Fraction Builders Slides GRADES 4–5 MATH WORKSHOP
Fraction Builders:
Adding & Subtracting Mixed Numbers
Using visual fraction bars to find common denominators and regroup wholes!
1 Whole
1 Whole
= ?
Today's Builder Toolkit
1
Mixed Numbers
A whole number + a fraction, like \( 2\frac{1}{4} \).
2
Same-Size Pieces
We need a common denominator so all pieces are the exact same size!
\( \frac{1}{2} = \frac{2}{4} \)
3
Regrouping
Trade 1 whole for fraction pieces, or trade full pieces for 1 whole!
\( 1\text{ whole} = \frac{4}{4} = \frac{6}{6} \)
ADDITION
Step 1: Make Same-Size Pieces
\( 1\frac{3}{4} + 1\frac{1}{2} \)
\( 1\frac{3}{4} \) (already in fourths)
1 Whole
\( 1\frac{1}{2} \rightarrow 1\frac{2}{4} \) (cut halves into fourths)
1 Whole
1
Find a common denominator for 4 and 2: use 4!
2
Rewrite \( 1\frac{1}{2} \) as an equivalent fraction:
\( 1\frac{1 \times 2}{2 \times 2} = 1\frac{2}{4} \)
New problem: \( 1\frac{3}{4} + 1\frac{2}{4} \)
ADDITION
Step 2: Add & Regroup!
\( 1\frac{3}{4} + 1\frac{2}{4} \)
Combine wholes + combine fourths:
1
1
4 fourths make 1 MORE whole! (\( \frac{4}{4} = 1 \))
1
1
1
Wholes: \( 1 + 1 = 2 \)
Fractions: \( \frac{3}{4} + \frac{2}{4} = \frac{5}{4} \)
Regroup \( \frac{5}{4} \):
\( \frac{5}{4} = \frac{4}{4} + \frac{1}{4} = 1\frac{1}{4} \)
\( 2 + 1\frac{1}{4} = 3\frac{1}{4} \)
SUBTRACTION
Step 1: Find Same-Size Pieces
\( 3\frac{1}{3} - 1\frac{5}{6} \)
Start with \( 3\frac{1}{3} \rightarrow 3\frac{2}{6} \):
1 Whole
1 Whole
1 Whole
We need to take away \( 1\frac{5}{6} \).
Uh-Oh! Not Enough Sixths!
We have \( \frac{2}{6} \), and we need to take away \( \frac{5}{6} \).
\( \frac{2}{6} - \frac{5}{6} \rightarrow \) We can't do that yet!
Solution: Trade 1 whole for \( \frac{6}{6} \)!
SUBTRACTION
Step 2: Break 1 Whole into Sixths
Before Regrouping: \( 3\frac{2}{6} \)
1
1
Trade!
Break that 1 whole into \( \frac{6}{6} \) and add it to \( \frac{2}{6} \):
After Regrouping: \( 2\frac{8}{6} \)
1
1
\( 3\frac{2}{6} = 2 + \frac{6}{6} + \frac{2}{6} = 2\frac{8}{6} \)
SUBTRACTION
Step 3: Subtract & Simplify
\( 2\frac{8}{6} - 1\frac{5}{6} \)
Subtract Wholes: \( 2 - 1 = 1 \)
Subtract Sixths: \( \frac{8}{6} - \frac{5}{6} = \frac{3}{6} \)
Simplify \( \frac{3}{6} \): \( \frac{3 \div 3}{6 \div 3} = \frac{1}{2} \)
Final Answer:
\( 1\frac{1}{2} \)
Always check: Is the fraction in simplest form?
Let's Build Together!
TRY A: ADD
\( 2\frac{2}{3} + 1\frac{5}{6} \)
1. Common denominator: 6
2. Add wholes & sixths
3. Regroup if numerator ≥ 6!
TRY B: SUBTRACT
\( 4\frac{1}{4} - 1\frac{1}{2} \)
1. Common denominator: 4
2. Need more fourths? Trade 1 whole!
3. Subtract & simplify
Fraction Builders Worksheet Fraction Builders Practice
GRADES 4–5
Name: ____________________________________
Date: __________________
ADD
Find same-size pieces (common denominator). 2. Add wholes & fractions. 3. Regroup extra pieces into a whole!
SUBTRACT
Find same-size pieces. 2. If top fraction is too small, trade 1 whole for fraction pieces. 3. Subtract & simplify!
Part 1: Visual Fraction Bar Warm-Up
Use the fraction bars to help you find same-size pieces, regroup, and solve. Show your steps in the box.
1. \( 1\frac{2}{3} + 1\frac{1}{2} = \) ____________
2. \( 2\frac{1}{4} - \frac{5}{8} = \) ____________
Part 2: Addition with Regrouping
3. \( 2\frac{3}{4} + 1\frac{3}{8} = \) __________
4. \( 1\frac{4}{5} + 2\frac{7}{10} = \) __________
Part 3: Subtraction with Regrouping
Find a common denominator, trade 1 whole when needed, and write your answer in simplest form.
5. \( 3\frac{1}{2} - 1\frac{3}{4} = \) __________
6. \( 4\frac{1}{3} - 2\frac{5}{6} = \) __________
7. \( 5\frac{1}{4} - 1\frac{5}{8} = \) __________
8. \( 3\frac{2}{5} - 1\frac{7}{10} = \) __________
Part 4: Workshop Challenge
9. Maya has a wooden board that is \( 4\frac{1}{3} \) feet long. She cuts off a piece that is \( 1\frac{3}{4} \) feet long to build a birdhouse. How many feet of wood does Maya have left?
Answer: ________________________ feet
Fraction Builders Answer Key Fraction Builders Answer Key
TEACHER GUIDE
Part 1: Visual Fraction Bar Warm-Up
1. \( 1\frac{2}{3} + 1\frac{1}{2} \)
Common denominator: \( 6 \)
\( 1\frac{4}{6} + 1\frac{3}{6} = 2\frac{7}{6} \)
Regroup: \( 2 + 1\frac{1}{6} = 3\frac{1}{6} \)
2. \( 2\frac{1}{4} - \frac{5}{8} \)
Common denominator: \( 8 \)
\( 2\frac{2}{8} - \frac{5}{8} \rightarrow \) Trade 1 whole: \( 1\frac{10}{8} - \frac{5}{8} \)
Answer: \( 1\frac{5}{8} \)
Part 2: Addition with Regrouping
3. \( 2\frac{3}{4} + 1\frac{3}{8} \)
Common denominator: \( 8 \)
\( 2\frac{6}{8} + 1\frac{3}{8} = 3\frac{9}{8} \)
Regroup: \( 3 + 1\frac{1}{8} = 4\frac{1}{8} \)
4. \( 1\frac{4}{5} + 2\frac{7}{10} \)
Common denominator: \( 10 \)
\( 1\frac{8}{10} + 2\frac{7}{10} = 3\frac{15}{10} = 4\frac{5}{10} \)
Simplify: \( 4\frac{1}{2} \)
Part 3: Subtraction with Regrouping
5. \( 3\frac{1}{2} - 1\frac{3}{4} \)
Common denominator: \( 4 \)
\( 3\frac{2}{4} - 1\frac{3}{4} \rightarrow 2\frac{6}{4} - 1\frac{3}{4} \)
Answer: \( 1\frac{3}{4} \)
6. \( 4\frac{1}{3} - 2\frac{5}{6} \)
Common denominator: \( 6 \)
\( 4\frac{2}{6} - 2\frac{5}{6} \rightarrow 3\frac{8}{6} - 2\frac{5}{6} = 1\frac{3}{6} \)
Simplify: \( 1\frac{1}{2} \)
7. \( 5\frac{1}{4} - 1\frac{5}{8} \)
Common denominator: \( 8 \)
\( 5\frac{2}{8} - 1\frac{5}{8} \rightarrow 4\frac{10}{8} - 1\frac{5}{8} \)
Answer: \( 3\frac{5}{8} \)
8. \( 3\frac{2}{5} - 1\frac{7}{10} \)
Common denominator: \( 10 \)
\( 3\frac{4}{10} - 1\frac{7}{10} \rightarrow 2\frac{14}{10} - 1\frac{7}{10} \)
Answer: \( 1\frac{7}{10} \)
Part 4: Workshop Challenge
9. \( 4\frac{1}{3} - 1\frac{3}{4} \)
Step 1: Find common denominator of \( 12 \): \( 4\frac{4}{12} - 1\frac{9}{12} \)
Step 2: Trade 1 whole for \( \frac{12}{12} \): \( 3\frac{16}{12} - 1\frac{9}{12} \)
Answer: Maya has \( 2\frac{7}{12} \) feet of wood left.
Slide 8 Guided Practice Key: Try A: \( 2\frac{4}{6} + 1\frac{5}{6} = 3\frac{9}{6} = 4\frac{3}{6} = \mathbf{4\frac{1}{2}} \) | Try B: \( 4\frac{1}{4} - 1\frac{2}{4} = 3\frac{5}{4} - 1\frac{2}{4} = \mathbf{2\frac{3}{4}} \)
