = 3 × 7 = 21 squares

Equation:
(2 × 4) / (3 × 7) = 8/21

✅ Show Step-by-Step Answer

1The garden is 2/3 of the backyard.
2Flowers cover 4/7 of the garden.
3Multiply the fractions: 2/3 × 4/7.
4Multiply numerators: 2 × 4 = 8.
5Multiply denominators: 3 × 7 = 21.
6The answer is 8/21 of the entire backyard.

CCSS 5.NF.B.4

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Activity 4Whole Number × Fractionquiz

Track Team Fraction of a Set

Question

There are 12 students on a track team. Of those students, 3/4 are sprinters. How many sprinters are on the team?

Instruction

Divide the 12 students into 4 equal groups, then count 3 of the groups.

💡 Teacher Hint

One fourth of 12 is 3. Three fourths is 3 groups of 3.

👁️ Show Visual Model: Set Model

Model Type: set-model

Group 1: [● ● ●]
Group 2: [● ● ●]
Group 3: [● ● ●]
Group 4: [● ● ●]

3/4 of the team = first 3 groups
3 + 3 + 3 = 9 sprinters

✅ Show Step-by-Step Answer

1There are 12 students.
2Divide them into 4 equal groups.
3Each group has 3 students.
43/4 means 3 of the 4 groups.
53 groups of 3 students equals 9.

CCSS 5.NF.B.6

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Activity 5Divide Unit Fraction by Whole Numberquiz

Lasagna Sharing

Question

A family has 1/3 of a large pan of lasagna left over. If 4 family members share the leftover piece equally, what fraction of the whole pan does each person get?

Instruction

Divide 1/3 by 4. Think of cutting the one-third piece into 4 smaller equal pieces.

💡 Teacher Hint

A third cut into 4 equal parts creates twelfths.

👁️ Show Visual Model: Partitioning a Fraction

Model Type: partition-model

Whole pan split into thirds:
[  1/3 Pan  ][   Empty   ][   Empty   ]

Now split the 1/3 pan into 4 equal pieces:
[●][ ][ ][ ] [   Empty   ][   Empty   ]

There are 12 possible equal tiny pieces in the whole pan.
Each person gets 1/12.

✅ Show Step-by-Step Answer

1Start with 1/3 of the pan.
2The leftover third is shared by 4 people.
3Divide the 1/3 piece into 4 equal parts.
4That creates 12 equal parts in the whole pan.
5Each person gets 1 of the 12 parts.
6Each person gets 1/12 of the whole pan.

CCSS 5.NF.B.7

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Activity 6Divide Whole Number by Unit Fractionquiz

Cheese Serving Division

Question

A chef has 5 blocks of cheese. If each serving requires 1/2 of a block of cheese, how many servings can the chef make?

Instruction

Find how many halves fit into 5 wholes.

💡 Teacher Hint

Each whole block has 2 halves.

👁️ Show Visual Model: Fraction Bar Cuts

Model Type: fraction-bar

[ 1 │ 2 ]  [ 3 │ 4 ]  [ 5 │ 6 ]  [ 7 │ 8 ]  [ 9 │ 10 ]

Each block is cut into 2 half-block servings.
5 blocks × 2 servings per block = 10 servings

✅ Show Step-by-Step Answer

1Each serving uses 1/2 block.
2Each whole block can be cut into 2 halves.
3There are 5 whole blocks.
45 × 2 = 10 halves.
5The chef can make 10 servings.

CCSS 5.NF.B.7

Exit Ticket

How can a visual model help when multiplying or dividing fractions?

Show Suggested Answer

A visual model shows what the fractions mean, how the parts are grouped, and why the operation gives the final amount.