Ratio Proportion Quiz: Master Ratio Proportion Quiz

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 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 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 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 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.

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 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.

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.

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 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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.