Si m p l i f y i n g Fr a ct i o n s
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A fraction can n am e a p a rt of a group or region. The region below is divided into
10 equal parts and 6 of the equal parts are shaded.b - N u m e r a t o r Read as ..six tenths
10 DenominatorTwo fractions th a t represent th e sam e value are called equivalent fractions.
You can find a fraction th at is equivalent to a given fraction by m ultiplying the
n um erator an d th e d en o m in ato r of th e given fraction by th e sam e n onzero num ber.
Ex a m p l e 1
Write five fractions that are equivalent to a.
3 3 2 6 3 3 3 9 3 3 • 4 12 3 = 3 • 5 = 15 3 3 • 6 18
55-2 10 55-3 15 55-4 20 555 25 556 30
q
The fraction g is in simplest form because its num erator and denom inator are relatively
prime, which m eans their only com m on factor is 1. To write a fraction in simplest form,
divide its num erator and its denom inator by their greatest com m on factor (GCF).
Ex a m p l e 2
c
Write 24 in sim plest form.
St e p 1 Find the GCF of 6 and 24.
6 = 2 * 3 M u ltip ly the common prime factors, 2 and 3.
2 4 = 2 • 2 • 2 • 3 GCF = 2 • 3 = 6.St e p 2 Divide the n u m era to r an d th e d en o m in ato r of ^ by th e GCF, 6.
6 _ 6 ± 6 _ 1 <- ■ i t
24 24 4 - 6 4 Simplify.Ex e r c i se s
Write five fractions that are equivalent to each fraction.
(^1) i.? — z. 7 — 16 4 — 8 4 17 — 5 — 6 f i — 10
Complete each statement.
7 3 M o 5 20 q U=44 1f1 12 _ ■ 44 50 1
'• 7 21 8 ■ 12 ■ 16 4 M ' 100 I
Is each fraction in sim plest form? If not, write the fraction in sim plest form.
- jg 14. gg 15. ^2 1 6- 22 1 7 ‘ 25
Write each fraction in sim plest form.
(^18)! 8. 16 — 1 19 — 9. 14 2 20 - 0. g (^21) 1. 30 — 2 22 — 2. 2Q 2 23 —4. 40 2