Test
Fractions
What are fractions and what are they used for?
Fractions are mathematical phenomena that represent a part of a whole. They consist of two numbers: the numerator (the number at the top) and the denominator (the number at the bottom), separated by a horizontal line. The numerator represents the part we are considering, and the denominator represents all the equal parts that make up the whole.
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Sample questions
- The glass is half full. Choose the fraction corresponding to this condition.
- The cake is divided into ___ parts. Tom ate ___ parts. Choose the fraction that describes the part of the cake eaten.
- Choose the fraction that describes ___ minutes part of an hour.
- Linda bought ___ apples, ___ pears, ___ peaches. What part of the purchases are peaches?
- The class consists of ___ students, ___ of whom are boys. What part of the classes are girls?
Fractions and operations with fractions
The numerator shows the number of selected parts, while the denominator shows how many equal parts form a whole. A fraction keeps the same value when its numerator and denominator are multiplied or divided by the same non-zero number.
Rules for operations
- For equal denominators, add or subtract only the numerators.
- For different denominators, find a common denominator first.
- For multiplication, multiply numerators and denominators.
- To divide by a fraction, multiply by its reciprocal.
Simplify the result and convert an improper fraction to a mixed number when appropriate. Estimating relative to 0, one half or 1 helps detect unreasonable answers.
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