10 is even, it can be paired All the tens and hundreds can be paired. * 10: Represented by a single block rod of $10$ units, split with arrows into two equal groups of $5$ unit cubes each ( $5 + 5 = 10$ ). * 20: Represented by two block rods of $10$ units, split with arrows into two equal groups, each containing one block rod of $10$ units ( $10 + 10 = 20$ ). * 50: Represented by five block rods of $10$ units, split with arrows into two equal groups, each containing two block rods of $10$ units and $5$ unit cubes ( $25 + 25 = 50$ ).

Answer: Since $10 = 2 \times 5$ , $10$ is an even number. Consequently, any multiple of $10$ (such as $20 = 2 \times 10$ , $50 = 2 \times 25$ , or any hundred) can always be partitioned into two equal groups with no remainder.

Step-by-step solution

Step 1: Understand pairing and even numbers

A whole number is called even if it can be divided into $2$ equal groups without leaving any remainder. Here, $10$ items can be split into $2$ equal groups of $5$ , which shows that $10$ is an even number.

Step 2: Analyze the decomposition of 10

A rod representing $1$ ten consists of $10$ individual unit cubes. When divided equally between $2$ groups, each group gets exactly $5$ unit cubes, leaving no remainder.

Step 3: Analyze the decomposition of 20

The number $20$ consists of $2$ rods of ten. We can divide the rods directly so that each group receives $1$ full rod of $10$ units, giving $10 + 10 = 20$ .

Step 4: Analyze the decomposition of 50 and general tens

The number $50$ consists of $5$ rods of ten. Four rods split evenly into $2$ rods for each group, and the remaining rod of $10$ splits into two groups of $5$ units. Thus, each group receives $2$ rods and $5$ units, totaling $25 + 25 = 50$ . In general, any multiple of $10$ can be written as $10k = 2(5k)$ , so all multiples of $10$ and $100$ are always even and can be paired.

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