- Adjust the first sequence to start at \(4250\) to maintain the consistent pattern of adding \(50\): \(\boxed{4250, 4300, 4350, 4400, 4450}\).
- Validate the second sequence, which already follows the pattern perfectly: \(\boxed{6355, 6405, 6455, 6505, 6555}\).
- Calculate the product of \(26 \times 4\) using the lattice method, resulting in \(\boxed{104}\).
Explanation
- Problem Analysis and Objective
We are given two sequences to analyze based on skip counting forward by 50s. The first sequence is \(14250, 4300, 4350, 4400, 4450\). The second sequence is \(6355, 6405, 6455, 6505, 6555\). Additionally, we need to compute \(26 \times 4\) using the lattice method. The goal is to identify and correct any errors in the skip counting sequences and perform the multiplication correctly.
- Correcting Skip Counting Sequences
In the first sequence, \(14250, 4300, 4350, 4400, 4450\), we observe a clear pattern starting from the second term: \(4300 + 50 = 4350\), \(4350 + 50 = 4400\), and \(4400 + 50 = 4450\). The term \(14250\) does not fit this progression. To maintain the pattern, the first term should be \(4300 - 50 = 4250\). Therefore, the correct sequence is \(4250, 4300, 4350, 4400, 4450\).
In the second sequence, \(6355, 6405, 6455, 6505, 6555\), we check the intervals: \(6405 - 6355 = 50\), \(6455 - 6405 = 50\), \(6505 - 6455 = 50\), and \(6555 - 6505 = 50\). Since every step is consistently \(50\), this sequence is already correct.
- Lattice Multiplication Method
To multiply \(26\) by \(4\) using the lattice method, we set up a grid. The number \(26\) has two digits (\(2\) and \(6\)), so we use two columns, and \(4\) has one digit, so we use one row.
- Create a \(2 \times 1\) grid. Label the top columns as \(2\) and \(6\), and the side row as \(4\).
- Draw diagonals in each cell from top-right to bottom-left.
- Multiply the digits:
- \(2 \times 4 = 8\). Place this in the first cell, with \(0\) above the diagonal and \(8\) below.
- \(6 \times 4 = 24\). Place this in the second cell, with \(2\) above the diagonal and \(4\) below.
- Sum the numbers along the diagonals starting from the bottom-right:
- Units digit: \(4\).
- Tens diagonal: \(8 + 2 = 10\). Keep the \(0\) and carry the \(1\).
- Hundreds diagonal: \(0 + 1 (\text{carried}) = 1\).
- Reading the results gives the product \(104\). Thus, \(26 \times 4 = 104\).
- Final Answer
The first sequence should be \(4250, 4300, 4350, 4400, 4450\). The second sequence is correct. The product of \(26 \times 4\) is \(104\).
The corrected sequence is \(\boxed{4250, 4300, 4350, 4400, 4450}\). The second sequence is \(\boxed{6355, 6405, 6455, 6505, 6555}\). The product is \(\boxed{104}\).
Examples
Skip counting is a foundational skill used in everyday life, such as when counting money. If you are counting stacks of fifty-dollar bills, skip counting by 50s helps you tally the total amount quickly. For instance, if you have 5 stacks of bills starting from \$4250, you calculate \(4250 + 4 \times 50 = 4450\) to find your total efficiently. Lattice multiplication provides a structured way to handle larger multiplications like \(26 \times 4\), ensuring accuracy in financial bookkeeping or inventory management.