WISKUNDE
GRAAD 10
NOG OEFENINGE
Optelling en aftrekking van algebraïese breuke : notas en voorbeelde.
MATHEMATICS
GRADE 10
MORE EXERCISES
addition and subtraction of algebraic fractions : notes and examples.
Notas.
Optelling of aftrekking van breuke : verander elke
noemer na die kleinste gemene noemer, (die KGV
van al die noemers), verander al die tellers
en vind dan die algebraïse som van al
die nuwe tellers en behou die gemene noemer.
Antwoorde moet altyd in die eenvoudigste vorm
gegee word. As geen noemer gegee word nie,
mag die noemer 1 gebruik word.
Notes.
To add or subtract fractions : change all the
denominators to the lowest common denominator,
(the LCM of all the denominators), change all the
numerators and then find the algebraical sum of the
new numerators and retain the common denominator.
Answers should always be given in the lowest terms.
When no denominator is expressed (shown), the
denominator 1 may be understood.
Voorbeelde / Examples
2 3
1. ── ┼ ── = ?
5 7
Bereken die KGV van al die noemers / Calculate the LCM of all the denominators.
KGV / LCM = 5 X 7 = 35
kleinste gemene noemer / lowest common denominator = 35
Verander elke noemer na die kleinste gemene noemer (35) en verander ook die teller. /
Change each numerator to the lowest common denominator (35) and also change the numerator.
2 2 X 7 14 3 3 X 5 15
── = ───── = ── ── = ──── = ───
5 5 X 7 35 7 7 X 5 35
14 15 29
Tel op / Add : ─── ┼ ─── = ───
35 35 35
2 3 2 X 7 + 3 X 5
Skryf die antwoord neer / Write down the answer : ─── ┼ ─── = ──────────
5 7 5 X 7
14 + 15
= ───────
35
29
= ───
35
ae 3c
2. ─── ┼ ──── = ?
2b 10d
Bereken die KGV van al die noemers / Calculate the LCM of all the denominators.
KGV / LCM = 2 X b X 5 X d = 10bd
kleinste gemene noemer / lowest common denominator = 10bd
Verander elke noemer na die kleinste gemene noemer (10bd) en verander ook die teller. /
Change each numerator to the lowest common denominator (10bd) and also change the numerator.
ae ae X 5d 5ade 3c 3c X b 3bc
─── = ────── = ───── ─── = ────── = ────
2b 2b X 5d 10bd 10d 10d X b 10bd
5ade 3bc 5ade + 3bc
Tel op / Add : ───── ┼ ──── = ─────────
10bd 10bd 10bd
ae 3bc ae X 5d + 3c X b
Skryf die antwoord neer / Write down the answer : ─── ┼ ──── = ──────────────
2b 10d 2b X 5d
5ade + 3bc
= ───────
10bd