Equivalent fractions with denominators of 10 and 100

The Equivalent fractions with denominators of 10 and 100 exercise appears under the 4th grade (U.S.) Math Mission. This exercise explores equivalent fractions that are formed by multiplying or dividing by ten in both numerator and denominator.

Types of Problems

There is one type of problem in this exercise:

1. Find the value of the star: This problem provides an equation with two fractions, one with a denominator of 10 and the other with 100. The student is provided one of the numerators and is asked to find the other numerator to make the equation true.

   

   Find the value of the star

Strategies

Knowledge of fraction simplification and an ability to multiply/divide by ten are encouraged to ensure success on this exercise.

1. To switch from the fraction over 100 into the fraction over ten, drop the zero. When changing from over ten to over 100, put an additional zero.
2. When the denominator is 10, the numerator will be a single digit except in the ${\frac{10}{10}=\frac{100}{100}}$ case.
3. When the denominator is 100, the numerator will always be a single digit followed by zero, except in the ${\frac{10}{10}=\frac{100}{100}}$ case.

Real-life Applications

1. Unsimplifying fractions is a common technique, needed for finding common denominators for adding and subtracting.
2. Converting between tens and hundreds has immediate applications to measurement in the metric system.