Use the Lattice method to solve the following:

Here are the solutions to your problems. 1. Use the Lattice method to solve the following: The lattice method is a visual way to multiply numbers. You draw a grid, write the digits of one number across the top and the other down the side. Then, you multiply each pair of digits, placing the tens digit in the top triangle of the cell and the units digit in the bottom triangle. Finally, you sum the numbers along the diagonals, carrying over any tens to the next diagonal. a) 675 × 58 Step 1: Set up a 3 × 2 grid. Write 675 across the top and 58 down the side. Step 2: Multiply each digit pair and fill the cells: • 5 × 6 = 30 • 5 × 7 = 35 • 5 × 5 = 25 • 8 × 6 = 48 • 8 × 7 = 56 • 8 × 5 = 40 Step 3: Sum the diagonals starting from the bottom right: • Units diagonal: 0 = 0 • Tens diagonal: 5 + 4 + 6 = 15 (write 5, carry 1) • Hundreds diagonal: 2 + 5 + 8 + 5 + 1 (carry) = 21 (write 1, carry 2) • Thousands diagonal: 3 + 4 + 2 (carry) = 9 • Ten Thousands diagonal: 3 = 3 The result is 39150. 675 × 58 = 39150 b) 974 × 79 Step 1: Set up a 3 × 2 grid. Write 974 across the top and 79 down the side. Step 2: Multiply each digit pair and fill the cells: • 7 × 9 = 63 • 7 × 7 = 49 • 7 × 4 = 28 • 9 × 9 = 81 • 9 × 7 = 63 • 9 × 4 = 36 Step 3: Sum the diagonals starting from the bottom right: • Units diagonal: 6 = 6 • Tens diagonal: 8 + 3 + 3 = 14 (write 4, carry 1) • Hundreds diagonal: 2 + 9 + 1 + 6 + 1 (carry) = 19 (write 9, carry 1) • Thousands diagonal: 3 + 4 + 8 + 1 (carry) = 16 (write 6, carry 1) • Ten Thousands diagonal: 6 + 1 (carry) = 7 The result is 76946. 974 × 79 = 76946 c) 795 × 74 Step 1: Set up a 3 × 2 grid. Write 795 across the top and 74 down the side. Step 2: Multiply each digit pair and fill the cells: • 7 × 7 = 49 • 7 × 9 = 63 • 7 × 5 = 35 • 4 × 7 = 28 • 4 × 9 = 36 • 4 × 5 = 20 Step 3: Sum the diagonals starting from the bottom right: • Units diagonal: 0 = 0 • Tens diagonal: 5 + 6 + 2 = 13 (write 3, carry 1) • Hundreds diagonal: 3 + 3 + 8 + 6 + 1 (carry) = 21 (write 1, carry 2) • Thousands diagonal: 9 + 2 + 2 (carry) = 13 (write 3, carry 1) • Ten Thousands diagonal: 4 + 1 (carry) = 5 The result is 58930. 795 × 74 = 58930 2. Circle the number that is divisible by [missing divisor] The divisor is missing from the question. Assuming the question asks to circle the numbers divisible by 6 (a common divisibility rule for elementary math), we check for divisibility by both 2 and 3. Numbers: 42, 24, 107, 318, 195, 23, 84 • A number is divisible by 2 if its last digit is even. • A number is divisible by 3 if the sum of its digits is divisible by 3. • A number is divisible by 6 if it is divisible by both 2 and 3. Step 1: Check divisibility by 2. • 42 (even) • 24 (even) • 107 (odd) • 318 (even) • 195 (odd) • 23 (odd) • 84 (even) Step 2: Check divisibility by 3. • 42 4+2=6 (divisible by 3) • 24 2+4=6 (divisible by 3) • 107 1+0+7=8 (not divisible by 3) • 318 3+1+8=12 (divisible by 3) • 195 1+9+5=15 (divisible by 3) • 23 2+3=5 (not divisible by 3) • 84 8+4=12 (divisible by 3) Step 3: Identify numbers divisible by both 2 and 3 (i.e., by 6). The numbers divisible by 6 are: 42, 24, 318, 84. 3. Circle the number that is divisible by [missing divisor] The divisor is missing from the question. Assuming the question asks to circle the numbers divisible by 6, we check for divisibility by both 2 and 3. Numbers: 54, 210, 108, 144, 212, 96 Step 1: Check divisibility by 2. • 54 (even) • 210 (even) • 108 (even) • 144 (even) • 212 (even) • 96 (even) All numbers in this list are divisible by 2. Step 2: Check divisibility by 3. • 54 5+4=9 (divisible by 3) • 210 2+1+0=3 (divisible by 3) • 108 1+0+8=9 (divisible by 3) • 144 1+4+4=9 (divisible by 3) • 212 2+1+2=5 (not divisible by 3) • 96 9+6=15 (divisible by 3) Step 3: Identify numbers divisible by both 2 and 3 (i.e., by 6). The numbers divisible by 6 are: 54, 210, 108, 144, 96. 4. Solve the ff (following): a) 6 )567 Step 1: Divide 56 by 6. 56 ÷ 6 = 9 with a remainder of 2. Step 2: Bring down the 7 to make 27. Divide 27 by 6. 27 ÷ 6 = 4 with a remainder of 3. So, 567 ÷ 6 = 94 with a remainder of 3. This can also be written as a mixed number or a decimal. As a mixed number: 94 (3)/(6) = 94 (1)/(2). As a decimal: 94.5. (567)/(6) = 94.5 b) sqrt(916) Step 1: Find the prime factorization of 916. 916 = 2 × 458 458 = 2 × 229 So, 916 = 2 × 2 × 229 = 2^2 × 229. Step 2: Take the square root. sqrt(916) = sqrt(2^2 × 229) = sqrt(2^2) × sqrt(229) = 2sqrt(229) The simplified form is 2sqrt(229). c) sqrt(891) Step 1: Find the prime factorization of 891. 891 = 9 × 99 9 = 3 × 3 99 = 9 × 11 = 3 × 3 × 11 So, 891 = 3 × 3 × 3 × 3 × 11 = 3^4 × 11. Step 2: Take the square root. sqrt(891) = sqrt(3^4 × 11) = sqrt((3^2)^2 × 11) = 3^2 sqrt(11) = 9sqrt(11) The simplified form is 9sqrt(11). Send me the next one 📸