Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Weight is a measure of how heavy an object is. We use standard units to measure weight so that it is the same for everyone. The two main units are Grams () for lighter objects like a pencil or a cookie, and Kilograms () for heavier objects like a school bag or a watermelon.
A weighing balance is a tool used to compare weights. It usually consists of a central beam and two pans hanging from either end. To find out if two objects weigh the same, we place them in opposite pans; if the beam stays straight and horizontal, the weights are equal.
Understanding the balance of weight visually: When one pan of a weighing balance is lower than the other, it indicates that the object in the lower pan is heavier. Conversely, the pan that is higher up contains the lighter object. Imagine a seesaw at the park; the person who is heavier stays on the ground while the lighter person is lifted up.
Standard weights are metal blocks of known quantities, such as , , , , or . To measure an unknown object, we place it in one pan and keep adding these standard weights to the other pan until the two pans are perfectly level or balanced.
Conversion between units is essential for calculation. Since is equal to , we multiply the number of kilograms by to get the weight in grams. To convert grams back to kilograms, we divide the value by .
Estimating weights helps us choose the correct unit. Small items like a gold ring or a spoon are measured in , while larger items like a human being, a sack of rice, or a chair are measured in . Visualizing a packet of salt can help you estimate if other objects are heavier or lighter than a kilogram.
When adding or subtracting weights, always keep the units separate. Add grams to grams and kilograms to kilograms. If the total grams exceed , convert them into kilograms and add them to the kilogram column (carry over).
📐Formulae
💡Examples
Problem 1:
Riya bought of apples and of mangoes. What is the total weight of the fruits she bought?
Solution:
Step 1: Write down the weights in columns for and . Step 2: Add the grams: . Step 3: Convert to and : . Step 4: Add the kilograms: . Total weight = .
Explanation:
To find the total weight, we add the grams and kilograms separately. Because the grams totaled more than , we carried over to the kilogram column.
Problem 2:
How many weights are needed to balance a block of wood?
Solution:
Step 1: Convert the weight of the wood block into grams so the units match. . Step 2: Divide the total weight by the size of the small weight. Number of weights = . Step 3: Calculate the division: . Result: weights.
Explanation:
To compare or divide weights, they must be in the same unit. Converting kilograms to grams first makes it easy to calculate how many smaller weights fit into the larger total.