48
Adding and subtracting mixed numbers
Textbook: Part 2, lesson 48, pp. 44–49
GoalAdd and subtract mixed numbers; breaking up a whole.
New words
whole parts · butun qismlarfractional parts · kasr qismlarbreaking up a whole · maydalashdifference · ayirma
Explanation
When we add mixed numbers, whole parts are added to whole parts and fractional parts to fractional parts. If the sum of the fractional parts is an improper fraction, we take the whole part out and add it to the sum of the whole parts. Subtraction also works part by part. If the fractional part of the minuend is smaller than that of the subtrahend, we break up one whole of the minuend: 5 1/6 = 4 7/6. The same is done when a mixed number is subtracted from a whole number: 4 = 3 5/5. The denominator always stays the same.
Worked examples
2 5/8 + 1 6/8: whole parts 2 + 1 = 3, fractions 5/8 + 6/8 = 11/8 = 1 3/8; total 3 + 1 3/8 = 4 3/8.
5 1/6 − 2 4/6: 1/6 < 4/6, so 5 1/6 = 4 7/6. Then 4 7/6 − 2 4/6 = 2 3/6.
Class activity
“Breaking up”: draw 3 whole circles and, to find 3 − 1 1/4, cut one circle into 4 quarters. How many whole circles and how many quarters remain?
Practice
1
Calculate 2 3/9 + 4 5/9.
6 8/9
2
Calculate 3 5/7 + 2 4/7.
6 2/7
3
Calculate 7 2/10 − 3 5/10.
3 7/10
4
Why do we write 6 as 5 4/4 when calculating 6 − 2 1/4?
The subtrahend has a fraction, so one whole of 6 must be broken into quarters: 6 = 5 + 4/4.