14
Adding and subtracting mixed numbers
Textbook, pp. 51–57
GoalLearn to add and subtract mixed numbers.
New words
mixed number · aralash sonwhole part · butun qismfractional part · kasr qismregrouping (borrowing from the whole) · butundan qarz olish
Explanation
To add mixed numbers, add the whole parts and the fractional parts separately. If the fractional sum is more than 1, take the whole out and add it to the whole part. To subtract, bring the fractional parts to a common denominator. If the fractional part of the minuend is smaller than that of the subtrahend, take one unit from the whole part and turn it into a fraction: 5 2/12 = 4 14/12. Then subtract the whole and fractional parts separately.
Worked examples
3 2/3 + 2 3/4 = 5 + 8/12 + 9/12 = 5 17/12 = 6 5/12.
5 1/6 − 2 3/4 = 5 2/12 − 2 9/12 = 4 14/12 − 2 9/12 = 2 5/12.
Class activity
“Recipe”: groups get a recipe (for example 2 1/2 cups of flour and 1 3/4 cups of sugar). They add to find the total cups and then subtract 1/2 cup of flour to see what is left.
Practice
1
Compute 2 1/2 + 3 2/3.
6 1/6
2
Compute 5 1/4 − 2 1/3.
2 11/12
3
A ribbon is 3 1/2 m long. 1 3/4 m was cut off. How many metres are left?
1 3/4
4
Why do we write 4 as 3 5/5 when computing 4 − 1 3/5?
We need a fractional part to subtract from: one unit becomes 5/5, so 3 5/5 − 1 3/5 = 2 2/5.