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Grade 5 (age 10-11)

Mixed Number Operations

Mixed Number Operations

Mixed and Improper Fractions
🍕 Understand mixed numbers via pizza
①2 whole pizzas + 3/5 slice = mixed number 2 and 3/5
②Counting only slices = 13/5 (improper)
③Converting mixed ↔ improper is key
2
3
5
Adding Mixed Numbers
1
4
💡 How to Add Mixed Numbers
①Add wholes and fractions separately
②If fraction sum ≥ 1, carry!
③Same denominators are required to add fractions
Summary
Mixed → Improper
a and b/c = a×c + bc
New numerator = whole × denominator + numerator
Improper → Mixed
135 = 2 and 35
Numerator ÷ denominator = whole ... remainder
Adding Mixed
wholes + fractions (carry)
If fractions sum > 1, carry 1 to wholes
🎯 Key Points
①Mixed = whole + proper fraction
②Improper: numerator ≥ denominator
③Convert: whole × denom + numer
④Adding: wholes and fractions separately
⑤Carry when fractions sum ≥ 1!
Examples and Unit Test
Example 1
Convert the mixed number 2 3/5 to an improper fraction.
1
New numerator = whole × denominator + numerator: 2 × 5 + 3 = 13.
2
The denominator stays 5, so it is 13/5.
▸ 135
Mixed → improper: (whole × denominator + numerator) / denominator.
Example 2
Convert the improper fraction 13/5 to a mixed number.
1
Divide numerator by denominator: 13 ÷ 5 = 2 remainder 3.
2
The quotient 2 is the whole, the remainder 3 is the new numerator: 2 3/5.
▸ 235
Improper → mixed: numerator ÷ denominator = whole ... remainder (new numerator).
Unit Test
What is the value of 1 2/5 + 1 1/5?
①215
②235
③2310
④335
▸ ② 235
1
Add the wholes: 1 + 1 = 2.
2
Add the fractions: 2/5 + 1/5 = 3/5. So it is 2 3/5.
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