Answer:
See Explanation
Step-by-step explanation:
Required
Write three equivalent ratios
To solve these questions, we do the following:
Whatever is being applied to a part of the ratio must be done on the other part
Solving (9):
[tex]Ratio = \frac{2}{7}[/tex]
Multiply through by 2
[tex]Ratio = \frac{2*2}{7*2} = \frac{4}{14}[/tex]
Multiply through by 3
[tex]Ratio = \frac{2*3}{7*3} = \frac{6}{21}[/tex]
Multiply through by 5
[tex]Ratio = \frac{2*5}{7*5} = \frac{10}{35}[/tex]
Hence, the equivalents are: [tex]\frac{4}{14}, \frac{6}{21}, \frac{10}{35}[/tex]
Solving (10):
Ratio = 1.5 to 3.5
Multiply by 2
[tex]Ratio = 1.5 * 2\ to\ 3.5 * 2[/tex]
[tex]Ratio = 3\ to\ 7[/tex]
Multiply by 3
[tex]Ratio = 1.5 * 3\ to\ 3.5 * 3[/tex]
[tex]Ratio = 4.5\ to\ 10.5[/tex]
Multiply by 4
[tex]Ratio = 1.5 * 4\ to\ 3.5 * 4[/tex]
[tex]Ratio = 6\ to\ 14[/tex]
Hence, the equivalents are: 3 to 7, 4.5 to 10.5 and 6 to 14
Solving (11):
Ratio = 6.25 to 1.25
Divide by 5
[tex]Ratio = 6.25/5\ to\ 1.25/5[/tex]
[tex]Ratio = 1.25\ to\ 0.25[/tex]
Multiply by 2
[tex]Ratio = 6.25*2\ to\ 1.25*2[/tex]
[tex]Ratio = 12.5\ to\ 2.5[/tex]
Multiply by 4
[tex]Ratio = 6.25*4\ to\ 1.25*4[/tex]
[tex]Ratio = 25\ to\ 5[/tex]
Hence, the equivalents are: 1.25 to 0.25, 12.5 to 2.5 and 25 to 5
Solving (12):
[tex]Ratio = 3 : 3\frac{1}{2}[/tex]
Multiply by 2
[tex]Ratio = 3 *2: 3\frac{1}{2}*2[/tex]
[tex]Ratio = 6: 7[/tex]
Multiply by 4
[tex]Ratio = 3 *4: 3\frac{1}{2}*4[/tex]
[tex]Ratio = 12: 14[/tex]
Multiply by 6
[tex]Ratio = 3 *6: 3\frac{1}{2}*6[/tex]
[tex]Ratio = 18: 21[/tex]
Hence, the equivalents are: 6:7, 12:14 and 18:21
Solving (13)
[tex]Ratio = 1\frac{2}{3} : \frac{5}{4}[/tex]
Convert mixed fraction to improper fraction
[tex]Ratio = \frac{5}{3} : \frac{5}{4}[/tex]
Multiply by 2
[tex]Ratio = \frac{5}{3}*2 : \frac{5}{4}*2[/tex]
[tex]Ratio = \frac{10}{3} : \frac{5}{2}[/tex]
Multiply by 3
[tex]Ratio = \frac{5}{3}*3 : \frac{5}{4}*3[/tex]
[tex]Ratio = 5 : \frac{15}{4}[/tex]
Multiply by 12
[tex]Ratio = \frac{5}{3}*12 : \frac{5}{4}*12[/tex]
[tex]Ratio = 20 : 15[/tex]
Hence, the equivalents are: 10/3:5/2, 5 : 15/4, and 20:15
