Percentages of a Number

Excitement buzzed through the air as Liam, Maya, and Zoey embarked on a thrilling cave adventure in Eureka Shores. Dressed in their explorer hats and carrying little flashlights, the trio followed a cheerful tour guide named Sparkle the Gnome. Inside the cave, the walls sparkled with crystals of every color imaginable, casting a magical glow that captured the children's wide-eyed wonder.

The cave seemed like a hidden treasure trove filled with sparkling gems, like a real-life fairy tale. As they journeyed deeper, Liam pointed to a cluster of crystals that shone like rainbows, and Maya marveled at the ones that glowed in the dark. Zoey, with her adventurous spirit, couldn't resist touching the cool, smooth surfaces of the crystals as they walked through the enchanted cavern.

Towards the end of the tour, Sparkle the Gnome gathered the kids around a particularly dazzling formation. With a twinkle in his eye, he shared a fascinating secret. "Guess what, little explorers? Twenty-five percent of these incredible crystals are likely over 500 years old! Imagine all the magical stories they could tell if they could talk!" he exclaimed, leaving Liam, Maya, and Zoey in awe of the ancient wonders hidden within the heart of the cave.

Zoey raised her hand, “And how many crystals are in this teensy cave?”

Sparkle the Gnome grinned, “Well Zoey, around 80!”

Zoey pondered to herself for a moment. How many crystals were over 500 years old, then? She would need to figure out how to find 25% of 80. Thankfully, Orion was on the trek with them, and he was a percentage genius.

Orion pointed up at the crystals, “First, we need to understand the percentage. We need to find out 25% of 80 magical crystals."

The group trekked forwards, coming across more amethyst crystals. The purple formations were so intricate and detailed.

“Then, we convert the percentage to a fraction. 25% is the same as 25/100. When we simplify that by dividing the numerator and denominator by 25, we get ¼. It's like saying we want one part out of four parts of the magical crystals."

That makes sense, Zoey thought, remembering the percentage rules.

"Now, multiply the fraction (1/4) by the total number of crystals (80). Only multiply the numerator, remember! So by multiplying 1 by 80, we get 80. When we divide that by the denominator, or 4, we get 20! So around 20 crystals are over 500 years old."

Maya listened to the conversation as they approached the other side of the cave. Wasn’t there another way to solve this problem without fractions?

“Wait, can’t you also convert the percentage to a decimal?” Maya asked curiously.

Orion nodded eagerly, “Yep! Let's journey down the decimal path. Converting 25% to a decimal, we move the decimal point two places to the left, so 25% becomes 0.25. Both 25% and 0.25 are equal to 25/100."

Maya remembered when Zoey had taught them about decimals, percentages, and fractions. They were more related than she had initially thought!

“Then, we multiply 0.25 by the total number of crystals (80), and we find the same result—20 magical crystals.”

Zoey added, "It's like we have multiple magical maps to guide us, each revealing the same hidden treasures using different mathematical methods."

When the group got back to the visitor center of the cave, they filled out a quick quiz in order to get a fancy junior ranger badge. And to their surprise, one of the questions asked about how many crystals were 500 years or older! The options were 21, 40, 5, and 78. Thanks to their calculations, they were able to choose the best guess, 21, and all got their junior ranger badges! Percentages really did come in handy.