Read the following statements and decide if they are true sometimes, always or never. Be sure...

Read the following statements and decide if they are true sometimes, always or never. Be sure to give a reason for each statement or use an example and the reason why it shows the statement is false. You can download this document in the module one section Fractions and attach it if you prefer.

All fractions are less than one
Improper fractions are greater than or equal to one
Proper fractions are less than one
Fractions are always part of a whole
All Fractions can be written as terminating decimals.
When you create an equivalent fraction, you are multiplying by one.
Numerators and denominators are always the same.

Solutions

Expert Solution

(1) All fractions are not always less than one.

If numerator is lesser than denominator, then it is less than one.

Example: 1/2, 1/3, 1/4, 1/5, 2/5, 3/5 etc. are less than one.

But 3/2, 4/3, 5/3, 9/7 etc. are greater than one, since numerator is greater than denominator.

(2). Improper fractions are always greater than one.

Since in improper fractions numerator is greater than denominator. Therefore improper fractions are always greater than one.

Example: 3/2, 4/3, 5/4 etc are improper fractions.

(3) Proper fractions are always less than one.

Since in proper fractions numerator is always less than denominator. Therefore proper fractions are always less than one.

Example: 2/3, 3/4, 4/5, 1/2 are proper fractions.

(4) Only proper fractions are part of a whole .

Since proper fractions are always less than one.

But improper fractions are always greater than one. Therefore it will never be part of whole.

(5) All fractions are not always can written as terminating decimals.

Since in a fraction if denominator is in form of 2^m or 5^m or (2×5)^m. Means if denominator has only factor 2 or 5 or 2and 5 both, then it is terminating decimals, otherwise not.

Example: 3/8=3/(2×2×2) is terminating decimals.

3/25=3/(5×5×5) is terminating decimals.

3/10=3/(2×5) is terminating decimals.

But 2/15=2/(3×5) is not terminating decimals.

1/21=1/(3×7) is not terminating decimals.

(6) For creating equivalent fractions we have to multiply numerator and denominator with same number. If we multiply by one then resulting fractions are same.

milcah answered 3 weeks ago

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