Compare the ratios in Table 1 and Table 2. Table 1 3 5 6 10 9 15 12 20 Table 2 7 10 14 20 21 30 28 40 Which statements about the ratios are true? Check all that apply. The ratio 3:5 is less than the ratio 7:10. The ratio 3:5 is greater than the ratio 7:10. The ratio 14:20 is less than the ratio 9:15. The ratio 14:20 is greater than the ratio 9:15. The ratios in Table 1 are less than the ratios in Table 2. The ratios in Table 1 are greater than the ratios in Table 2.
Answers
All table 1 Ratios are less than the ratios in Table 2
Step-by-step explanation:
Table 1
3:5 , 6 : 10 , 9 :15 , 12 : 20
Table 2
7 : 10 , 14 : 20 , 21 : 30 , 28 : 40
All table 1 Ratios are equal
All table 2 Ratios are equal
3 : 5
= 6 : 10
6 < 7
=> 6 : 10 < 7 : 10
=> 3 : 5 < 7 : 10
=> The ratio 3:5 is less than the ratio 7:10
All table 1 Ratios are equal
All table 2 Ratios are equal
=> All table 1 Ratios are less than the ratios in Table 2
The ratio 14:20 is greater than the ratio 9:15.
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The tables 1 and 2 can be represented in a readable form in the following way :
The ratios listed in Table 1 are - 3 : 5, 6 : 10, 9 : 15, 12 : 20
The ratios listed in Table 2 are - 7 : 10, 14 : 20, 21 : 30, 28 : 40
• To compare two ratios, we need to equalise the second terms of both the ratios by finding their L.C.M.
• In the ratios 3 : 5 and 7 : 10, the second terms are 5 and 10 respectively. Their L.C.M. is 10.
• Now, the ratio 3 : 5 can be represented as 3 / 5 and the ratio 7 : 10 can be represented as 7 / 10.
• Then, the L.C.M. 10 is divided by the denominator of each fraction, and the quotient is multiplied by both the numerator and denominator.
• For 3 / 5,
L.C.M. / denominator = 10 / 5 = 2 (quotient)
Now, (3 × 2) / (5 × 2) = 6 / 10
• For 7 / 10,
L.C.M. / denominator = 10 / 10 = 1 (quotient)
Now, (7 × 1) / (10 × 1) = 7 / 10
• When the denominators are equal, the fraction with the smaller numerator is smaller.
• Numerator 6 < Numerator 7
=> 6 / 10 < 7 / 10.
=> 3 / 5 < 7 / 10
=> 3 : 5 < 7 : 10
Hence, the statement, "The ratio 3 : 5 is less than the ratio 7 : 10" is correct.
• Similarly, for 14 : 20 and 9 : 15, the second terms are 20 and 15 respectively.
• 14 : 20 = 14 / 20
9 : 15 = 9 / 15
• L.C.M. of 20 and 15 = 60
• For 14 / 20,
L.C.M. / denominator = 60 / 20 = 3
Now, (14 × 3) / (20 × 3) = 42 / 60
• For, 9 / 15,
L.C.M. / denominator = 60 / 15 = 4
Now, (9 × 4) / (15 × 4) = 36 / 60
• Numerator 42 > Numerator 36
=> 42 / 60 > 36 / 60
=> 14 : 20 = 9 : 15
The statement, "The ratio 14 : 20 is greater than the ratio 9 : 15" is true.
• From the above two calculations, it can be stated that the ratios in table 1 are less than those in table 2.