Ratio Proportion Quiz: Master Ratio Proportion Quiz

Write 3:4 as the fraction 3/4. Divide 3 by 4 to get 0.75. Option B inverts the fraction but keeps the decimal, making the pair inconsistent. Option C has the right fraction but the wrong decimal. Option D adds the ratio terms as the denominator giving 3/7, which misrepresents the ratio.

Set up the proportion: flour divided by 150 = 2 divided by 5. Flour = 150 times (2 divided by 5) = 300 divided by 5 = 60 g. Check: 60:150 divided by 30 gives 2:5, confirming the ratio. Option A gives 50 g, requiring the ratio 1:3. Option B gives 55 g, which has no clean ratio to 150. Option D gives 65 g, also no clean ratio. Only 60 g satisfies the 2:5 proportion.

The answer is True. The greatest common factor of 44 and 66 is 22. Dividing both terms by 22 gives 44÷22=2 and 66÷22=3, producing the simplified ratio 2:3. No further simplification is possible since 2 and 3 share no common factors other than 1. The statement is confirmed correct.

14:21 simplifies by dividing both by 7 to give 2:3, confirming A. Multiplying 2:3 by 14 gives 28:42, confirming B. The ratio 6:9 simplifies by dividing by 3 to give 2:3, confirming C. Option D gives 4:7, which would require dividing 14 by 3.5 and 21 by 3, different factors, so it is not equivalent to 14:21.

Set up the proportion: bike speed divided by 80 = 3 divided by 5. Bike speed = 80 times (3 divided by 5) = 240 divided by 5 = 48 km/h. Option A gives 45, requiring the ratio to be 9:16. Option C gives 50, requiring 5:8. Option D gives 52, which has no clean ratio relationship to 80. Only 48 satisfies the 3:5 proportion.

The greatest common factor of 300, 200, and 100 is 100. Dividing all three terms by 100 gives 300÷100=3, 200÷100=2, 100÷100=1, producing the simplified ratio 3:2:1. Option B gives 6:4:2, which divides only by 50 and can be simplified further. Option C reverses the order. Option D rearranges the terms incorrectly.

The scale factor is 32 divided by 4 = 8. Apply the same factor to the second term: b = 7 times 8 = 56. Check: 32:56 divided by 8 gives 4:7, confirming the ratio. Option A gives 49 = 7 times 7, using scale factor 7. Option B gives 52, which has no clean relationship to the ratio. Option D gives 63 = 7 times 9, using scale factor 9.

The answer is True. In a ratio of 2:3, the two terms represent separate parts of a whole. Adding the parts gives 2 plus 3 = 5 total parts. This means that in any group of marbles with this ratio, every 5 marbles contain 2 red and 3 blue. The total parts concept is fundamental to dividing quantities in a given ratio.

Real distance = 3 times 250,000 = 750,000 cm. Converting to kilometres: 750,000 divided by 100,000 = 7.5 km. Option B gives 6.0 km = 600,000 cm, which would require a map distance of 2.4 cm. Option C gives 5.0 km = 500,000 cm, requiring 2 cm. Option D gives 3.0 km = 300,000 cm, requiring 1.2 cm. Only 7.5 km correctly multiplies 3 by the scale factor.

12:30 simplifies by dividing both by 6 to give 2:5, confirming A. Dividing 2 by 5 gives 0.4, confirming B. The ratio 4:10 simplifies by dividing by 2 to give 2:5, confirming C. Option D gives 5:2, which equals 2.5 and is the inverse ratio, not equivalent to 12:30.

The greatest common factor of 18 and 24 is 6. Dividing both terms by 6 gives 18÷6=3 and 24÷6=4, so the simplified ratio is 3:4. Option B gives 2:3, which would require dividing by 9 and 12 respectively, not the same factor. Options C and D bear no relationship to the original terms.

The greatest common factor of 63 and 81 is 9. Dividing both terms by 9 gives 63÷9=7 and 81÷9=9, so the simplified ratio is 7:9. Option A gives 6:8, which simplifies further to 3:4 and has no relationship to 63 and 81. Option B gives 8:9, which does not result from dividing 63 and 81 by the same factor. Option D gives 5:7, also unrelated.

The answer is True. The greatest common factor of 28 and 35 is 7. Dividing both terms by 7 gives 28÷7=4 and 35÷7=5, producing the ratio 4:5. No further simplification is possible since 4 and 5 share no common factors other than 1. The statement is confirmed correct.

The greatest common factor of 300 and 500 is 100. Dividing both by 100 gives 300÷100=3 and 500÷100=5, so the simplified ratio is 3:5. Option A gives 2:3, which would require different original values. Options C and D have no relationship to 300 and 500.

Set up the proportion: boys divided by 35 = 5 divided by 7. Boys = 35 times (5 divided by 7) = 175 divided by 7 = 25. Option A gives 20, which would require the ratio to be 4:7. Option C gives 30, requiring a ratio of 6:7. Option D gives 35, which would mean a 1:1 ratio. Only 25 satisfies the 5:7 proportion.

Multiplying both terms of 5:8 by 2 gives 10:16, confirming A. Multiplying by 3 gives 15:24, confirming B. Multiplying by 4 gives 20:32, confirming C. Option D gives 5:7, which changes the second term from 8 to 7 and is therefore a different ratio entirely, not equivalent to 5:8.

The greatest common factor of 4 and 6 is 2. Dividing both terms by 2 gives 4÷2=2 and 6÷2=3, so the simplest form is 2:3. Option B gives 3:4, which has no relationship to 4:6. Option C gives 4:5, which is already a different ratio. Option D gives 6:9, which is equivalent to 2:3 but is not in simplest form.

The greatest common factor of 21 and 14 is 7. Dividing both terms by 7 gives 21÷7=3 and 14÷7=2, so the simplified ratio is 3:2. Note the order matters — 21 comes first so the simplified form is 3:2 not 2:3. Options A, C, and D do not result from dividing 21 and 14 by any common factor.

The answer is True. The greatest common factor of 15 and 20 is 5. Dividing both terms by 5 gives 15÷5=3 and 20÷5=4, producing the simplified ratio 3:4. No further simplification is possible since 3 and 4 share no common factors other than 1.

The greatest common factor of 45 and 60 is 15. Dividing both by 15 gives 45÷15=3 and 60÷15=4, so the ratio is 3:4. Option A gives 2:3, which does not result from any common factor of 45 and 60. Options C and D bear no relationship to the given values.