Fraction - A comparison between two quantities, a division problem. A number expressed in the form a/b such that b ¹ 0.

Numerator - The top of a fraction. 3 Þ numerator

4 Þ denominator

Denominator - The bottom of a fraction.

Proper Fraction - A fraction where the numerator is less than the denominator, 3/4, 2/3, 5/16.

Improper Fraction - A fraction where the numerator is greater than or equal to the numerator, 4/3, 10/3, 5/5.

Mixed Numeral - A proper fraction and a whole number, 3 1/2, 4 4/7.

Equivalent Fraction - Two or more fractions which are equal.

Checking Equivalent Fractions - Equivalent fractions are checked by cross multiplying. The denominator of the first fraction is multiplied by the numerator of the second fraction. This product must equal the product of the second denominator the times the first numerator.

3 = 9 4 x 9 = 36 & 12 x 3 = 36, thus the fractions are equivalent

4 12

3 = 15 5 x 15 = 75 & 20 x 3 = 60, thus these are not equivalent

5 20

Generating Equivalent Fractions -

To generate an equivalent fraction the numerator and the denominator must be multiplied or divided by the same number.

3 x 2 = 6 3 x 3 = 9

4 x 2 = 8 4 x 3 = 12

Simplifying or Reducing a Proper Fraction - Writing a fraction so the numerator and denominator have no factors in common.

Techniques to simplify a proper fraction -

1. GCF Method
1. Divisibility & Prime Number Chart

GCF Method -

1. Find the GCF of the numerator and denominator.
1. Divide the GCF out of both numerator and denominator.

Example - 30/36

GCF of 30 & 36 is 6; 30 ¸ 6 = 5 & 36 ¸ 6 = 6 5/6

Divisibility & Prime Number Chart -

1. Using your rules of divisibility & your prime number chart, see if both numbers are divisible by 2, then 3, then 5, then 7, then 11, etc.
1. Divide until one or both numerator and denominator are prime.

Example - 30/36

30 & 36 are both divisible by two Þ 15/18

15 & 18 are both divisible by three Þ 5/6

5 is prime and does not divide evenly into 6, so 5/6 is the answer.

To simplify an improper fraction -

1. Write a division problem.
1. Solve the division problem.
1. Write the mixed Numeral.
1. Simplify the proper fraction if needed.

Example - 20/6

1. 6Ö 20 3 r 2

2. 6Ö 20

18

2

3. Quotient = Whole Number

Remainder = numerator

Divisor = denominator

4. 3 2/6 = 3 1/3

To change a mixed numeral to an improper fraction -

1. Multiply the denominator times the whole number.
1. Add the product of step 1 to the numerator.
1. Keep the old denominator.

3 1/2 = 3 x2 = 6, 6 + 1 = 7, 7/2

Comparing Fractions - Determining if the left fraction is greater than (>), less than (<) or equal to (=) the right fraction.

To solve comparing fractions either use cross-multiplying or common denominator technique.

Cross-Multiplying -

1. Multiply the denominator of one fraction times the numerator of the other fraction.
1. Multiply the other denominator by the other numerator.
1. Compare the two products.

4/5 ? 11/13 5x11 = 55 & 13x4 = 52 55 > 52, thus 4/5 <52 11/13

Common Denominators -

1. Find a common denominator for both fractions, multiply the two denominators.
1. Find new numerators for both fractions, use equivalent fractions.
1. Compare numerators.

4/5 ? 11/13 common denominator = 65

new numerators = 52 & 55 52/65 & 55/65, thus 52/65 <55/65

Terminating Decimal - A decimal which comes to a definite end.

Repeating Decimal - A decimal which repeats in a specific pattern every time.

Changing fractions to decimals - Finding the decimal equivalent of a given fraction.

To solve -

1. Write fraction as a division problem.
1. Add decimal point and zeros.
1. If it repeats put a bar over the repeating pattern of decimal.

.833.... .8

5/6 Þ 6Ö 5 Þ 6Ö 5.0000 4/5 Þ 5Ö 4 Þ 5Ö 4.00

4.8 4.0

20 0

18

20

18

2

To solve -

1. Determine the place value of the decimal.
1. Write the place value as the denominator.
1. Numerator is the decimal numeral without the decimal point or preceding zeros.
1. Simplify if possible.

Example -

.36 Þ place value is hundredths Þ 36/100 Þ 9/25

Ordering Fractions - Determining the order of a group of fractions either smallest to largest or largest to smallest. Change the fractions to decimals, then compare the decimals.

Smallest to largest -

5/6, 5/8, 3/4, 7/9 5/6 = .8333... 5/8 = .625 3/4 = .75 7/9 = .77...

.625 .75 .777.. .833.. Þ 5/8, 3/4, 7/9, 5/6