seegongsik
Grade 5 (age 10-11)

grade 5 Mixed Number Operations

A mixed number like 2 3/5 is a whole number and a proper fraction written together, and an improper fraction like 13/5 has a numerator equal to or bigger than its denominator. If you have 2 whole pizzas and 3/5 of another, counting pizzas gives 2 3/5 and counting only fifths gives 13/5: the same amount written two ways. To add mixed numbers, add the whole numbers and the fractions separately, and if the fractions add up to 1 or more, carry 1 over to the whole numbers. The first picture draws a mixed number as circle pieces and turns it into an improper fraction; the second adds two mixed numbers step by step.

Mixed and Improper Fractions

🍕 Mixed numbers as pizza slices
①In the first picture, the orange circles are whole pizzas and the circle partly shaded green holds the leftover slices. The starting values are 2 whole pizzas and 3/5 of another, so 2 3/5
②Each pizza has 5 slices, so the 2 whole pizzas are 2 × 5 = 10 slices; add 3 more and you get 13 slices, so 2 3/5 = 13/5
③Going the other way, to turn 13/5 into a mixed number, work out 13 ÷ 5 = 2 R 3: the quotient 2 is the whole number and the remainder 3 is the numerator
④Set the numerator to 0 and only whole pizzas are left; change the denominator and each pizza is cut into a different number of slices
2
3
5

Adding Mixed Numbers

💡 Adding mixed numbers
①Add the whole numbers and the fractions separately. The starting values are 2 3/5 + 1 4/5, so the wholes give 2 + 1 = 3 and the fractions give 3/5 + 4/5 = 7/5
②7/5 is more than 1, so rewrite it as 1 2/5 and carry the 1 over: 3 + 1 = 4, and the answer is 4 2/5
③Fractions can only be added directly when they share a denominator, so the two numbers in the picture always use the same one. If the denominators differ, rewrite the fractions with a common denominator first
④Turning both into improper fractions, 13/5 + 9/5 = 22/5, gives the same answer
1
4

Summary

Mixed number to improper fraction
a and b/c = a×c + bc
Whole number × denominator + numerator becomes the new numerator; the denominator stays the same
Improper fraction to mixed number
135 = 2 and 35
The quotient of numerator ÷ denominator is the whole number and the remainder is the new numerator
Adding mixed numbers
Add the wholes, add the fractions
If the fractions add up to 1 or more, carry 1 over to the whole numbers
🎯 At a glance
①Mixed number: a whole number and a proper fraction together
②Improper fraction: numerator equal to or bigger than the denominator
③Mixed to improper: whole number × denominator + numerator, over the same denominator
④Adding mixed numbers: add the wholes and the fractions separately
⑤If the fractions make 1 or more, carry 1

Examples and Unit Test

Example 1
Write the mixed number 2 3/5 as an improper fraction.
1
Whole number × denominator + numerator: 2 × 5 + 3 = 13.
2
The denominator stays 5, so it is 13/5.
▸ 135
This is the starting setting of the first picture, where 2 × 5 + 3 = 13 pieces is written under the circles.
Example 2
Write the improper fraction 13/5 as a mixed number.
1
13 ÷ 5 = 2 remainder 3.
2
The quotient 2 is the whole number and the remainder 3 is the numerator: 2 3/5.
▸ 235
To turn an improper fraction into a mixed number, use the quotient and remainder of numerator ÷ denominator.
Unit Test
What is the value of 1 2/5 + 1 1/5?
①215
②235
③2310
④335
▸ ② 235
1
Add the whole numbers: 1 + 1 = 2.
2
Add the fractions: 2/5 + 1/5 = 3/5, which is less than 1, so there is no carry and the answer is 2 3/5.
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Decimal Multiplication & Division
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Mixed Operations

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