 45.1: By what fraction must 53 be multiplied to get a product of 1?
 45.2: How many $20 bills equal one thousand dollars?
 45.3: Cindy made 23 of her 24 shots at the basket. Each basket was worth2...
 45.4: 3 4.5
 45.5: 8 0.24
 45.6: 5 0.8
 45.7: What is the least common multiple (LCM) of 2, 4, 6, and 8?
 45.8: Find each unknown number. Remember to check your work.236 m 2 310
 45.9: Find each unknown number. Remember to check your work.g 225 545
 45.10: Find each unknown number. Remember to check your work.m 1.56 = 1.44
 45.11: Find each unknown number. Remember to check your work.32 n = 5.39
 45.12: Find each unknown number. Remember to check your work.438 218
 45.13: Find each unknown number. Remember to check your work.83 52
 45.14: Estimate the product of 694 and 412.
 45.15: 0.7 0.6 0.5
 45.16: 0.46 0.17
 45.17: Mrs. Lopezs car traveled 177.6 miles on 8 gallons of gas.Her car tr...
 45.18: What number is 38 of 6? What operation did you use to find your ans...
 45.19: A shirt regularly priced at $40 is on sale for 25% off. Mentallycal...
 45.20: Write a fraction equal to 56 that has 12 as the denominator. Then s...
 45.21: The area of a square is 36 ft2. a. How long is each side of the squ...
 45.22: Write 27% as a fraction. Then write the fraction as a decimal number.
 45.23: Use a ruler to find the length of this rectangle to thenearest eigh...
 45.24: Seventyfive percent of the 20 answers were correct. Write75% as a ...
 45.25: The product of 12 and 23 is 13.12 23 13Arrange these fractions to f...
 45.26: Which percent best describes theshaded portion of this circle? Expl...
 45.27: Write nine hundredths a. as a fraction. b. as a decimal number.
 45.28: orm an equivalent division problem for 5 13by multiplying both thed...
 45.29: The average number of students in three classrooms was 24. Altogeth...
 45.30: Coach ORourke has a measuringwheel that records the distance the wh...
Solutions for Chapter 45: Dividing a Decimal Number by a Whole Number
Full solutions for Saxon Math, Course 1  1st Edition
ISBN: 9781591417835
Solutions for Chapter 45: Dividing a Decimal Number by a Whole Number
Get Full SolutionsSince 30 problems in chapter 45: Dividing a Decimal Number by a Whole Number have been answered, more than 35194 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 45: Dividing a Decimal Number by a Whole Number includes 30 full stepbystep solutions. Saxon Math, Course 1 was written by and is associated to the ISBN: 9781591417835. This textbook survival guide was created for the textbook: Saxon Math, Course 1, edition: 1.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.