Question

multiplying 2 digits by 2 digits (renaming)
1.
( \begin{array}{r} 22 \\ \times 19 \\ hline end{array} ) (a)
( \begin{array}{r} 32 \\ \times 41 \\ hline end{array} ) (b)
( \begin{array}{r} 72 \\ \times 18 \\ hline end{array} ) (c)
( \begin{array}{r} 45 \\ \times 15 \\ hline end{array} ) (d)
( \begin{array}{r} 48 \\ \times 20 \\ hline end{array} ) (e)
( \begin{array}{r} 77 \\ \times 22 \\ hline end{array} ) (f)
2.
( \begin{array}{r} 63 \\ \times 24 \\ hline end{array} )
( \begin{array}{r} 52 \\ \times 48 \\ hline end{array} )
( \begin{array}{r} 28 \\ \times 25 \\ hline end{array} )
( \begin{array}{r} 77 \\ \times 30 \\ hline end{array} )
( \begin{array}{r} 33 \\ \times 29 \\ hline end{array} )
( \begin{array}{r} 90 \\ \times 70 \\ hline end{array} )
3.
( \begin{array}{r} 57 \\ \times 23 \\ hline end{array} )
( \begin{array}{r} 18 \\ \times 18 \\ hline end{array} )
( \begin{array}{r} 77 \\ \times 27 \\ hline end{array} )
( \begin{array}{r} 65 \\ \times 17 \\ hline end{array} )
( \begin{array}{r} 88 \\ \times 22 \\ hline end{array} )
( \begin{array}{r} 90 \\ \times 20 \\ hline end{array} )
4.
( \begin{array}{r} 37 \\ \times 23 \\ hline end{array} )
( \begin{array}{r} 91 \\ \times 38 \\ hline end{array} )
( \begin{array}{r} 44 \\ \times 43 \\ hline end{array} )
( \begin{array}{r} 17 \\ \times 13 \\ hline end{array} )
( \begin{array}{r} 88 \\ \times 17 \\ hline end{array} )
( \begin{array}{r} 55 \\ \times 38 \\ hline end{array} )
chapter 4, lesson 8
multiplication

Explanation:

Step1: Calculate 2-digit × 2-digit (Set 1)

a. $22 \times 19$:

Break into $(20+2) \times 19 = 20\times19 + 2\times19 = 380 + 38 = 418$

b. $32 \times 41$:

Break into $32\times(40+1) = 32\times40 + 32\times1 = 1280 + 32 = 1312$

c. $72 \times 18$:

Break into $72\times(20-2) = 72\times20 - 72\times2 = 1440 - 144 = 1296$

d. $45 \times 15$:

Break into $45\times(10+5) = 45\times10 + 45\times5 = 450 + 225 = 675$

e. $48 \times 20$:

Multiply directly: $48\times2\times10 = 96\times10 = 960$

f. $77 \times 22$:

Break into $77\times(20+2) = 77\times20 + 77\times2 = 1540 + 154 = 1694$

Step2: Calculate 2-digit × 2-digit (Set 2)

a. $63 \times 24$:

Break into $63\times(20+4) = 63\times20 + 63\times4 = 1260 + 252 = 1512$

b. $52 \times 48$:

Break into $52\times(50-2) = 52\times50 - 52\times2 = 2600 - 104 = 2496$

c. $28 \times 25$:

Break into $7\times(4\times25) = 7\times100 = 700$

d. $77 \times 30$:

Multiply directly: $77\times3\times10 = 231\times10 = 2310$

e. $33 \times 29$:

Break into $33\times(30-1) = 33\times30 - 33\times1 = 990 - 33 = 957$

f. $90 \times 70$:

Multiply directly: $9\times7\times100 = 63\times100 = 6300$

Step3: Calculate 2-digit × 2-digit (Set 3)

a. $57 \times 23$:

Break into $(50+7)\times23 = 50\times23 + 7\times23 = 1150 + 161 = 1311$

b. $18 \times 18$:

Use square formula: $(20-2)^2 = 20^2 - 2\times20\times2 + 2^2 = 400 - 80 + 4 = 324$

c. $77 \times 27$:

Break into $77\times(20+7) = 77\times20 + 77\times7 = 1540 + 539 = 2079$

d. $65 \times 17$:

Break into $65\times(10+7) = 65\times10 + 65\times7 = 650 + 455 = 1105$

e. $88 \times 22$:

Break into $88\times(20+2) = 88\times20 + 88\times2 = 1760 + 176 = 1936$

f. $90 \times 20$:

Multiply directly: $9\times2\times100 = 18\times100 = 1800$

Step4: Calculate 2-digit × 2-digit (Set 4)

a. $37 \times 23$:

Break into $(30+7)\times23 = 30\times23 + 7\times23 = 690 + 161 = 851$

b. $91 \times 38$:

Break into $(90+1)\times38 = 90\times38 + 1\times38 = 3420 + 38 = 3458$

c. $44 \times 43$:

Break into $44\times(40+3) = 44\times40 + 44\times3 = 1760 + 132 = 1892$

d. $17 \times 13$:

Use difference of squares: $(15+2)(15-2) = 15^2 - 2^2 = 225 - 4 = 221$

e. $88 \times 17$:

Break into $88\times(10+7) = 88\times10 + 88\times7 = 880 + 616 = 1496$

f. $55 \times 38$:

Break into $(50+5)\times38 = 50\times38 + 5\times38 = 1900 + 190 = 2090$

Answer:

1. a. 418, b. 1312, c. 1296, d. 675, e. 960, f. 1694
2. a. 1512, b. 2496, c. 700, d. 2310, e. 957, f. 6300
3. a. 1311, b. 324, c. 2079, d. 1105, e. 1936, f. 1800
4. a. 851, b. 3458, c. 1892, d. 221, e. 1496, f. 2090