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DSPM 0700 CHAPTER 2 REVIEW
- Find the least common multiple and the greatest common factor of 25, 30, and 40.
The least common multiple (LCM) is the smallest number that is a multiple of all the
numbers. The greatest common factor (GCF) is the largest number that is a factor of all
the numbers.
You can find the prime factorization of all of the numbers. The LCM will have the
primes that appear in at least one line raised to the highest power in any one line. The
GCF will have the primes that appear in all the lines raised to the lowest power in any
one line or 1 if there are no common primes.
2
3
The LCM must have some 2’s, 3’s, and 5’s. It needs three 2’s (from 40), one 3 (from
30), and two 5’s (from 25). The GCF will have only 5’s (since no 2’s and 3’s appear in
25), and there is only one 5 in 30 and 40.
3 2 2 3 5
600
LCM
GCF 5
- Find the equivalent fraction with the given denominator:
To find an equivalent fraction with a larger denominator, find the factor the given
denominator is multiplied by to get the desired denominator. Multiply the numerator by
that factor.
- Reduce
to lowest terms.
To find an equivalent fraction with a smaller denominator, find the factor the given
denominator is divided by to get the desired denominator and divide the numerator. A
fraction is in lowest terms if there is no common factor other than 1. Therefore, use the
GCF to reduce to lowest terms.
Change the following to a mixed number equivalent in lowest terms:
To change an improper fraction to a mixed number, divide numerator by denominator.
The whole number part is the quotient, the remainder is the numerator, and the original
denominator is the denominator.
- Change
to an improper fraction.
To change a mixed number to an improper fraction, multiply the whole number by the
denominator, add the numerator, and place the result over the denominator.
- Change 25 to an improper fraction with a denominator of 14.
Simply multiply the whole number by the desired denominator and place the result over
the denominator.
You can change
5 16 to a decimal if there is a mixed number.
- Determine the larger of
and 9 11
. Show the change to common denominators.
- Place these fractions and decimals in order from smallest to largest by changing
fractions to decimals:
- Add:
Find common denominators if necessary, and if mixed numbers add whole number parts
and fractions separately. Regroup if fractions add to an improper fraction.
- The studs of an outside wall are
in. thick. The inside wallboard is
in. thick
and the outside covering is
in. thick. What is the total thickness of the wall?
7 9 in. 16 16
- Subtract:
Find a common denominator. If mixed numbers, subtract whole number parts and
fractions separately. If fractions cannot subtract, regroup one unit from whole number
part and include that in fraction part so that you can subtract.
- Divide. If necessary, change improper fractions to mixed numbers in lowest terms:
2 1
3 7
Multiply the first fraction by the reciprocal of the second.
- An I-beam measures 14 ft. long. How many whole
2 -ft. 16
pieces can be cut from
this length?
There will be 6 whole pieces that can be cut from this length.
