Rational number operations can often be simplified by converting mixed numbers to improper fractions Add ( 2) EXAMPLE: 2 Multiply 1 Negative fractions can be written with the negative number in the numerator EXAMPLE: can also be written as To add or subtract rational number operations Convert all mixed numbers to improper fractions (if required) find a common denominator (a number that is divisible by both denominators) Apply the rules of integer operations to the numerators and denominators When dividing by a rational number, you have to multiply by its reciprocal 1
To add or subtract rational number operations Convert all mixed numbers to improper fractions (if required) find a common denominator (a number that is divisible by both denominators) Apply the rules of integer operations to the numerators and denominators WARM UP Adding and Subtracting Fractions Evaluate the following and express in lowest terms if required: 1 Common 1 (a) denominator (b) 2 = 12 (1) 1() 1 12 () 1(1) 12 Common denominator = 12 2 1 12 2 12
To add or subtract rational number operations Convert all mixed numbers to improper fractions (if required) find a common denominator (a number that is divisible by both denominators) Apply the rules of integer operations to the numerators and denominators WARM UP Adding and Subtracting Fractions Evaluate the following and express in lowest terms if required: (c) Common + 6 denominator (d) 20 = 20 1 () (1) 6 1 20 20 () 6(2) 1 0 20 12 12 0 Common denominator = 0 0
To add or subtract rational number operations Convert all mixed numbers to improper fractions (if required) find a common denominator (a number that is divisible by both denominators) Apply the rules of integer operations to the numerators and denominators EXAMPLE 1 Adding and Subtracting Mixed Numbers Evaluate the following and express each answer in lowest terms. If the answer is an improper fraction, express the answer as a mixed fraction (a) 2 ( 2) 1 1(2) 26 (1) Common denominator =
To add or subtract rational number operations Convert all mixed numbers to improper fractions (if required) find a common denominator (a number that is divisible by both denominators) Apply the rules of integer operations to the numerators and denominators EXAMPLE 1 1 Adding and Subtracting Mixed Numbers Evaluate the following and express each answer in lowest terms. If the answer is an improper fraction, express the answer as a mixed fraction 1 + (b) 12 1 ( ) 1 1 1(6) (1) Common denominator =
To add or subtract rational number operations Convert all mixed numbers to improper fractions (if required) find a common denominator (a number that is divisible by both denominators) Apply the rules of integer operations to the numerators and denominators EXAMPLE 1 Adding and Subtracting Mixed Numbers Evaluate the following and express each answer in lowest terms. If the answer is an improper fraction, express the answer as a mixed fraction (c) 1 6 ( 6 ) 1 6 2 6 2() () Common denominator = 1 1 6 0
EXAMPLE 2 Multiplying Fractions When multiplying fractions you multiply the numerators together you multiply the denominators together Evaluate the following by multiplying the fractions. Express each answer in lowest terms and express as a mixed number where required. (a) 2 6 (b) 6 1
EXAMPLE 2 Multiplying Fractions When multiplying fractions you multiply the numerators together you multiply the denominators together Evaluate the following by multiplying the fractions. Express each answer in lowest terms and express as a mixed number where required. (c) 2 * Change to improper fraction ( 2) 22 2 1 1 1
EXAMPLE Dividing Fractions When dividing by a rational number, you have to multiply by its reciprocal You can find the reciprocal by inverting or flipping the fraction Evaluate the following by dividing the fractions. Express each answer in lowest terms and express as a mixed fraction where required. (a) * Find the 2 (b) 21 2 reciprocal by flipping the fraction * Change from division to multiplication
EXAMPLE Dividing Fractions When dividing by a rational number, you have to multiply by its reciprocal You can find the reciprocal by inverting or flipping the fraction Evaluate the following by dividing the fractions. Express each answer in lowest terms and express as a mixed fraction where required. (a) * Change to 2 (b) improper fraction 21 2 ( ) 1 1 2 2 2 * Find the reciprocal by flipping the fraction * Change from division to multiplication
EXAMPLE Dividing Fractions When dividing by a rational number, you have to multiply by its reciprocal You can find the reciprocal by inverting or flipping the fraction Evaluate the following by dividing the fractions. Express each answer in lowest terms and express as a mixed fraction where required. (a) * Change to 2 (b) improper fraction 21 2 ( ) 1 1 2 2 2 1 1
EXAMPLE Dividing Fractions When dividing by a rational number, you have to multiply by its reciprocal You can find the reciprocal by inverting or flipping the fraction Evaluate the following by dividing the fractions. Express each answer in lowest terms and express as a mixed fraction where required. (c) 1 2 2 ( 2) 1 ( ) 2 1 2 2 * Change to improper fraction * Find the 0 0 reciprocal by flipping the fraction * Change from division to multiplication
EXAMPLE Putting It All Together Evaluate the expression below and express the answer in lowest terms and express as a mixed fraction where required. ( ) 1 1 * Change to improper fraction
EXAMPLE Putting It All Together Evaluate the expression below and express the answer in lowest terms and express as a mixed fraction where required. 1 1 * Change to improper fraction
EXAMPLE Putting It All Together Evaluate the expression below and express the answer in lowest terms and express as a mixed fraction where required. 62 62 + 1 1 1 1 (2) 1(1) 1 1 * Change to improper fraction * Simplify terms in the brackets Common denominator = 1 62 * Find the reciprocal by flipping the fraction * Change from division to multiplication 62 1 6 1
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