Equivalent Ratios

Show your work for each problem.

1.
Which ratio is equivalent to ?
1. a)
2. b)
3. c)
4. d)
Answer:
because and . The other options are not equivalent because they don't maintain the same ratio.
2.
Complete:
Answer: 10
Since , we multiply 5 by 2 as well: . So .
3.
Are and equivalent ratios?
1. a)No, they have different numbers
2. b)Yes, both simplify to
3. c)No, is larger
4. d)Yes, but only if you add 3 to each
Answer: Yes, both simplify to
simplifies to when you divide both parts by 4. Since , they are equivalent ratios.
4.
Find two ratios equivalent to .
Answer: 10:4, 15:6
1. Multiply both parts by 2: and 10:4
2. Now multiply both parts by 3: and 15:6
5.
Simplify to its simplest form.
Answer: 2:3
The GCF of 8 and 12 is 4. Dividing both by 4: and . So .
6.
A recipe uses flour and sugar in a ratio of . If you use 12 cups of flour, how much sugar do you need?
Answer: 8
1. What is the original flour amount in the ratio? 3
2. What multiplier turns 3 into 12? 4
3. Apply the same multiplier to sugar: 8
7.
Which pair of ratios is NOT equivalent?
1. a) and
2. b) and
3. c) and
4. d) and
Answer: and
, not . The other pairs are all equivalent: , , .
8.
Complete:
Answer: 12
Since , we multiply 3 by 4 as well: . So .
9.
Complete the ratio table for : Find values when the first number is 8, 12, and 20.
Answer: 14, 21, 35
1. For 8: What is ? So 14
2. For 12: What is ? So 21
3. For 20: What is ? So 35
10.
If you add 2 to both parts of , do you get an equivalent ratio?
1. a)Yes, adding keeps the ratio the same
2. b)No, you should subtract instead
3. c)Yes, both parts changed equally
4. d)No, is not equivalent to
Answer: No, is not equivalent to
Adding does NOT create equivalent ratios! means , but means . Only multiplying or dividing by the same number keeps ratios equivalent.
11.
Are and equivalent? Show your work.
Answer: Yes
1. Simplify by dividing both by 5: 3:5
2. Simplify by dividing both by 3: 3:5
3. Are they the same simplified ratio? yes
12.
A map scale is . If two cities are 3.5 cm apart on the map, what is the real distance in km?
Answer: 1.75
cm = m = km.
13.
Paint is mixed in a ratio of red:white = . If you have 35 liters of white paint, how much red paint do you need?
Answer: 10
1. What is the white part in the ratio? 7
2. What multiplier turns 7 into 35? 5
3. Apply the same multiplier to red: 10
14.
Which ratio is equivalent to ?
1. a)
2. b)
3. c)
4. d)
Answer:
The GCF of 6, 9, and 12 is 3. , , . So .
15.
If and , what is the value of ?
Answer: 15
Since , we multiply 5 by 3: . So .
16.
A school has students in the ratio of boys:girls = . If there are 420 girls, how many students are there in total?
Answer: 720
1. What multiplier turns 7 into 420? 60
2. How many boys are there? 300
3. What is the total? 720