Measurement (capacity)
Capacity is the amount of liquid a container can hold. Examples include water in a bottle, juice in a glass, or milk in a jug.
Units of Capacity:
– Liter (L): This is the basic unit of capacity. It is used to measure larger quantities of liquid.
– Milliliter (mL): This is a smaller unit used to measure smaller quantities of liquid.
– Conversion:
– 1 Liter = 1000 Milliliters.
Tools to Measure Capacity:
– Measuring Jugs or Cups: These often have marks to show amounts in liters and milliliters.
– Containers: Sometimes labeled to show their capacity in liters or milliliters.
Conversion of millilitres into liters and vise-versa
Key Concept:
– 1 liter (L) = 1000 milliliters (mL)
This means that:
– To convert liters to milliliters, you multiply by 1000.
– To convert milliliters to liters, you divide by 1000.
Converting Liters to Milliliters:
When you convert liters to milliliters, you’re moving from a larger unit to a smaller one, so you multiply by 1000.
Example 1:
Convert 2 liters to milliliters.
– Since 1 liter = 1000 milliliters,
2 L x 1000 = 2000 mL.
– Answer: 2 liters = 2000 milliliters.
Example 2:
Convert 5 liters to milliliters.
5 L x 1000 = 5000 mL.
– Answer: 5 liters = 5000 milliliters.
Converting Milliliters to Liters:
When you convert milliliters to liters, you’re moving from a smaller unit to a larger one, so you divide by 1000.
Example 1:
Convert 1500 milliliters to liters.
– Divide by 1000:
1500 mL ÷ 1000 = 1.5 L.
– Answer: 1500 milliliters = 1.5 liters.
Example 2:
Convert 750 milliliters to liters.
– 750 mL ÷ 1000 = 0.75 L.
– Answer: 750 milliliters = 0.75 liters.
How to Remember:
– Liters to milliliters: Multiply by 1000 (L → mL = big to small, so multiply).
– Milliliters to liters: Divide by 1000 (mL → L = small to big, so divide).
Practice Problems:
1. Convert 3 liters to milliliters.
– Solution: 3 L x 1000 = 3000 mL.
2. Convert 2500 milliliters to liters.
– Solution: 2500 mL ÷ 1000 = 2.5 L.
3. Convert 0.75 liters to milliliters.
– Solution: 0.75 L x 1000 = 750 mL
Addition and subtraction of capacity
Key Concepts:
– Units of capacity: The two main units are liters (L) and milliliters (mL).
– Conversions: Sometimes, you may need to convert between liters and milliliters to solve addition and subtraction problems.
– 1 liter (L) = 1000 milliliters (mL).
Addition of Capacity:
When adding capacities, make sure the units are the same. If they’re not, convert them to the same unit before adding.
Example 1:
“Ravi has a 1-liter bottle of water, and his friend has a 500 mL bottle. How much water do they have together?”
Step-by-Step Solution:
1. Convert liters to milliliters:
1 liter = 1000 mL.
2. Add the capacities:
1000 mL + 500 mL = 1500 mL .
3. Answer: They have 1500 milliliters (or 1.5 liters of water together.
Example 2:
“An oil can holds 3 liters of oil. Another can holds 1200 mL. How much oil do they hold in total?”
Step-by-Step Solution:
1. Convert 3 liters to milliliters:
3 x 1000 = 3000 mL.
2. Add the capacities:
3000 mL + 1200 mL = 4200 mL.
3. Answer: The two cans together hold 4200 milliliters or 4.2 liters .
Subtraction of Capacity:
When subtracting capacities, again, ensure the units are the same. If they are not, convert them first.
Example 1:
“A 2-liter bottle of juice has 800 mL left after some was poured out. How much juice was poured out?”
**Step-by-Step Solution**:
1. Convert liters to milliliters:
2. Subtract the remaining juice:
2000 mL – 800 mL = 1200 mL.
3. Answer: 1200 milliliters of juice was poured out.
Example 2:
“Priya has a 1.5-liter bottle of soda. She drinks 500 mL. How much soda is left?”
Step-by-Step Solution:
1. Convert liters to milliliters:
1.5 liters = 1500 mL.
2. Subtract the amount Priya drank: 1500 mL – 500 mL = 1000 mL.
3. Answer: 1000 milliliters or 1 liter of soda is left.
Tips for Addition and Subtraction of Capacity:
– Always check if the units (liters or milliliters) are the same.
– If liters and milliliters are given, convert one to match the other.
– Add or subtract the values once they are in the same unit.
– After adding or subtracting, you can convert back to the required unit (if needed).
Word problem
Priya has a juice jug that can hold 5 liters of juice. She uses the jug to fill smaller cups. Each cup can hold 1 liter of juice. If Priya fills 3 cups, how much juice will be left in the jug?
Step-by-Step Explanation:
1. Understand the Capacity of the Jug:
Priya has a jug that can hold 5 liters of juice. This means the jug is full with 5 liters of juice to start with.
2. Understand the Capacity of the Cups:
Each cup Priya uses can hold 1 liter of juice.
3. Number of Cups Used:
Priya fills 3 cups with juice.
4. Calculate the Total Juice Used:
Since each cup holds 1 liter and Priya fills 3 cups, the total juice used is:
1 liter × 3 cups = 3 liters.
5. Find How Much Juice is Left in the Jug:
Priya started with 5 liters in the jug, and she used 3 liters. So, to find how much is left, subtract:
5 liters – 3 liters = 2 liters.
Answer:
After filling 3 cups, Priya will have 2 liters of juice left in the jug.