Answer to Question #206681 in Algebra for Nonkululeko

Question

a. Arrange the following fractions from biggest to smallest: 5/8; 4/4; 2/6; 3/7; 1/2

b. Compare the following fractions according to the instruction Bellow:

The symbol: < means less then; the symbol > means greater than, and the symbol = means equal to

Fill, in<,> or =

a. 1/2 [ ] 1/3 b. 1/2 [ ] 2/6

c. 1/3 [ ] 3/6 d. 1/2 [ ] 2/3

e. 2/3 [ ] 1/6 f. 5/6 [ ] 2/3

g. 2/3 [ ] 6/6 h. 1/3 [ ] 4/6

I. 4/6 [ ] 1/2 j. 1/2 [ ] 3/3

k. 1/2 [ ] 1/6 l. 5/6 [ ] 1/2

Answer 1

We know that for the fractions having the same denominator, the fraction with largest numerator is the largest. 

So to solve this problem we want to make denominator of all the given 5 fractions in to a same number.

Here we are using LCM(Least common multiple) as the common denominator.

a). Numbers in the denominator are:-

8,4,6,7,2

L. C. M of 8,4,6,7,2 is:-

So make denominators of all the fractions into:-168

$\frac{5}{8}=\frac{5×21}{8×21}=\frac{105}{168}$

$\frac{4}{4}=\frac{4×42}{4×42}=\frac{168}{168}$

$\frac{2}{6}=\frac{2×28}{6×28}=\frac{56}{168}$

$\frac{3}{7}=\frac{3×24}{7×24}=\frac{72}{168}$

$\frac{1}{2}=\frac{84}{168}$

So the fractions given from the biggest to the smallest is:-

$\frac{4}{4},\frac{5}{8},\frac{1}{2},\frac{3}{7},\frac{2}{6}$

b)

(a)

$\frac{1}{2}=\frac{3}{6},\frac{1}{3}=\frac{2}{6}$

$\frac{1}{2}>\frac {1}{3}$

(b) $\frac{1}{2}=\frac{3}{6},\frac{2}{6}$

$\frac{1}{2}>\frac{2}{6}$

(c) $\frac{1}{3}=\frac{2}{6},\frac{3}{6}$

$\frac{1}{3}<\frac{3}{6}$

(d)$\frac{1}{2}=\frac{3}{6},\frac{2}{3}=\frac{4}{6}$

$\frac{1}{2}<\frac{2}{3}$

(e) $\frac{2}{3}=\frac{4}{6},\frac{1}{6}$

$\frac{2}{3}>\frac{1}{6}$

(f) $\frac{5}{6},\frac{2}{3}=\frac{4}{6}$

$\frac{5}{6}>\frac{2}{3}$

(g) $\frac{2}{3}=\frac{4}{6},\frac{6}{6}$

$\frac{2}{3}<\frac{6}{6}$

(h) $\frac{1}{3}=\frac{2}{6},\frac{4}{6}$

$\frac{1}{3}<\frac{4}{6}$

(i) $\frac{4}{6},\frac{1}{2}=\frac{3}{6}$

$\frac{4}{6}>\frac{1}{2}$

(j) $\frac{1}{2}=\frac{3}{6},\frac{3}{3}=\frac{6}{6}$

$\frac{1}{2}<\frac{3}{3}$

(k) $\frac{1}{2}=\frac{3}{6},\frac{1}{6}$

$\frac{1}{2}<\frac{1}{6}$

(l) $\frac{5}{6},\frac{1}{2}=\frac{3}{6}$

$\frac{5}{6}>\frac{1}{2}$