Chapter 4.1 - 4.5

Question 1

complex fraction

Answer 1

A complex fraction is a fraction in which the numerator or the denominator contains a fraction.

Question 2

equivalent fractions

Answer 2

Equivalent fractions are two or more fractions that have the same value.

Question 3

fraction

Answer 3

A fraction is written. In a fraction,is the numerator andis the denominator. A fraction represents parts of a whole. The denominatoris the number of equal parts the whole has been divided into, and the numerator indicates how many parts are included.

Question 4

least common denominator (LCD)

Answer 4

The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.

Question 5

mixed number

Answer 5

A mixed number consists of a whole numberand a fractionwhere. It is written as, where c does not equal zero.

Question 6

proper and improper fractions

Answer 6

The fraction “a/b” is proper if “a is less than b” and improper if “a is greater than b”.

Question 7

reciprocal

Answer 7

lThe reciprocal of the fraction “a/b” is “b/a” where “a is less than 0” and “b is less than zero”.

Question 8

simplified fraction

Answer 8

A fraction is considered simplified if there are no common factors in the numerator and denominator.

Question 9

Property of One

Answer 9

Any number, except zero, divided by itself is one. a/a = 1, where a does not equal 0.

Question 10

mixed number

Answer 10

A mixed number consists of a whole number “a” and a fraction “ b/c”, where c does not equal 0. It is written as follows: “a b/c”, where c does not equal 0.

Question 11

Proper and Improper Fractions

Answer 11

The fraction “a/b” is a proper fraction if “a is less than b”, and an improper fraction is “a is greater than or equal to b”.

Question 12

Convert an improper fraction to a mixed number.

Answer 12

Step 1. Divide the denominator into the numerator. Step 2. identify the quotient, remainder, and divisor., Step 3. Write the mixed number as “quotient + remainder/divisor”.

Question 13

Convert a mixed number to an improper fraction

Answer 13

Step 1. Multiply the whole number by the denominator. Step 2. Add the numerator to the product found in Step 1. Step 3. Write the final sum over the original denominator.

Question 14

Equivalent Fractions Property

Answer 14

If a, b, and c are numbers where “b does not equal 0”, “c does not equal 0”, then “a/b = (a x c)/(b x c)”.

Question 15

Equivalent Fractions Property

Answer 15

If a, b, c are numbers where “b does not equal 0”, “c does not equal 0”, then “(a/b) = (a x c)/(b x c)” and “(a x c)/(b x c) = a/b”.

Question 16

Simplify a fraction.

Answer 16

Step 1. Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers. Step 2. simplify, using the equivalent fractions property, by removing common factors. Multiply any remaining factors.

Question 17

Fraction Multplication

Answer 17

If a,b,c and d are numbers where “b does not equal 0” and “d does not equal 0”, then “(a/b) x (c/d)” = “(ac/bd)”.

Question 18

reciprocal

Answer 18

A number and its reciprocal have a product of 1. “a/b” x “b/a” = 1.

Question 19

Opposite

Answer 19

Has opposite sign.

Question 20

Absolute Value

Answer 20

Is never negative.

Question 21

reciprocal

Answer 21

Has same sign, fraction inverts.

Question 22

Fraction Division

Answer 22

To divide fractions, multiply the first fraction by the reciprocal of the second. If a,b,c and d are numbers where “b does not equal 0”, “c does not equal 0” and “d does not equal 0”, then “(a/b)” / “(c/d)” = “(a/b)” x “(d/c)”.

Question 23

Multiply or Divide Mixed Numbers

Answer 23

Step 1. Convert the mixed numbers to improper fractions. Step 2. Follow the rules for fraction multiplication or division. Step 3. Simplify if possible.

Question 24

Simplify a Complex Fraction

Answer 24

Step 1. Rewrite the complex fraction as a division problem. Step 2. Follow the rules for dividing fractions. Step 3. simplify if possible.

Question 25

Placement of negative sign in a fraction.

Answer 25

For any positive numbers “a” and “b”, “(-a) / (b)” = “(a) / (-b)” = -“(a) / (b)”.

Question 26

Simplify an expression with a fraction bar

Answer 26

Step 1. Simplify the numerator. Step 2. simplify the donominator. Step 3. Simplify the fraction.

Question 27

Fraction Addition

Answer 27

To add fractions, add the numerators and place the sum over the common denominator. If a,b,c are numbers where “c does not equal 0”, then “a/c” + “b/c” = “(a+b)”/”c”.

Question 28

Fraction Subtraction

Answer 28

If a,b, and c are numbers where “c does not equal 0”, then “(a/c)” - “(b/c)” =”( a-b)”/c.

Question 29

Find the Least Common Denominator (LCD) of two fractions.

Answer 29

Step 1. Factor each denominator into its primes. Step 2. List the primes, matching primes in columns when possible. Step 3. Bring down the columns. Step 4. Multiply the factors, The product if the LCM of the donominators. Step 5. The LCM of the denominators is the LDC of the fractions.

Question 30

Convert two fractions to equivalent fractions with their LCD as the common denominator.

Answer 30

Step 1. Find the LCD. Step 2. For each fraction, determine the number needed to multiply the denominator to get the LCD. Step 3. Use the Equivalent Fractions Property to multiply the numerator and denominator by the number from Step 2. Step 4. Simplify the numerator and denominator.

Question 31

Add or subtract fraction with different denominators.

Answer 31

Step 1. Find the LCD. Step 2. Convert ech fraction to an equivalent form with the LCD as the denominator. Step 3. Add or subtract the fractions. Step 4. Write the result in simplified form.