Comparing Weight and Capacity

Comparing weight and capacity means looking at two or more objects or containers and deciding which one is heavier, lighter, holds more, or holds less. This skill uses everyday comparison words like heavier, lighter, more, less, and the same as, and it is the foundation for later work with exact units and numbers.

Weight tells us how heavy an object is. When we compare weight, we are not measuring an exact number yet; we are simply deciding which object is heavier or lighter, or if they weigh the same. A balance scale is one of the best tools for this because it tips down on the side with the heavier object and up on the side with the lighter object.

In the picture above, the rock's side of the scale goes down while the feather's side goes up. This tells us the rock is heavier than the feather, and the feather is lighter than the rock. If both sides of the scale stayed level, the two objects would weigh the same amount.

Once objects have been measured with real units such as grams, kilograms, ounces, or pounds, comparing becomes even more precise because you can compare the numbers directly. For a closer look at how those units are measured, see Measuring weight.

Capacity tells us how much a container can hold, such as water, juice, or sand. When comparing capacity, we decide which container holds more, which holds less, or if they hold the same amount.

One way to compare capacity without any numbers is to fill one container with liquid and pour it into another. If liquid overflows, the first container held more. If there is empty space left, the first container held less. If the liquid fills the second container exactly to the top, the two containers hold the same amount. For details on the standard units used once you start measuring capacity exactly, such as milliliters, liters, cups, and gallons, check out Measuring capacity.

Once weight or capacity has been measured, comparing turns into comparing numbers, but only when the units match. For example, \(3\) kilograms is heavier than \(2\) kilograms because \(3 \gt 2\). But you cannot say \(3\) kilograms is heavier than \(5\) pounds just by comparing \(3\) and \(5\), since kilograms and pounds are different units. Always check that the units are the same before comparing the numbers.

Example 1: A bag of apples weighs \(4\) kilograms and a bag of oranges weighs \(6\) kilograms. Which bag is heavier?

Since both weights use the same unit, kilograms, we compare \(4\) and \(6\). Because \(6 \gt 4\), the bag of oranges is heavier, and the bag of apples is lighter.

Example 2: A water bottle holds \(500\) milliliters and a jug holds \(2\) liters. Which container has the greater capacity?

Here the units are different, so first change \(2\) liters into milliliters: \(2 \times 1000 = 2000\) milliliters. Now compare \(500\) milliliters to \(2000\) milliliters. Since \(2000 \gt 500\), the jug has the greater capacity.

Sometimes you must compare three or more objects or containers at once. The strategy is the same: line up the measurements in the same unit, then arrange them from smallest to largest or from largest to smallest.

Example 3: Three bags weigh \(2\) kilograms, \(5\) kilograms, and \(3\) kilograms. Ordering them from lightest to heaviest gives \(2\) kilograms, \(3\) kilograms, \(5\) kilograms.

Before comparing, make sure both measurements use the same type of unit, since you can only compare weight with weight and capacity with capacity, never one against the other. It also helps to picture a balance scale for weight and a pouring test for capacity, even when the problem only gives you numbers. When you are not given exact measurements at all, comparing often starts with a reasonable guess about size or heaviness, which is explored further in Estimating weight and capacity.

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