Chapter 4 — cumulative chapter review
Semester 4A · Chapter 4 · 33 questions
This review integrates every chapter learning objective. Try questions before revealing answers.
Calculate 24 × 8 using a split or friendly number.
Show answer & reasoning
Split 24 into 20 + 4. Then multiply each part by 8 and add the partial products.
Calculate 45 × 3.
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45 × 3 = (40 × 3) + (5 × 3) = 135. Each partial product uses its correct place value.
Calculate 72 × 7.
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72 × 7 = (70 × 7) + (2 × 7) = 504. Each partial product uses its correct place value.
Calculate 82 × 80.
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80 represents 8 tens. Multiply by 8, then scale by 10 to obtain 6,560.
Find 38 × 30 using an area model or partial products.
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Expand (30+8)(30+0) = 900+0+240+0 = 1140.
Find 361 × 55 using an area model or partial products.
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Expand (360+1)(50+5) = 18000+1800+50+5 = 19855.
Calculate 26 × 6 using a split or friendly number.
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Split 26 into 20 + 6. Then multiply each part by 6 and add the partial products.
Calculate 51 × 3.
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51 × 3 = (50 × 3) + (1 × 3) = 153. Each partial product uses its correct place value.
Calculate 18 × 5.
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18 × 5 = (10 × 5) + (8 × 5) = 90. Each partial product uses its correct place value.
Calculate 182 × 30.
Show answer & reasoning
30 represents 3 tens. Multiply by 3, then scale by 10 to obtain 5,460.
Find 66 × 18 using an area model or partial products.
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Expand (60+6)(10+8) = 600+480+60+48 = 1188.
Find 177 × 20 using an area model or partial products.
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Expand (170+7)(20+0) = 3400+0+140+0 = 3540.
Calculate 25 × 9 using a split or friendly number.
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Split 25 into 20 + 5. Then multiply each part by 9 and add the partial products.
Calculate 88 × 7.
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88 × 7 = (80 × 7) + (8 × 7) = 616. Each partial product uses its correct place value.
Calculate 158 × 7.
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158 × 7 = (150 × 7) + (8 × 7) = 1106. Each partial product uses its correct place value.
Calculate 189 × 30.
Show answer & reasoning
30 represents 3 tens. Multiply by 3, then scale by 10 to obtain 5,670.
Find 66 × 50 using an area model or partial products.
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Expand (60+6)(50+0) = 3000+0+300+0 = 3300.
Find 357 × 15 using an area model or partial products.
Show answer & reasoning
Expand (350+7)(10+5) = 3500+1750+70+35 = 5355.
Calculate 23 × 4 using a split or friendly number.
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Split 23 into 20 + 3. Then multiply each part by 4 and add the partial products.
Calculate 59 × 4.
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59 × 4 = (50 × 4) + (9 × 4) = 236. Each partial product uses its correct place value.
Calculate 111 × 9.
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111 × 9 = (110 × 9) + (1 × 9) = 999. Each partial product uses its correct place value.
Calculate 415 × 90.
Show answer & reasoning
90 represents 9 tens. Multiply by 9, then scale by 10 to obtain 37,350.
Find 65 × 52 using an area model or partial products.
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Expand (60+5)(50+2) = 3000+120+250+10 = 3380.
Find 412 × 26 using an area model or partial products.
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Expand (410+2)(20+6) = 8200+2460+40+12 = 10712.
Calculate 26 × 8 using a split or friendly number.
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Split 26 into 20 + 6. Then multiply each part by 8 and add the partial products.
Calculate 77 × 4.
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77 × 4 = (70 × 4) + (7 × 4) = 308. Each partial product uses its correct place value.
Calculate 166 × 3.
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166 × 3 = (160 × 3) + (6 × 3) = 498. Each partial product uses its correct place value.
A student calculates 43 × 5 using only its tens: 40 × 5. What partial product is missing and what is the correct total?
Show answer & reasoning
The ones part 3 × 5 = 15 must also be included. The complete product is 215.
A student calculates 84 × 8 using only its tens: 80 × 8. What partial product is missing and what is the correct total?
Show answer & reasoning
The ones part 4 × 8 = 32 must also be included. The complete product is 672.
A student calculates 30 × 6 using only its tens: 30 × 6. What partial product is missing and what is the correct total?
Show answer & reasoning
The ones part 0 × 6 = 0 must also be included. The complete product is 180.
A student calculates 43 × 90 as 387. Explain why this is ten times too small and correct it.
Show answer & reasoning
90 is 9 tens. Multiply 43 by 9 and then by 10, giving 3870.
A student calculates 37 × 40 by multiplying 37 by the tens digit 4 and the ones digit 0, then adding both results without shifting the tens. Explain the error and give the correct product.
Show answer & reasoning
The tens digit is worth 40, not 4. Correct: 37 × 40 + 37 × 0 = 1480.
A student calculates 27 × 35 by multiplying 27 by the tens digit 3 and the ones digit 5, then adding both results without shifting the tens. Explain the error and give the correct product.
Show answer & reasoning
The tens digit is worth 30, not 3. Correct: 27 × 30 + 27 × 5 = 945.