Convert Units Using Ratio Reasoning - 6th Grade Math

1. What is $2\ \text{kg}$ in grams using ratio reasoning?

   $2000\ \text{g}$. Multiply: $2\ \text{kg} \times \frac{1000\ \text{g}}{1\ \text{kg}} = 2000\ \text{g}$.

2. What is the key rule for placing units in a conversion factor so units cancel?

   Put the unwanted unit in the denominator so it cancels. This ensures units cancel when multiplying.

3. What conversion factor equals $1$ for converting meters to centimeters?

   $\frac{100\ \text{cm}}{1\ \text{m}}$. Since $100\ \text{cm} = 1\ \text{m}$, this fraction equals $1$.

4. What conversion factor equals $1$ for converting hours to minutes?

   $\frac{60\ \text{min}}{1\ \text{h}}$. Since $60\ \text{min} = 1\ \text{h}$, this fraction equals $1$.

5. What is $750\ \text{mL}$ in liters using ratio reasoning?

   $0.75\ \text{L}$. Multiply: $750\ \text{mL} \times \frac{1\ \text{L}}{1000\ \text{mL}} = 0.75\ \text{L}$.

6. What is $3\ \text{m}^2$ in $\text{cm}^2$?

   $30000\ \text{cm}^2$. Since $1\ \text{m} = 100\ \text{cm}$, then $1\ \text{m}^2 = 10000\ \text{cm}^2$.

7. What is $60\ \text{mi/hr}$ in $\text{mi/min}$?

   $1\ \text{mi/min}$. Divide 60 by 60 to convert hours to minutes in the rate.

8. What is $4\ \text{h}$ in minutes?

   $240\ \text{min}$. $4\ \text{h} \times \frac{60\ \text{min}}{1\ \text{h}} = 240\ \text{min}$

9. What conversion factor equals $1$ for converting centimeters to meters?

   $\frac{1\ \text{m}}{100\ \text{cm}}$. Since 1 meter equals 100 centimeters, this fraction equals 1.

10. What is $90\ \text{min}$ in hours?

    $1.5\ \text{h}$. $90\ \text{min} \times \frac{1\ \text{h}}{60\ \text{min}} = 1.5\ \text{h}$

11. What conversion factor equals $1$ for converting inches to feet?

    $\frac{1\ \text{ft}}{12\ \text{in}}$. Since $1\ \text{ft} = 12\ \text{in}$, this fraction equals $1$.

12. What is $250\ \text{cm}$ in meters using ratio reasoning?

    $2.5\ \text{m}$. Multiply: $250\ \text{cm} \times \frac{1\ \text{m}}{100\ \text{cm}} = 2.5\ \text{m}$.

13. What conversion factor equals $1$ for converting liters to milliliters?

    $\frac{1000\ \text{mL}}{1\ \text{L}}$. Since $1000\ \text{mL} = 1\ \text{L}$, this fraction equals $1$.

14. What is $36\ \text{in}$ in feet?

    $3\ \text{ft}$. $36\ \text{in} \times \frac{1\ \text{ft}}{12\ \text{in}} = 3\ \text{ft}$

15. What conversion factor equals $1$ for converting minutes to hours?

    $\frac{1\ \text{hr}}{60\ \text{min}}$. Since $1 \text{ hour} = 60 \text{ minutes}$, this fraction equals 1.

16. What is $2500\ \text{g}$ in kilograms?

    $2.5\ \text{kg}$. Divide 2500 by 1000 since there are 1000 g per kg.

17. What is $1200\ \text{g}$ in kilograms?

    $1.2\ \text{kg}$. $1200\ \text{g} \times \frac{1\ \text{kg}}{1000\ \text{g}} = 1.2\ \text{kg}$

18. What is $1500\ \text{g}$ in kilograms using ratio reasoning?

    $1.5\ \text{kg}$. Multiply: $1500\ \text{g} \times \frac{1\ \text{kg}}{1000\ \text{g}} = 1.5\ \text{kg}$.

19. What is $1250\ \text{mL}$ in liters?

    $1.25\ \text{L}$. Divide 1250 by 1000 since there are 1000 mL per liter.

20. Identify the unit that cancels when you multiply $5\ \text{ft}$ by $\frac{12\ \text{in}}{1\ \text{ft}}$.

    $\text{ft}$. The ft units cancel: $\frac{5\ \text{ft} \cdot 12\ \text{in}}{1\ \text{ft}}$.

21. What conversion factor equals $1$ for converting minutes to seconds?

    $\frac{60\ \text{s}}{1\ \text{min}}$. Since $60\ \text{s} = 1\ \text{min}$, this fraction equals $1$.

22. What is $3.2\ \text{m}$ in centimeters?

    $320\ \text{cm}$. $3.2\ \text{m} \times \frac{100\ \text{cm}}{1\ \text{m}} = 320\ \text{cm}$

23. What is $2.5\ \text{ft}$ in inches?

    $30\ \text{in}$. $2.5\ \text{ft} \times \frac{12\ \text{in}}{1\ \text{ft}} = 30\ \text{in}$

24. What is $2.5\ \text{h}$ in minutes using ratio reasoning?

    $150\ \text{min}$. Multiply: $2.5\ \text{h} \times \frac{60\ \text{min}}{1\ \text{h}} = 150\ \text{min}$.

25. What is $2.5\ \text{L}$ in milliliters?

    $2500\ \text{mL}$. $2.5\ \text{L} \times \frac{1000\ \text{mL}}{1\ \text{L}} = 2500\ \text{mL}$

26. Find the speed in $\text{ft}/\text{s}$: $60 \text{ft}$ in $5 \text{s}$.

    $12 \text{ft}/\text{s}$. Divide distance by time: $\frac{60 \text{ft}}{5 \text{s}} = 12 \text{ft}/\text{s}$.

27. What is $150 \text{s}$ in minutes?

    $2.5 \text{min}$. $150 \text{s} \times \frac{1 \text{min}}{60 \text{s}} = 2.5 \text{min}$

28. What is $0.75\ \text{kg}$ in grams?

    $750\ \text{g}$. $0.75\ \text{kg} \times \frac{1000\ \text{g}}{1\ \text{kg}} = 750\ \text{g}$

29. What conversion factor equals $1$ for converting grams to kilograms?

    $\frac{1\ \text{kg}}{1000\ \text{g}}$. Since 1 kilogram equals 1000 grams, this fraction equals 1.

30. What is the correct setup to convert $36\ \text{in}$ to feet using unit fractions?

    $36\ \text{in}\times\frac{1\ \text{ft}}{12\ \text{in}}$. Multiply by the conversion factor to cancel inches.

31. What is $3.6\ \text{m}$ in centimeters using ratio reasoning?

    $360\ \text{cm}$. Multiply: $3.6\ \text{m} \times \frac{100\ \text{cm}}{1\ \text{m}} = 360\ \text{cm}$.

32. What is $3 \text{ min}$ in seconds?

    $180 \text{ s}$. $3 \text{ min} \times \frac{60 \text{ s}}{1 \text{ min}} = 180 \text{ s}$

33. What conversion factor equals $1$ for converting milliliters to liters?

    $\frac{1\ \text{L}}{1000\ \text{mL}}$. Since 1 liter equals 1000 milliliters, this fraction equals 1.

34. What is $180\ \text{s}$ in minutes using ratio reasoning?

    $3\ \text{min}$. Multiply: $180\ \text{s} \times \frac{1\ \text{min}}{60\ \text{s}} = 3\ \text{min}$

35. What is $2.5\ \text{hr}$ in minutes?

    $150\ \text{min}$. Multiply 2.5 by 60 since there are 60 minutes per hour.

36. What is $1.2\ \text{L}$ in milliliters using ratio reasoning?

    $1200\ \text{mL}$. Multiply: $1.2\ \text{L} \times \frac{1000\ \text{mL}}{1\ \text{L}} = 1200\ \text{mL}$.

37. What conversion factor equals $1$ for converting kilograms to grams?

    $\frac{1000\ \text{g}}{1\ \text{kg}}$. Since $1000\ \text{g} = 1\ \text{kg}$, this fraction equals $1$.

38. What is $600\ \text{mL}$ in liters?

    $0.6\ \text{L}$. $600\ \text{mL} \times \frac{1\ \text{L}}{1000\ \text{mL}} = 0.6\ \text{L}$

39. What is $450\ \text{cm}$ in meters?

    $4.5\ \text{m}$. $450\ \text{cm} \times \frac{1\ \text{m}}{100\ \text{cm}} = 4.5\ \text{m}$

40. What is $2\ \text{m/s}$ in $\text{m/min}$?

    $120\ \text{m/min}$. Multiply 2 by 60 to convert seconds to minutes in the rate.

41. What is $48\ \text{in}$ in feet using ratio reasoning?

    $4\ \text{ft}$. Multiply: $48\ \text{in} \times \frac{1\ \text{ft}}{12\ \text{in}} = 4\ \text{ft}$.

42. What conversion factor equals $1$ for converting feet to inches?

    $\frac{12\ \text{in}}{1\ \text{ft}}$. Since $12\ \text{in} = 1\ \text{ft}$, this fraction equals $1$.

43. What is $3\ \text{L}$ in milliliters?

    $3000\ \text{mL}$. Multiply 3 by 1000 since there are 1000 mL per liter.

44. What is $3\ \text{ft}$ in inches using ratio reasoning?

    $36\ \text{in}$. Multiply: $3\ \text{ft} \times \frac{12\ \text{in}}{1\ \text{ft}} = 36\ \text{in}$.

Study these flashcards