rational numbers. mental math warm up number from 1-6 48+ 21= 56+38= 15+18+17= 125+186= 530+280=...
TRANSCRIPT
Mental Math Warm Up
• Number from 1-6
• 48+ 21=
• 56+38=
• 15+18+17=
• 125+186=
• 530+280=
• 176+125=
INTEGERSINTEGERS
• WHAT IS AN INTEGER?WHAT IS AN INTEGER?
• The The integersintegers consist of the positive consist of the positive natural numbersnatural numbers ( (11, , 22, , 33, …), their , …), their negativesnegatives (−1, −2, −3, ...) and the (−1, −2, −3, ...) and the number number zerozero. .
RATIONAL NUMBERSRATIONAL NUMBERS
• WHAT IS A RATIONAL NUMBER?WHAT IS A RATIONAL NUMBER?
• In In mathematicsmathematics, a , a rational numberrational number (commonly called a (commonly called a fractionfraction) is a ) is a ratioratio or quotient of two or quotient of two integersintegers, usually , usually written as awritten as a fraction fraction aa//bb, where , where bb is not is not zerozero..
RATIONAL NUMBERSRATIONAL NUMBERS
• WHAT IS A RATIONAL NUMBER?WHAT IS A RATIONAL NUMBER?
• In In mathematicsmathematics, a , a rational numberrational number (commonly called a (commonly called a fractionfraction) is a ) is a ratioratio or quotient of two or quotient of two integersintegers, usually , usually written as awritten as a fraction fraction aa//bb, where , where bb is not is not zerozero..
• EXAMPLES:EXAMPLES:•
14
RATIONAL NUMBERSRATIONAL NUMBERS
• WHAT IS A RATIONAL NUMBER?WHAT IS A RATIONAL NUMBER?
• In In mathematicsmathematics, a , a rational numberrational number (commonly called a (commonly called a fractionfraction) is a ) is a ratioratio or quotient of two or quotient of two integersintegers, , usually written as ausually written as a fraction fraction aa//bb, , where where bb is not is not zerozero..
• EXAMPLES:EXAMPLES:
• , , 0.250.2514
RATIONAL NUMBERSRATIONAL NUMBERS
• WHAT IS A RATIONAL NUMBER?WHAT IS A RATIONAL NUMBER?
• In mathematics, a In mathematics, a rational numberrational number (commonly called a (commonly called a fractionfraction) is a ) is a ratio or quotient of two integers, ratio or quotient of two integers, usually written as a fraction usually written as a fraction aa//bb, , where where bb is not zero. is not zero.
• EXAMPLES:EXAMPLES:
• , , 0.25, 0.25, 14
-5 4
RATIONAL NUMBERSRATIONAL NUMBERS
• WHAT IS A RATIONAL NUMBER?WHAT IS A RATIONAL NUMBER?
• In In mathematicsmathematics, a , a rational numberrational number (commonly called a (commonly called a fractionfraction) is a ) is a ratioratio or quotient of two integers, or quotient of two integers, usually written as a fraction usually written as a fraction aa//bb, , where where bb is not zero. is not zero.
• EXAMPLES:EXAMPLES:
• , , 0.25, , -0.1250.25, , -0.12514
-5 4
ADDING FRACTIONS
To add two fractions with the same denominator, add the numerators and place that sum over the common denominator
EXAMPLE:
35
+ 15
= 45
ADDING FRACTIONS
To Add Fractions with different denominators:
Find the Least Common Denominator (LCD) of the fractions
Rename the fractions to have the LCD Add the numerators of the fractions Simplify the Fraction
To make the denominator of the first fraction 12, multiply both the numerator and denominator by 3.
Adding Fractions
14
+13 ?=
x3
x3
?12
+ =
To make the denominator of the second fraction 12, multiply both the numerator and denominator by 4.
Adding Fractions
14
+13 ?=
x4
x4
312
+ ?12
=
To make the denominator of the second fraction 12, multiply both the numerator and denominator by 4.
Adding Fractions
14
+ 13 ?=
x4
x4
312
+4
12=
SUBTRACTING FRACTIONS
To Subtract Fractions with different denominators:
Find the Lowest Common Denominator (LCD) of the fractions
Rename the fractions to have the LCD Subtract the numerators of the fractions The difference will be the numerator and the
LCD will be the denominator of the answer. Simplify the Fraction
MULTIPLYING FRACTIONSMULTIPLYING FRACTIONS
To Multiply Fractions: To Multiply Fractions:
Multiply the numerators of the Multiply the numerators of the fractions fractions
Multiply the denominators of the Multiply the denominators of the fractions fractions
Place the product of the numerators Place the product of the numerators over the product of the denominators over the product of the denominators
Simplify the Fraction Simplify the Fraction
To multiply fractions, simply To multiply fractions, simply multiply the two numeratorsmultiply the two numerators
Multiplying FractionsMultiplying Fractions
35
x13
=
x =
??
Then simply multiply the two Then simply multiply the two denominators. denominators.
35
x13
=
x =
3?
Multiplying FractionsMultiplying Fractions
Place the numerator over the Place the numerator over the denominator.denominator.
35
x13
=
x =
315
Multiplying FractionsMultiplying Fractions
If possible, state in simplest If possible, state in simplest form. form.
35
x13
=3
15=
15
Multiplying FractionsMultiplying Fractions
DIVIDING FRACTIONSDIVIDING FRACTIONS
To Divide Fractions: To Divide Fractions: Multiply the reciprocal of the second term Multiply the reciprocal of the second term
( fraction)( fraction) Multiply the numerators of the fractions Multiply the numerators of the fractions Multiply the denominators of the fractions Multiply the denominators of the fractions Place the product of the numerators over Place the product of the numerators over
the product of the denominators the product of the denominators Simplify the Fraction Simplify the Fraction
Example:Example:
35
÷ 13
Dividing FractionsDividing Fractions
=
35
x 31
=
Multiply by the reciprocal…
95