2-Digit Multiplication and Solving for x

• 2-digit multiplication involves multiplying a number with two digits by another number, which could be single or double digits.
• Solving for x in equations like (a/b)x = c requires isolating x by multiplying both sides of the equation by the reciprocal of the fraction (b/a).

Steps for 2-Digit Multiplication

• Write the numbers vertically, one above the other, aligning the digits by place value (ones, tens).
• Multiply each digit of the bottom number by each digit of the top number, starting from the ones place.
• Write the partial products, aligning them correctly by place value.
• Add the partial products to get the final product.
• Example: 23 x 12.
• Multiply 2 by 3 to get 6.
• Multiply 2 by 2 to get 4. The first partial product is 46.
• Multiply 1 (tens place) by 3 to get 3, write this under the tens place.
• Multiply 1 by 2 to get 2, write this under the hundreds place. The second partial product is 230.
• Add 46 and 230 to get 276, which is the final product.

Example 2-Digit Multiplication Problems

• 34 x 21:
  • Set up the problem vertically.
  • 1 x 4 = 4.
  • 1 x 3 = 3. First partial product: 34.
  • 2 x 4 = 8 (write under the tens place).
  • 2 x 3 = 6 (write under the hundreds place). Second partial product: 680.
  • Add 34 and 680 to get 714.
• 56 x 15:
  • Set up the problem vertically.
  • 5 x 6 = 30 (write down 0, carry over 3).
  • 5 x 5 = 25 + 3 (carried over) = 28. First partial product: 280.
  • 1 x 6 = 6 (write under the tens place).
  • 1 x 5 = 5 (write under the hundreds place). Second partial product: 560.
  • Add 280 and 560 to get 840.
• 78 x 43:
  • Set up the problem vertically.
  • 3 x 8 = 24 (write down 4, carry over 2).
  • 3 x 7 = 21 + 2 (carried over) = 23. First partial product: 234.
  • 4 x 8 = 32 (write down 2 under the tens place, carry over 3).
  • 4 x 7 = 28 + 3 (carried over) = 31. Second partial product: 3120.
  • Add 234 and 3120 to get 3354.

Solving for x with Fractions

• The goal is to isolate x on one side of the equation.
• If x is multiplied by a fraction (a/b), multiply both sides of the equation by the reciprocal of the fraction (b/a).
• The reciprocal of a fraction switches the numerator and denominator.
• Example: (2/3)x = 8.
• To solve for x, multiply both sides by the reciprocal of 2/3, which is 3/2.
• (3/2) * (2/3)x = 8 * (3/2).
• The left side simplifies to x because (3/2) * (2/3) = 1.
• The right side becomes 8 * (3/2) = 24/2 = 12.
• Therefore, x = 12.

Additional Examples of Solving for x

• (1/4)x = 5:
  • Multiply both sides by 4/1 (or simply 4).
  • 4 * (1/4)x = 5 * 4.
  • x = 20.
• (3/5)x = 9:
  • Multiply both sides by 5/3.
  • (5/3) * (3/5)x = 9 * (5/3).
  • x = 45/3.
  • x = 15.
• (5/2)x = 10:
  • Multiply both sides by 2/5.
  • (2/5) * (5/2)x = 10 * (2/5).
  • x = 20/5.
  • x = 4.
• (7/3)x = 14:
  • Multiply both sides by 3/7.
  • (3/7) * (7/3)x = 14 * (3/7).
  • x = 42/7.
  • x = 6.
• (4/9)x = 8:
  • Multiply both sides by 9/4.
  • (9/4) * (4/9)x = 8 * (9/4).
  • x = 72/4.
  • x = 18.

Learn how to perform 2-digit multiplication by hand and solve algebraic equations for x. The multiplication process involves writing numbers vertically and adding partial products. Solving for x requires isolating the variable.