9/40

Show various properties and calculations for 9/40

Fraction properties, decimal, percentage, and related fraction items

Fraction Picture

Analyze Fraction

Numerator = 9

Denominator = 40

Fraction on a Number Line (3.NF.A.2)

Classify Fraction

Proper Fractions have Numerator < Denominator

Imroper Fractions have Numerator > Denominator

Whole Fractions have Numerator = Denominator

Since 9 < 40
9/40 is a(n) Proper fraction

Convert fraction to decimal

9/40 to decimal = 0.225

Long Division with Remainder

9/40 long division = 0 remainder 9

Click here for the math

Convert fraction to percentage

9/40 to percentage =	9 x 100%
	40

9/40 to percentage =	900
	40

9/40 to percentage

Calculate unit fraction

Unit fractions have 1 for the numerator
and we keep the original denominator of 40

Unit fraction =	1
	40

Calculate the fraction reciprocal

Reciprocal =	Denominator
	Numerator

Reciprocal =	40
	9

Determine characteristics for 9/40

Rational
Irrational
Natural
Whole
Imaginary

Fraction Check

Since 9/40 is a fraction, we use our long division decimal calculator to get 0.225

Natural Number Test

Counting numbers > 0: 1,2,3,4,5,...

Since 0.225 is not both positive and a counting number, 0.225 is not a natural number

Whole Number Test

Whole Numbers are positive numbers

They include 0

They have no decimal or fractional parts

Since 0.225 is not >= 0 and an integer, 0.225 is not a whole number

Integer Test

Integers have no fractions or decimals

-5,-4,-3,-2,-1,0,1,2,3,4,5,...

0.225 is not an integer

Rational Number Test

Check for integer or decimal

Rationals = a/b

where a and b are integers<

and b ≠ 0.

Since 0.225 is an integer or decimal from above, 0.225 is also a rational

Irational Number Test

They do not form a ratio between two integers

They are not an imaginary number.

Imaginary Number Test

Test for square root of a negative

Since 0.225 is not the square root of a negative number, it is not imaginary

Equivalent Fractions: Check if we can simplify our fraction

GCF (9, 40) = 1

Multiply top and bottom by 2

9 x 2
40 x 2

Multiply top and bottom by 3

9 x 3
40 x 3

120

Multiply top and bottom by 4

9 x 4
40 x 4

160

Multiply top and bottom by 5

9 x 5
40 x 5

200

Multiply top and bottom by 6

9 x 6
40 x 6

240

Multiply top and bottom by 7

9 x 7
40 x 7

280

Multiply top and bottom by 8

9 x 8
40 x 8

320

Multiply top and bottom by 9

9 x 9
40 x 9

360

Multiply top and bottom by 10

9 x 10
40 x 10

400

Multiply top and bottom by 11

9 x 11
40 x 11

440

Multiply top and bottom by 12

9 x 12
40 x 12

108

480

Multiply top and bottom by 13

9 x 13
40 x 13

117

520

Multiply top and bottom by 14

9 x 14
40 x 14

126

560

Multiply top and bottom by 15

9 x 15
40 x 15

135

600

Multiply top and bottom by 16

9 x 16
40 x 16

144

640

Multiply top and bottom by 17

9 x 17
40 x 17

153

680

Multiply top and bottom by 18

9 x 18
40 x 18

162

720

Multiply top and bottom by 19

9 x 19
40 x 19

171

760

Multiply top and bottom by 20

9 x 20
40 x 20

180

800

Final Answer

Numerator = 9
Denominator = 40
9/40 is a(n) Proper fraction
9/40 to decimal = 0.225
9/40 long division = 0 remainder 9
9/40 to percentage = 22.5%
Unit fraction = 1/40
Reciprocal = 40/9
9/40 is Rational
Equivalent Fraction = 18/80
Equivalent Fraction = 27/120
Equivalent Fraction = 36/160
Equivalent Fraction = 45/200
Equivalent Fraction = 54/240
Equivalent Fraction = 63/280
Equivalent Fraction = 72/320
Equivalent Fraction = 81/360
Equivalent Fraction = 90/400
Equivalent Fraction = 99/440
Equivalent Fraction = 108/480
Equivalent Fraction = 117/520
Equivalent Fraction = 126/560
Equivalent Fraction = 135/600
Equivalent Fraction = 144/640
Equivalent Fraction = 153/680
Equivalent Fraction = 162/720
Equivalent Fraction = 171/760
Equivalent Fraction = 180/800

Common Core State Standards In This Lesson

3.NF.A.2, 3.NF.A.3.C

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What 10 concepts are covered in the Fractions Calculator?

addition: math operation involving the sum of elements
denominator: The bottom portion of a fraction. For a/b, b is the denominator
division: separate a number into parts
fraction: how many parts of a certain size exist
a/b where a is the numerator and b is the denominator
mixed number: a number consisting of an integer and a proper fraction.
multiplication: math operation involving the product of elements
numerator: the number above the line in a common fraction
reciprocal: a number which when multiplied by x yields the multiplicative identity, 1
simplify: reducing the expression/fraction/problem in a simpler form.
subtraction: math operation involving the difference of elements