Ratio Conversion Quiz: Converting Ratios to Fractions and Decimals

12:30 written as a fraction is 12/30. Dividing by 6 gives 2/5, confirming A. Dividing 2 by 5 gives 0.4, confirming B. The fraction 4/10 simplifies to 2/5, confirming C. Option D gives 5/2 which equals 2.5, not 0.4, so it is not equivalent to 12:30.

0.2 equals 1/5, so the ratio 1:5 confirms A. The fraction 2/10 simplifies to 1/5 = 0.2, confirming B. The ratio 20:100 simplifies to 1:5 = 0.2, confirming C. Option D gives 5:1 which equals 5.0, not 0.2 — this is the inverted ratio.

Simplify 9/12 by dividing numerator and denominator by 3 to get 3/4. Divide 3 by 4 to get 0.75. Option A gives the unsimplified fraction. Option B gives 2/3, which equals 0.666..., not 0.75. Option C gives 1/4, which equals 0.25, not 0.75. Only 3/4 is the simplified form that produces the stated decimal.

The answer is False. Write 1:8 as 1/8. Divide 1 by 8 to get 0.125, not 0.08. The value 0.08 corresponds to 8/100 or 2/25, not 1/8. A common error is confusing 1/8 with 8/100 because of the 8 in the denominator, but the correct decimal for 1/8 is 0.125.

Write 4:25 as 4/25. Divide 4 by 25 to get 0.16. Option A inverts the ratio. Option C gives 2/5 which equals 0.4, not 0.16 — this would require simplifying 4/25 to 2/5, but 4 and 25 share no common factor so the fraction is already in simplest form. Option D has the right fraction but the wrong decimal, 4 divided by 25 is 0.16 not 0.14.

Simplify 45/60 by dividing by 15 to get 3/4, confirming A. Divide 3 by 4 to get 0.75, confirming B. The fraction 9/12 simplifies to 3/4, confirming C. Option D gives 4/3 which equals 1.333..., not 0.75, so it is not equivalent to 45:60.

Write 13:20 as 13/20. Divide 13 by 20 to get 0.65. Option A gives 0.60, which corresponds to 12/20. Option B gives 0.75, which corresponds to 15/20. Option C gives 0.50, which corresponds to 10/20. Only 0.65 correctly results from dividing 13 by 20.

Write 2:5 as the fraction 2/5. Divide 2 by 5 to get 0.4. Option A inverts the ratio giving 5/2 which equals 2.5. Option B gives 2/10, which simplifies to 1/5 not 2/5. Option C gives 1/5, which equals 0.2 not 0.4. Only 2/5 correctly represents the ratio and produces the stated decimal.

The answer is True. Write 7:8 as 7/8. Divide 7 by 8: 8 times 0.8 = 6.4, 8 times 0.87 = 6.96, 8 times 0.875 = 7.00. So 7 divided by 8 = 0.875 exactly. This is a terminating decimal because the denominator 8 has only factors of 2. The statement is confirmed correct.

Write 7:3 as 7/3. Divide 7 by 3 to get 2.333... with the digit 3 repeating. Option A inverts the fraction and gives the decimal for 3/7. Option C has the right fraction but incorrectly truncates the decimal at 2.3 rather than showing it as repeating. Option D gives an unsimplified equivalent fraction but also truncates incorrectly.

Write 3:4 as the fraction 3/4. Divide 3 by 4 to get 0.75. The fraction is already in simplest form since 3 and 4 share no common factors. Option B inverts the fraction. Option C has the wrong decimal. Option D adds the terms as a denominator giving 3/7, which misrepresents the ratio.

Simplify 6/15 by dividing numerator and denominator by 3, giving 2/5. Divide 2 by 5 to get 0.4. Option A gives the unsimplified fraction with the wrong decimal. Option B gives the wrong simplified fraction — 6 divided by 15 in lowest terms is 2/5 not 3/5. Option D has the right fraction but the wrong decimal, 2 divided by 5 is 0.4 not 0.5.

Write 3:8 as the fraction 3/8. Divide 3 by 8 to get 0.375. Option A inverts the ratio. Option B gives 3/5, which equals 0.6 not 0.375. Option C gives 1/3, which equals 0.333... not 0.375. Only 3/8 correctly represents the ratio and produces the stated decimal.

The answer is True. Write 14:21 as 14/21. Divide numerator and denominator by 7 to get 2/3. Performing division, 2 divided by 3 = 0.666... with 6 repeating. Both the simplification step and the decimal conversion are correct, confirming the statement.

Write 11:4 as 11/4. Divide 11 by 4: 4 times 2 = 8, remainder 3, giving 2 and 3/4 = 2.75. Option A has the right fraction but the wrong decimal, 2.25 corresponds to 9/4. Option B inverts the fraction. Option C gives an equivalent unsimplified fraction but pairs it with the wrong decimal 2.25. Only option D has both the correct fraction and correct decimal.

8:20 written as a fraction is 8/20. Dividing numerator and denominator by 4 gives 2/5, confirming A. Dividing 2 by 5 gives 0.4, confirming B. The fraction 4/10 simplifies to 2/5, confirming C. Option D gives 5/2 which equals 2.5, not 0.4, so it is not equivalent to 8:20.

Simplify 9/12 by dividing numerator and denominator by 3, giving 3/4. Divide 3 by 4 to get 0.75. Option B gives the unsimplified fraction with the correct decimal but does not simplify as required. Option C has the right fraction but the wrong decimal. Option D inverts the fraction to 4/3, which equals 1.333, not 0.75.

Write 7:10 as the fraction 7/10. Divide 7 by 10 to get 0.7. Option A inverts the ratio. Option B places 7 over 100 instead of 10, giving 0.07 not 0.7. Option C gives 1/7, which equals approximately 0.143, not 0.7. Only 7/10 correctly represents the ratio and produces the stated decimal.

The answer is True. Write 2:3 as 2/3. Performing long division, 2 divided by 3 gives 0.666... with the digit 6 repeating infinitely. This is a non-terminating repeating decimal, often written as 0.6 with a bar over the 6. The fraction 2/3 is already in simplest form since 2 and 3 share no common factors.

Write 5:2 as the fraction 5/2. Divide 5 by 2 to get 2.5. Option B inverts the fraction and gives the wrong decimal. Option C has the fraction right but the wrong decimal — 5 divided by 2 is 2.5 not 0.5. Option D inverts the fraction but pairs it with the correct decimal for 5/2, making it inconsistent.