Perform Operations With Multi-Digit Decimals - 6th Grade Math

1. What is $8.4 \div 0.7$ using the standard division algorithm?

   $12$. Convert to $84 \div 7 = 12$ by multiplying both by 10.

2. Identify the correct placement of the decimal in the quotient for $3.6 \div 0.12$.

   Convert to $360 \div 12$, so the quotient is $30$. Multiply both by 100 to eliminate decimals in divisor.

3. What is $0.48 \times 3.5$ using the standard multiplication algorithm?

   $1.68$. $48 \times 35 = 1680$; place decimal 3 places from right.

4. What is $12.5 \times 0.06$ using the standard multiplication algorithm?

   $0.75$. $125 \times 6 = 750$; place decimal 3 places from right.

5. What is $9.2 - 3.45$ using the standard subtraction algorithm?

   $5.75$. Align as $9.20 - 3.45$, then subtract place by place.

6. What is $12.5 - 0.86$?

   $11.64$. Align as $12.50 - 0.86$ and subtract.

7. What is $0.36 \times 0.5$?

   $0.18$. Half of $0.36$ gives $0.18$.

8. Find the missing number: $x \div 0.4 = 12.5$.

   $x = 5$. Multiply both sides by $0.4$: $12.5 \times 0.4 = 5$.

9. Find the missing number: $x - 4.096 = 2.5$.

   $x = 6.596$. Add $4.096$ to both sides: $2.5 + 4.096 = 6.596$.

10. What is the rule for placing the decimal in $3.2 \times 1.45$ using the standard algorithm?

    Total decimal places in product equals sum of decimal places in factors. Count all decimal places in both factors.

11. Find the missing number: $7.2 + x = 10.05$.

    $x = 2.85$. Subtract $7.2$ from both sides: $10.05 - 7.2 = 2.85$.

12. Identify the missing number: $0.8 \times \square = 6.4$.

    $8$. Divide: $6.4 \div 0.8 = 8$.

13. What is $4.38 + 7.6$?

    $11.98$. Add $4.38 + 7.60$ with aligned decimals.

14. What is $2.3 \times 4.56$ using the standard multiplication algorithm?

    $10.488$. $23 \times 456 = 10488$; place decimal 3 places from right.

15. What is $7.2 \div 0.03$?

    $240$. Convert to $720 \div 3 = 240$.

16. What is $9.45 \div 0.15$ using the standard division algorithm?

    $63$. Convert to $945 \div 15 = 63$ by multiplying both by 100.

17. State the first step of the standard algorithm for subtracting decimals such as $9.2 - 3.45$.

    Align decimal points and add zeros as needed before subtracting. Ensures equal decimal places for proper subtraction.

18. What is $9.45 \div 0.7$?

    $13.5$. Convert to $94.5 \div 7 = 13.5$.

19. State the first step for dividing by a decimal in $15.6 \div 0.3$ using the standard algorithm.

    Multiply dividend and divisor by $10^n$ to make the divisor a whole number. Eliminates decimal in divisor for standard long division.

20. What is $50.00 - 18.735$ using the standard subtraction algorithm?

    $31.265$. Regroup from tens: $50.000 - 18.735 = 31.265$.

21. Identify the missing number: $\square - 2.75 = 10.5$.

    $13.25$. Add: $10.5 + 2.75 = 13.25$.

22. What is $12.5 \div 0.5$?

    $25$. Convert to $125 \div 5 = 25$.

23. Find the missing number: $0.25 \times x = 3.5$.

    $x = 14$. Divide both sides by $0.25$: $3.5 \div 0.25 = 14$.

24. What is the standard method to divide $15.6 \div 0.3$ when the divisor is a decimal?

    Multiply dividend and divisor by the same power of $10$ to make divisor whole. Converts to $156 \div 3$ for easier division.

25. What is $63.09 + 8.015$ using the standard addition algorithm?

    $71.105$. Align and add: $63.090 + 8.015 = 71.105$.

26. What is $4.8 \div 0.6$?

    $8$. Convert to $48 \div 6 = 8$.

27. Identify the rule for placing the decimal point in a product like $2.3 \times 4.56$.

    Decimal places in product = sum of decimal places in factors. Count total decimal places in both factors.

28. What is the correct first step to subtract $9.2 - 3.45$ using the standard algorithm?

    Align decimal points and add trailing zeros if needed. Zeros make subtraction possible: $9.20 - 3.45$.

29. What is $6.72 \div 0.8$ using the standard division algorithm?

    $8.4$. Convert to $67.2 \div 8 = 8.4$ by multiplying both by 10.

30. What is the correct first step to add $3.47 + 12.6$ using the standard algorithm?

    Align the decimal points vertically, then add place values. Ensures place values match for accurate addition.

31. What is $6.04 - 2.9$?

    $3.14$. Write as $6.04 - 2.90$ for easier subtraction.

32. What is $4.38 + 12.7$ using the standard addition algorithm?

    $17.08$. Align decimals: $4.38 + 12.70 = 17.08$.

33. What is $3.07 \times 0.2$?

    $0.614$. $307 \times 2 = 614$, place decimal for 3 places.

34. What is $6.3 \div 0.9$?

    $7$. Convert to $63 \div 9 = 7$.

35. What is $15.002 + 0.89$?

    $15.892$. Align decimals: $15.002 + 0.890 = 15.892$.

36. What is $2.4 \times 3.5$?

    $8.4$. Multiply $24 \times 35 = 840$, place decimal for 2 places.

37. What is $15.6 \div 0.3$ using the standard division algorithm?

    $52$. Convert to $156 \div 3 = 52$ by multiplying both by 10.

38. What is $8.00 - 3.57$?

    $4.43$. Subtract with borrowing: $8.00 - 3.57 = 4.43$.

39. What is $1.25 \times 0.4$?

    $0.5$. $125 \times 4 = 500$, place decimal for 3 places.

40. State the first step of the standard algorithm for adding decimals such as $3.47 + 12.6$.

    Align the decimal points, then add digits by place value. Ensures place values match for accurate addition.

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