10. Compare the following ratios :
(i) 2 : 3 or 4 : 7
(ii) 11 : 15 or 14 : 25
(iii) 15 : 27 or 2 : 9 (iv) 108 : 63 or 18 : 21
11. Divide 360 in the ratio 7: 8.
1
12. Divide 440 in the ratio
1
[HOTS]
5 6
13. Divide 560 in the ratio 1:3 : 4.
14. The sides of a triangle are in the ratio 4: 5: 2. Find the sides of the triangle, if its
perimeter is 660 cm.
15. The boys and the girls in a school are in the ratio 6 : 5. If total strength of the school
be 880, find the number of boys and girls.
16. The ratio of monthly income to the savings of a family is 7 : 2. If the savings be
500, find the income and expenditure.
17. The ratio of zinc and copper in an alloy is 7: 9. If the weight of the copper in the alloy
is 11.7kg, find the weight of the zinc in the alloy.
18. Find the ratio of consonants to vowels in MATHEMATICS SUCCESS.
[Hors]
Answers
Answer:
In comparison of ratios, we first need to convert them into like fractions by using the following steps and then compare them.
Step I: Obtain the given ratios.
Step II: Now we express each of the given ratios as a fraction in the simplest form.
Step III: Find the L.C.M (least common multiple) of the denominators of the fractions obtained in the above step (Step II).
Step IV: Obtain the first fraction and its denominator. Divide the L.C.M (least common multiple) obtained in the above step (Step III) by the denominator to get a number z (say).
Now, multiply the numerator and denominator of the fraction by the z (L.C.M). Similarly apply the same procedure to the all other fraction.
In other words convert each fraction to its equivalent fractions with denominator equal to the L.C.M (least common multiple).
Thus, the denominators of all the fractions are be same.
Step V: Compare the numerators of the equivalent fractions whose denominators are same.
Compare the numerators of the fractions obtained in the above step (Step IV). The fraction having larger numerator will be larger than the other fraction.
Two or more ratios can be compared by writing their equivalent fractions with common denominators.
Solved examples of comparison of ratios:
1. Compare the ratios 4 : 5 and 2 : 3.
Solution:
Express the given ratios as fraction
4 : 5 = 4/5 and 2 : 3 =2/3
Now find the L.C.M (least common multiple) of 5 and 3
The L.C.M (least common multiple) of 5 and 3 is 15.
Making the denominator of each fraction equal to 15, we have
4/5 = (4 ×3)/(5 ×3) = 12/15 and 2/3 = (2 ×5)/(3 ×5) = 10/15
Clearly, 12 > 10
Now, 12/15 > 10/15
Therefore, 4 : 5 > 2 : 3.
2. Compare the ratios 5 : 6 and 7 : 9.
Solution:
Express the given ratios as fraction
5 : 6 = 5/6 and 7 : 9 =7/9
Now find the L.C.M (least common multiple) of 6 and 9
The L.C.M (least common multiple) of 6 and 9 is 18.
Making the denominator of each fraction equal to 18, we have
5/6 = (5 ×3)/(6 ×3) = 15/18 and 7/9 = (7 ×2)/(9 ×2) = 14/18
Clearly, 15 > 14
Now, 15/18 > 14/18
Therefore, 5 : 6 > 7 : 9.
3. Compare the ratios 1.2 : 2.5 and 3.5 : 7.
Solution:
1.2 : 2.5 = 1.2/2.5 and 3.5 : 7 =3.5/7
1.2/2.5 = (1.2 ×10)/(2.5 ×10 ) = 12/25 and 3.5/7 = (3.5 ×10)/(7 ×10) = 35/70 = 1/2
[We removed the decimal point from the ratios now, we will compare the ratio]
Now find the L.C.M (least common multiple) of 25 and 2
The L.C.M (least common multiple) of 25 and 2 is 50.
Making the denominator of each fraction equal to 50, we have
= 12/25 = (12 ×2)/(25 ×2) = 24/50 and 1/2 = (1 ×25)/(2 ×25) = 25/50
Now, 25/50 > 24/50
Therefore,the answer is 3.5 : 7 > 1.2 : 2.5.
Step-by-step explanation:If my answer is right please thank me and add me as brainly list.
Answer:
on vomparing5:15and2:3,we find that the smaller ration is