Ch 2: Fractions

Question 1

Writing and Ordering Fractions: Equivalent Fractions

Answer 1

A fraction is often used to name a part of a whole. It is possible to represent a fraction with a diagram. The fraction 2/3 has a numerator of 2 and a denominator of 3. The numerator and denominator can be referred to as the terms of a fraction.

The fractions 2/3 and 6/9 are equivalent fractions because they represent the same part of a whole. To create an equivalent fraction in higher terms, multiply both the numerator and denominator by the same whole number greater than 1. To create an equivalent fraction in lower terms, divide both the numerator and the denominator by the same whole number greater than 1.

Question 2

Lowest Terms

Answer 2

To write a fraction in lowest terms, also known as simplest form, divide the numerator and denominator by their greatest common factor (GCF). A factor divides evenly into a number, and here is no remainder. To find the GCF, list the factors of the numerator and the denominator. Choose the greatest factor that appears in both lists. Writing fractions in simplest form is sometimes called reducing to lowest terms or simplifying.

Question 3

Ordering Fractions

Answer 3

To order a set of numbers, write them in a list from least to greatest or greatest to least. To order fractions, start by writing equivalent fractions with the same denominator.

Use the least common multiple (LCM) of the original denominators as the denominator of the equivalent fractions. The LCM of two numbers is the least whole number that is a multiple of both numbers. Multiply each number by 1, 2, 3, 4,… to obtain a list of multiples for each number.

The LCM of the original denominators is also called the lease common denominator (LCD).

Question 4

Converting Between Improper Fractions and Mixed Numbers: Improper Fractions to Mixed Numbers

Answer 4

A proper fraction is a fraction in which the numerator is less than the denominator, such as 2/7, 1/3, or 8/10. An improper fraction is a fraction in which the numerator is greater than or equal to the denominator, such as 15/7, 5/1, or 3/3. An improper fraction has a value greater than or equal to 1. A mixed number, such as 12 3/4, is a whole number together with a fraction.

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The whole number in the quotient becomes the whole number part in the mixed number. Any remainder becomes the numerator of the fraction part of the mixed number. Use the original denominator in the fraction.

Be sure to multiply or divide the numerator and the denominator by the same number.

If the numerator equals the denominator, the fraction is equal to 1. If the denominator equals 1, the fraction is equal to the numerator.

Question 5

Mixed Numbers to Improper Fractions

Answer 5

To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction part of the mixed number. Add the product to the numerator of the fraction part of the mixed number. This equals the numerator of the improper fraction. Retain the denominator from the fraction part of the mixed number.

Question 6

Adding Fractions: Fractions with Like Denominators

Answer 6

To add fractions that have the same denominator, add the numerators only. The denominator will remain the same.

Question 7

Unlike Denominators

Answer 7

To add fractions that have unlike denominators, start by writing equivalent fractions with the same denominator. This is also referred to as the least common denominator (LCD). Remember, the LCD is the least common multiple (LCM) of the denominators.

To get an equivalent fraction, multiply the original denominator by the number that gives the LCM. Multiply the numerator and denominator by the same number so that the value of the fraction is not changed.

When the fractions have the same denominator, add them together as you did in previous examples.

The least common multiple (LCM) of a set of denominator is called he least common denominator (LCD).

Question 8

Mixed Numbers

Answer 8

To add mixed numbers, the fractional parts of the mixed numbers must have the same denominator.

Question 9

Proper Fractions

Answer 9

To subtract two fractions that have the same denominator, subtract the numerators only. The denominator will remain the same.

Question 10

Fractions from Whole Numbers

Answer 10

To subtract a fraction from a whole number, start by rewriting the whole number as a mixed number. The fraction part of the mixed number should have the same denominator as the original fraction.

It is possible to write the number 1 as a fraction with any denominator, except 0. When 1 is written as a fraction, the numerator and the denominator are teh same.

Question 11

Mixed Numbers, Whole Numbers, and Fractions

Answer 11

If a subtraction problem contains whole numbers or mixed numbers, subtract the fraction parts and whole number parts in separate columns. Be sure the fractions have a common denominator.

If the fraction in the mixed number you are subtracting is larger than the fraction in the mixed number you are subtracting from, just “borrow” 1 from the whole number and write it as a fraction.

Question 12

Subtracting Fractions: Proper Fractions

Answer 12

To multiply fractions, first multiply the numerators to find the numerator of the product. Then multiply the denominators to find the denominator of the product.

Question 13

Mixed Numbers, Whole Numbers, and Fractions

Answer 13

If a multiplication problem contains a fraction or a mixed number, express all factors in a fraction from. Convert whole numbers and mixed numbers to improper fractions.

Question 14

Order of Operations

Answer 14

The order in which operations are performed is based on some basic agreements made by mathematicians so that both problems give the same answer. These agreements are in the form of a series of steps to be followed. If a step does not apply to the expression, go to the next step.

Order of Operations

• Complete all calculations within grouping symbols such as parentheses.
• Perform all multiplications and divisions in order from left to right.
• Perform all additions and subtractions in order from left to right.

When a fraction has some operations in the numerator or denominator, it is implied that the numerator and denominator are placed in parentheses. It is very important that you include these parentheses when you use your calculator.

Question 15

Dividing Fractions and Mixed Numbers: Proper Fractions

Answer 15

To divide by a fraction, multiply by its reciprocal. To get the reciprocal of a fraction, interchange the numerator and the denominator. To find he reciprocal of a mixed number, first write the number as an improper fraction.

Finding the reciprocal of a fraction is sometimes called inverting the fraction because the numerator and the denominator switch places.

Question 16

Mixed Numbers, Whole Numbers, and Fractions

Answer 16

If a division problem contains a fraction or a mixed number, express both dividend and divisor in fraction form. Convert whole numbers and mixed numbers to improper fractions.
Express both dividend and divisor in fraction form.

Question 17

Reading A Customary Rule

Answer 17

Most lengths in the customary or English system of measurement are given in inches (in.), feet (ft), and yards (yd). One yard is equal to 3 feet, or 36 inches. One foot is equal to 12 inches.

Most rulers and tape measures have tick marks of different lengths. The longest tick mark between any two numbers is at 1/2 inch. The next longest tick marks are at 1/4 and 3/4 inch. Shorter marks are used for eights, and the shortest marks are used for sixteenths.

Question 18

Converting Between Customary Units of Length

Answer 18

Customary Units of Linear Measure
1 yard (yd) = 3 feet (ft)
1  yard (yd) = 36 inches (in.)
1 foot (ft) = 12 inches (in.)
To convert from one unit to another, multiply by a fraction made from one of the lines in the above table.  The denominator of the fraction will have the given unit and the numerator will have the unit to which you are converting.