Grade: Grade 5 Subject: Mathematics Unit: Fraction Operations SAT: Algebra ACT: Math

Guided Practice: Fraction Operations

Work through problems step-by-step with hints and scaffolding. Build your confidence before tackling independent practice!

Your Progress

0 of 10 problems completed

Part 1: Adding Fractions Step-by-Step

Remember the Steps

1. Check if denominators are the same. 2. If not, find the LCD. 3. Make equivalent fractions. 4. Add numerators. 5. Simplify.

Guided Problem 1: Adding with Like Denominators

2 7 + 3 7 = ?

1 Check the denominators

Both fractions have denominator 7. Since they're the same, we can add directly!

2 Add the numerators

Add the top numbers: 2 + 3 = 5

Keep the denominator: 7

3 Write the answer

2 7

3 7

5 7

5/7 is already in lowest terms (5 and 7 share no common factors).

Now you try! What is 2/7 + 3/7?

Guided Problem 2: Adding with Unlike Denominators

1 4 + 2 3 = ?

1 Find the LCD of 4 and 3

Multiples of 4: 4, 8, 12, 16...

Multiples of 3: 3, 6, 9, 12, 15...

LCD = 12

2 Convert 1/4 to twelfths

12 / 4 = 3, so multiply top and bottom by 3:

1 x 3 4 x 3

3 12

3 Convert 2/3 to twelfths

12 / 3 = 4, so multiply top and bottom by 4:

2 x 4 3 x 4

8 12

4 Add and simplify

3 12

8 12

11 12

11/12 is already in lowest terms!

Now you try! What is 1/4 + 2/3?

Part 2: Subtracting Fractions Step-by-Step

Guided Problem 3: Subtracting with Unlike Denominators

5 6 - 1 4 = ?

1 Find the LCD of 6 and 4

Multiples of 6: 6, 12, 18, 24...

Multiples of 4: 4, 8, 12, 16...

LCD = 12

2 Convert both fractions

5/6 = 10/12 (multiply by 2/2)

1/4 = 3/12 (multiply by 3/3)

3 Subtract the numerators

10 12

3 12

7 12

Now you try! What is 5/6 - 1/4?

Part 3: Multiplying Fractions Step-by-Step

Remember: For multiplication, you do NOT need common denominators. Just multiply straight across!

Guided Problem 4: Multiplying Fractions

2 5 x 3 4 = ?

1 Multiply the numerators

2 x 3 = 6 (this is your new numerator)

2 Multiply the denominators

5 x 4 = 20 (this is your new denominator)

3 Simplify if possible

6/20: Both 6 and 20 are divisible by 2

6 20

3 10

Now you try! What is 2/5 x 3/4?

Part 4: Dividing Fractions Step-by-Step

Keep - Change - Flip

Keep the first fraction. Change division to multiplication. Flip the second fraction. Then multiply!

Guided Problem 5: Dividing Fractions

3 4 ÷ 2 5 = ?

1 KEEP the first fraction

Keep 3/4 exactly as it is.

2 CHANGE division to multiplication

Change ÷ to x

3 FLIP the second fraction

Flip 2/5 to get 5/2

3 4

5 2

4 Multiply and simplify

3 x 5 4 x 2

15 8

= 1 7/8

Now you try! What is 3/4 ÷ 2/5? (Enter as improper fraction)

Independent Practice

Now try these problems on your own! Use the steps you learned.

Problem 6: Addition

3 8 + 1 8 = ?

Problem 7: Subtraction

4 5 - 1 3 = ?

Problem 8: Multiplication

4 7 x 2 3 = ?

Problem 9: Division

5 6 ÷ 2 3 = ?

Problem 10: Mixed Operations

What is 1/2 + 1/3 simplified?

Key Takeaways

Adding/Subtracting

Need same denominators. Find LCD, convert, then add/subtract numerators.

Multiplying

No common denominator needed! Multiply top x top, bottom x bottom.

Dividing

Keep-Change-Flip: Keep first, change to multiplication, flip second.

Always Simplify

Reduce your final answer to lowest terms by dividing by the GCF.

Ready for more? Move on to Word Problems to apply these skills to real-life situations!