Explanation:
We are simplifying fractions — that means reducing them to their lowest terms. To do this, we find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number.
Let’s go through each problem step by step and simplify:
1) $ \frac{12}{8} $
GCD of 12 and 8 is 4.
$ 12 ÷ 4 = 3 $, $ 8 ÷ 4 = 2 $ → $ \frac{3}{2} $
2) $ \frac{22}{14} $
GCD of 22 and 14 is 2.
$ 22 ÷ 2 = 11 $, $ 14 ÷ 2 = 7 $ → $ \frac{11}{7} $
3) $ \frac{36}{27} $
GCD of 36 and 27 is 9.
$ 36 ÷ 9 = 4 $, $ 27 ÷ 9 = 3 $ → $ \frac{4}{3} $
4) $ \frac{42}{72} $
GCD of 42 and 72 is 6.
$ 42 ÷ 6 = 7 $, $ 72 ÷ 6 = 12 $ → $ \frac{7}{12} $
5) $ \frac{24}{15} $
GCD of 24 and 15 is 3.
$ 24 ÷ 3 = 8 $, $ 15 ÷ 3 = 5 $ → $ \frac{8}{5} $
6) $ \frac{96}{40} $
GCD of 96 and 40 is 8.
$ 96 ÷ 8 = 12 $, $ 40 ÷ 8 = 5 $ → $ \frac{12}{5} $
7) $ \frac{52}{13} $
13 divides 52 exactly: $ 52 ÷ 13 = 4 $, so $ \frac{4}{1} = 4 $
8) $ \frac{56}{21} $
GCD of 56 and 21 is 7.
$ 56 ÷ 7 = 8 $, $ 21 ÷ 7 = 3 $ → $ \frac{8}{3} $
9) $ \frac{62}{26} $
GCD of 62 and 26 is 2.
$ 62 ÷ 2 = 31 $, $ 26 ÷ 2 = 13 $ → $ \frac{31}{13} $
10) $ \frac{108}{27} $
27 divides 108: $ 108 ÷ 27 = 4 $ → $ \frac{4}{1} = 4 $
11) $ \frac{121}{55} $
GCD of 121 and 55 is 11.
$ 121 ÷ 11 = 11 $, $ 55 ÷ 11 = 5 $ → $ \frac{11}{5} $
12) $ \frac{52}{28} $
GCD of 52 and 28 is 4.
$ 52 ÷ 4 = 13 $, $ 28 ÷ 4 = 7 $ → $ \frac{13}{7} $
13) $ \frac{80}{140} $
GCD of 80 and 140 is 20.
$ 80 ÷ 20 = 4 $, $ 140 ÷ 20 = 7 $ → $ \frac{4}{7} $
14) $ \frac{45}{135} $
GCD of 45 and 135 is 45.
$ 45 ÷ 45 = 1 $, $ 135 ÷ 45 = 3 $ → $ \frac{1}{3} $
15) $ \frac{66}{42} $
GCD of 66 and 42 is 6.
$ 66 ÷ 6 = 11 $, $ 42 ÷ 6 = 7 $ → $ \frac{11}{7} $
16) $ \frac{140}{50} $
GCD of 140 and 50 is 10.
$ 140 ÷ 10 = 14 $, $ 50 ÷ 10 = 5 $ → $ \frac{14}{5} $
17) $ \frac{108}{144} $
GCD of 108 and 144 is 36.
$ 108 ÷ 36 = 3 $, $ 144 ÷ 36 = 4 $ → $ \frac{3}{4} $
18) $ \frac{60}{200} $
GCD of 60 and 200 is 20.
$ 60 ÷ 20 = 3 $, $ 200 ÷ 20 = 10 $ → $ \frac{3}{10} $
Let me double-check a few tricky ones:
- #11: 121 = 11×11, 55 = 5×11 → yes, $ \frac{11}{5} $
- #14: 45 × 3 = 135 → yes, $ \frac{1}{3} $
- #17: 108/144 = divide by 12 → 9/12 = 3/4 → correct.
- #18: 60/200 = 6/20 = 3/10 → correct.
All simplified correctly.
Final Answer:
1) $ \frac{3}{2} $
2) $ \frac{11}{7} $
3) $ \frac{4}{3} $
4) $ \frac{7}{12} $
5) $ \frac{8}{5} $
6) $ \frac{12}{5} $
7) $ 4 $
8) $ \frac{8}{3} $
9) $ \frac{31}{13} $
10) $ 4 $
11) $ \frac{11}{5} $
12) $ \frac{13}{7} $
13) $ \frac{4}{7} $
14) $ \frac{1}{3} $
15) $ \frac{11}{7} $
16) $ \frac{14}{5} $
17) $ \frac{3}{4} $
18) $ \frac{3}{10} $
Parent Tip: Review the logic above to help your child master the concept of simplifying fractions worksheet grade 6.
