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Grade 5 (age 10-11)

Mixed Number Operations

Mixed Number Operations

A mixed number joins a whole number with a proper fraction, like two pizzas and three fifths written as two and three fifths. Counting only the slices makes an improper fraction such as thirteen fifths, so switching between the two forms is the key skill. Slide the parts to watch the pie slices show each conversion and the carry when adding.

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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