44
Adding and subtracting fractions with the same denominator
Textbook: Part 2, lesson 44, pp. 31–34
GoalAdd and subtract fractions with the same denominator; simple equations with fractions.
New words
addend · qo‘shiluvchisum · yig‘indiminuend · kamayuvchidifference · ayirma
Explanation
When we add fractions with the same denominator, the numerators are added and the denominator stays the same: a/c + b/c = (a + b)/c. When we subtract, the numerator of the subtrahend is taken from that of the minuend and the denominator again stays the same: a/c − b/c = (a − b)/c. It is easy to see with a cake cut into pieces: 2 fifths and 1 more fifth make 3 fifths. The name of the pieces (the denominator) does not change, only their number does. Equations work the same way: unknown addend = sum − known addend, unknown minuend = difference + subtrahend.
Worked examples
3/11 + 6/11 = (3 + 6)/11 = 9/11; 10/11 − 4/11 = (10 − 4)/11 = 6/11.
Equation x + 2/9 = 7/9: x = 7/9 − 2/9 = 5/9. Check: 5/9 + 2/9 = 7/9, correct.
Class activity
“Collecting shares”: use a 12-square strip. Colour 5/12, then 4/12 more, and then cross out 3/12 of the 9/12 you have. Check the result on the strip.
Practice
1
Calculate 7/15 + 6/15.
13/15
2
Calculate 17/20 − 9/20.
8/20
3
3/8 of a jug is water, and juice fills another 2/8. What part of the jug is full?
5/8
4
Why is it wrong to say 3/10 + 4/10 = 7/20?
The size of the shares (the denominator) does not change; only numerators are added, the answer is 7/10.