COMPARING FRACTIONS WITH DIFFERENT DENOMINATORS

Determine which fraction is greater.

Problem 2 :

5/8, 13/20

Solution :

By considering the denominator (8 and 20), they are not same. So, we will take the least common multiple.

LCM (8, 20) = 40

= (5/8) x (5/5) ==> 25/40

= (13/20) x (2/2) ==> 26/40

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

26/40 > 25/40

13/20 > 5/8

Problem 3 :

7/12, 11/15

Solution :

By considering the denominator (12 and 15), they are not same. So, we will take the least common multiple.

LCM (12, 15) = 60

= (7/12) x (5/5) ==> 35/60

= (11/15) x (4/4) ==> 44/60

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

44/60 > 35/60

11/15 > 7/12

Problem 4 :

5/16, 3/10

Solution :

By considering the denominator (16 and 10), they are not same. So, we will take the least common multiple.

LCM (16, 10) = 80

= (5/16) x (5/5) ==> 25/80

= (3/10) x (8/8) ==> 24/80

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

25/80 > 24/80

5/16 > 3/10

Problem 5 :

3/4, 5/8

Solution :

By considering the denominator (4 and 8), they are not same. So, we will take the least common multiple.

LCD (4, 8) = 8

= (3/4) x (2/2) ==> 6/8

= (5/8) x (1/1) ==> 5/8

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

6/8 > 5/8

3/4 > 5/8

Problem 6 :

2/3, 13/16

Solution :

By considering the denominator (3 and 16), they are not same. So, we will take the least common multiple.

LCD (3, 16) = 48

= (2/3) x (16/16) ==> 32/48

= (13/16) x (3/3) ==> 39/48

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

39/48 > 32/48

13/16 > 2/3

Problem 7 :

2/5, 3/8

Solution :

By considering the denominator (5 and 8), they are not same. So, we will take the least common multiple.

LCD (5, 8) = 40

= (2/5) x (8/8) ==> 16/40

= (3/8) x (5/5) ==> 15/40

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

16/40 > 15/40

2/5 > 3/8

Problem 8 :

3/4, 7/10

Solution :

By considering the denominator (4 and 10), they are not same. So, we will take the least common multiple.

LCD (4, 10) = 20

= (3/4) x (5/5) ==> 15/20

= (7/10) x (2/2) ==> 14/20

15/20 > 14/20

3/4 > 7/10

Tell which number is greater :

Problem 9 :

0.9, 95%

Solution :

0.9 = 9/10

95% = 95/100

Least common multiple of 10 and 100 is 100.

9/10 x 10/10 = 90/100

Comapring the fraction 90/100 and 95/100

90/100 < 95/100

So, 95% is greater.

Problem 9 :

You make 75% of your shots, your sister makes 13/20 of her shots, and your friend makes 0.7 of his shots. Who made the most shots?

Solution :

Your shots = 75%

= 75/100

Number of shots your sister make = 13/20

= 13/20 x 5/5

= 65/100

Shots your friend make = 0.7

= 0.7 x 10/10

= 7/10

Least common multiple of 10 and 100 is 100.

= 7/10 x 10/10

= 70/100

Comparing 75/100, 65/100 and 70/100, 75/100 is greater. That is, you made more shots.

Problem 10 :

How would you decide whether 3/5 or 59% is greater? Explain.

Solution :

3/5

59% = 59/100

Least common multiple of 5 and 100 is 100.

= 3/5 x 20/20

= 60/100

Comparing 60/10 and 59/100, 60/100 is greater. Then 3/5 is greater.

Problem 11 :

You answer 21 out of 25 questions correctly on a test. Did you reach your goal of getting 80% or better?

Solution :

Your answer = 21/25

Goal = 80%

= 80/100

Least common multiple of 25 and 100 is 100.

= 21/25 x 4/4

= 84/100

You have reached the goal. Your score is better