Early one November morning at the Denver Zoo, a polar bear named Ulu gave birth to two baby bears. She cleaned them off, then left them lying on the cold cement floor of the hallway that led to her den. When Gary, the polar bear keeper, came to work, he heard soft crying. Gary could see that Ulu was in her den, but there were two small shapes in the hallway. When he looked closer, he found the newborn polar bear twins that Ulu had abandoned. Gary tucked the babies inside his jacket and rushed them to the zoo hospital.

COMMON DENOMINATORS

Fractions that have the same denominators are said to have common denominators. It is easy to add fractions if they have common denominators — you can simply add the numerators (the denominator does not change). In the example below, the two fractions from Hereare added together.

In the resulting fraction, both the numerator and the denominator are 3. When the numerator and the denominator are the same, a fraction is equal to 1, or one whole set.

Dr. Kenny, the zoo veterinarian, examined the cubs. They had fine white hair covering their pink skin, and their eyes were closed. They weighed slightly over one pound each, a typical weight for newborn polar bears. Gary, the keeper, named the male cub Klondike and the female cub Snow. Klondike had a cut on his head, possibly caused by Ulu picking him up in her mouth to move him. Both cubs were frail and very cold. Dr. Kenny didn't think they would live.

However, he asked Cindy, a veterinary technician, to take care of the bears, because she had raised many baby animals. The bears were put in a human infant incubator to raise their body temperatures. Several hours later, when Klondike had warmed up, Dr. Kenny stitched the cut on his head.

MAKING POLAR BEAR MILK

Cindy used a recipe to make polar bear milk. She mixed 1 cup of puppy milk with 2 cups of half-and-half to create a whole amount of 3 cups.

Since the whole amount was in three equal parts, you could say:

One part, or 1/3, was puppy milk. Two parts, or 2/3, were half-and-half.

After the milk was mixed, cod-liver oil and vitamins were added.

Because the cubs were very weak, Cindy fed them sugar water at first. Soon they would need milk. But what formula would be just right for polar bear cubs? Cindy did some research and learned that polar bear milk looks like heavy cream, smells fishy, and is high in fat. When zoos have to make milk for a baby bear, they use puppy milk formula because it's most like mother bear's milk. So Cindy mixed puppy milk with half-and-half (half milk and half cream) for extra fat, then added cod-liver oil and vitamins.

That night Cindy took the twins home with her. She didn't sleep at all — she was too busy tube-feeding milk to the cubs, cleaning them, and checking on every little cry. When dawn came, the small bears were still clinging to life.

DIVIDING A MONTH INTO THREE PARTS

To figure out how many times a month Cindy took the bears home with her, we can circle every third day on the calendar below. By counting the circled days, we can see that Cindy took the bears home ten times in a month that is thirty days long.

The chart below shows that this month can be divided into three equal parts of ten days each. Each part is equal to 1/3, or one-third of the month. So Cindy, Denny, and Dr. Kenny each spend 1/3, or one-third, of the month taking care of the bears at night.

At first the cubs needed to eat every two hours, or twelve times a day. Dr. Kenny, Cindy, and Denny (another veterinary technician) took turns bringing them home at night. Every third night, it was Cindy's turn. At five o'clock she put the two bears into a box padded with fleece to keep them warm, packed lots of bottles of milk, and loaded the cubs, their food, and a portable incubator into her car. Once home, she unpacked, made dinner, then fed and cleaned the bears. Snow was no trouble. She drank her bottle and went right back to sleep. But Klondike screamed a lot.

TWELFTHS AND THIRDS

When Klondike and Snow were two weeks old, they each drank twelve bottles of milk in one full day. Since one bear's daily portion of milk — the set — was twelve bottles, each bottle was 1/12, or one-twelfth, of the set.

The chart below shows that one-twelfth is a smaller fraction than one-third. When the denominator is a bigger number, the whole amount is divided into more parts, so each part is smaller. You can also see that the fraction four-twelfths, or 4/12, is equal to one-third, or 1/3. These two equal fractions are called equivalent fractions.

After two weeks, the cubs' weight had doubled. Snow was doing well, but Klondike had a tight, swollen belly. He didn't seem to be digesting the milk he was being fed.

Dr. Kenny ran some tests and consulted with other doctors. They decided not to add cod-liver oil to the milk anymore, but to use safflower oil instead. The doctors also felt that the bears were drinking too much milk.

With a smaller amount of the new milk, Klondike started to feel better. He was still fussy at night, so sometimes Cindy put him in a sleeping bag with her and let him suck on her finger. As the cubs' fur grew thicker, their bodies stayed warm enough outside the incubator. Both of them liked to sleep on Cindy's pillow.

EIGHTHS AND TWELFTHS

By the time Klondike and Snow were one month old, they drank more milk but they were fed less often. In a full day each bear drank eight bottles of milk. For each bear the whole amount, or set, was eight bottles, so one bottle was 1/8, or one-eighth, of the set.

You can see on the chart below that 1/12, or one-twelfth, is a smaller fraction than 1/8, or one-eighth.

When the bears were one month old, they slept in a wooden box together. Klondike liked to be near Snow. He pulled himself over to his sister and sucked on her paw. Then he would continue moving around, climbing on top of Snow or burrowing underneath her.

Sometimes Snow acted like she was in pain, crying out between feedings. She didn't like it when Klondike touched her. Cindy began to worry that Snow was too quiet and inactive. Dr. Kenny took X rays of the bears. The X rays showed that both bears had tiny breaks in many of their bones. Klondike and Snow had a disease called rickets.

FRACTIONS OF A 24-HOUR DAY

Klondike and Snow were at the zoo hospital every day from eight in the morning until five o'clock at night. They spent nine hours at the zoo. The next fifteen hours they spent at the home of Cindy, Denny, or Dr. Kenny.

Since there are twenty-four hours in a day, you can see from the chart below that three hours is equal to 1/8, or one-eighth, of a day. Nine hours is three times that much. It is equal to 3/8, or three-eighths, of a day. Fifteen hours is equal to 5/8, or five-eighths, of a...