NAME_______________________________________________TEST DATE________________
FRACTION STUDY GUIDE/EXTRA PRACTICE
PART 1: PRIME OR COMPOSITE?
A prime number is a number that has exactly 2 factors, one and itself.
Examples: 2, 3, 5, 11, 31

2 is the only even number that is prime.
A composite number is a number that has three or more factors.
Examples: 4 (1, 2, 4) 8 (1, 2, 4, 8) 9 (1, 3, 9)
(factors are listed in parenthesis)

All even numbers, except 2, are composite because they are divisible by 2.

The number 1 is not considered to be prime or composite because it has only one factor.
Decide if the following numbers are prime or composite. Write P for prime or C for composite.
85 _______ 18 _______
17 _______ 12 _______
54 _______ 21 _______
7 ________ 29 _______

PART 2: WHAT IS THE GREATEST COMMON FACTOR (GCF)?
The greatest common factor is the biggest number that can be evenly divided into the numbers that you are given.
Factors are the numbers in a multiplication problem. They can divide evenly into the product.
A product is the answer to a multiplication problem.
What is this used for? The GCF helps you reduce/simplify fractions to lowest terms.
Example:
Find the GCF for the numbers 24 and 36. Start by listing all of the factors for each number.
24 → 1, 2, 3, 4, 6, 8, 12, 24
36 → 1, 2, 3, 4, 6, 9, 12, 18, 36
Circle the largest number that is in both factor lists. That number is the greatest common factor. The GCF of 24 and 36 is 12.
Find the GCF for each set of numbers. You MUST list all of the factors for each number.
1.
18→ 4. 15→
12→ 25→
2.
9 → 5. 19 →
6 → 13 →
3.
50→
20→

PART 3: WHAT IS THE LEAST COMMON MULTIPLE (LCM)?
The least common multiple is the smallest multiple that given numbers have in common. The number zero is never the LCM.
Multiples are the list of numbers you say when you count by a certain number. For examples, the multiples of 3 are 0, 3, 6, 9, 12, 15, 18…….
3 divides evenly into each of its multiples.
What is this used for? The LCM will help you add and subtract fractions with unlike denominators.
Example:
Find the LCM for 10 and 12.
First, list the multiples for each number.
10→ 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
12→0, 12, 24, 36, 48, 60, 72, 84, 96
The least common multiple of 10 and 12 is 60. It is the smallest number that is in both lists, not counting zero.
Find the LCM for the given sets of numbers. You must list the multiples for the numbers.
1.
9 → 3. 12 →
6 → 15 →
2.
8 → 4. 10 →
12 → 6 →

PART 4: HOW DO I FIND EQUIVALENT FRACTIONS?
If you multiply or divide the numerator (top number) and the denominator(bottom number) by the same number, you will get an equivalent fraction.
Examples:
is equal to because you can multiply the numerator and denominator by 3 to get the equivalent fraction.
is equal to because you can divide the numerator and denominator by 7 to get the equivalent fraction.
To figure out a missing part of an equivalent fraction, use basic facts.
= Think: 2 times 5 equals 10 in the numerator, so 8 times 5 equals 40 for the denominator.
To find out if two fractions are equal, test to see if you can multiply or divide by the same number.
Is equal to ? For the numerators, 5 times 2 equals 10. For the denominators, 10 times 2 equals 20. The fractions are equal because the numerator and denominator of the first fraction were both multiplied by 2.
Fill in the missing numerators or denominators.
1.
2.
= 3. = 5. =
3.
= 4. = 6. =

PART 5: HOW DO I CONVERT (CHANGE) A MIXED NUMBER TO AN IMPROPER FRACTION?
A mixed number has a whole number and a fraction.
An improper fraction has a larger numerator than denominator.
Procedure: Multiply the whole number by the denominator and then add the numerator. This will be the new numerator. Use the same denominator as in the problem.
Examples:
= The whole number (5) multiplied by the denominator (2) equals 10. Then add 10 plus the numerator (1) to get 11, which is the numerator in the improper fraction. The denominator stays the same.
= 1 (whole number) x 3 (denominator) = 3 3 + 2 (numerator) = 5 The denominator stays the same.
Try these:
1.
3 ½ =
2.
=
3.
=
4.
=
5.
=
6.
=

PART 6: HOW DO I CONVERT (CHANGE) AN IMPROPER FRACTION TO A MIXED NUMBER?
Procedure:

Divide the denominator into the numerator.

The number of times the denominator goes into the numerator becomes the whole number.

The remainder becomes the new numerator.

Use the same denominator as in the improper fraction.

Reduce the fraction to lowest terms if possible.

If there is no remainder, the answer will be a whole number. Do not write the number zero in a fraction.
Example:
=
10 divides into 17 one time, so the whole number is 1.
The remainder is 7, so the new numerator is 7. The denominator stays ten.
Try some.
1.
=
2.
=
3.
4.
=
=
5.
=
6.
=

PART 7: HOW DO I REDUCE A FRACTION TO LOWEST TERMS? (OR SIMPLIFY A FRACTION)
Lowest terms is when a fraction uses the smallest numbers possible so that the fraction is easier to understand and picture.
Procedure:

Find the GCF for each number in the fraction.

Divide the numerator and the denominator by the GCF.
Example:
=
Factors of 10 are 1, 2, 5 and 10.
Factors of 15 are 1, 3, 5, and 15.
The greatest common factor is 5, so divide by 5.
Other terms that are used to me lowest terms: reduce, simplify
You can be sure a fraction is in lowest terms if:

The numerator is the number one.

The numbers are in counting order.

Both numbers are prime.

The greatest common factor is one.
Reduce each fraction to lowest terms.
1.
= 4.
2.
= 5.
3.
= 6. =

PART 8: HOW DO I COMPARE FRACTIONS?
Procedures:

If the denominators are the same, just look at the numerators. The smaller numerator will be the smaller fraction.

If the denominators are different, find the least common multiple for the denominators.

Make equivalent fractions for each fraction using the LCM as the new denominator.

Compare the fractions with common denominators.
Examples:
Two-fifths is less than four-fifths. The denominators are the same so just look at the numerators.
Multiples of 5 → 0, 5, 10, 15, 20
Multiples of 10 → 0, 10, 20, 30, 40
The LCM is 10 so make an equivalent fraction – two-fifths equals four-tenths.
Compare.
Comparing to ½

If the numerator is more than half of the denominator, the fraction is greater than ½

If the numerator is less than half of the denominator, the fraction is less than ½

Example: ¾ is larger than ½ because 3 is more than half of 4.
Comparing to 1

If the fraction is proper, it is less than 1. A proper fraction has a numerator that is smaller than the denominator.

If the fraction is improper, it is greater than 1.

Compare. Show your equivalent fractions when the denominators are different.
1.
2.
3.
4.
5.
6.
7.

PART 9: FRACTION TYPES/VOCABULARY
The numerator is the top number in a fraction.
The denominator is the bottom number in a fraction.
Proper fractions have a smaller numerator than denominator.
Improper fractions have a numerator that is larger than or equal to the denominator.
Mixed numbers have a whole number and a fraction.
Whole numbers are normal, everyday numbers. They do not have fractions beside them.
Write the fraction type beside each number/fraction.
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6 ________________________________________
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PART 10: HOW DO I ADD AND SUBTRACT FRACTIONS WITH COMMON DENOMINATORS?
Procedures:

If the denominators are the same, just add or subtract the numerators.

Keep the denominator the same.

If the sum or difference is an improper fraction, convert it to a mixed number.

If the sum or difference can be reduced, reduce it.
Examples:
=
=
How to regroup in subtraction:
To subtract 3 – 4 (the numerators), you must regroup. When regrouping, take one whole from the whole number, then add the numerator and the denominator. This will be your new numerator. Then subtract.
Try a few.
1.
3. =
2.
4.

PART 11: HOW DO I ADD AND SUBTRACT FRACTIONS WITH UNLIKE DENOMINATORS?
Procedures:

Find the LCM and make equivalent fractions.

Add or subtract the same way that you do when you are given like denominators.
Regroup in subtraction if you need to.

Simplify your answer.
Examples:
+ = -
__________ _________
Find the sums and differences of these fractions/mixed numbers. You may rewrite the problem vertically.
1.
2.
3.
4.